title: Lancaster, Pennsylvania

text: Electricity in Lancaster is provided by PPL Corporation in Allentown. UGI Utilities supplies natural gas to the city. The City of Lancaster Water Department provides water service to residents and businesses in the city. The city's Public Works department provides wastewater service to Lancaster, operating the City of Lancaster Advanced Wastewater Treatment Plant which serves the city and surrounding municipalities. Trash and recycling collection is provided by the city's Public Works department.


title: Excretory system

text: The excretory system is a passive biological system that removes excess, unnecessary materials from the body fluids of an organism, so as to help maintain internal chemical homeostasis and prevent damage to the body. The dual function of excretory systems is the elimination of the waste products of metabolism and to drain the body of used up and broken down components in a liquid and gaseous state. In humans and other amniotes (mammals, birds and reptiles) most of these substances leave the body as urine and to some degree exhalation, mammals also expel them through sweating.


title: Excretory system

text: Only the organs specifically used for the excretion are considered a part of the excretory system. In the narrow sense, the term refers to the urinary system. However, as excretion involves several functions that are only superficially related, it is not usually used in more formal classifications of anatomy or function.


title: Excretory system

text: As most healthy functioning organs produce metabolic and other wastes, the entire organism depends on the function of the system. Breaking down of one of more of the systems is a serious health condition, for example kidney failure.


title: Excretory system

text: The kidneys are large, bean-shaped organs which are present on each side of the vertebral column in the abdominal cavity. Humans have two kidneys and each kidney is supplied with blood from the renal artery. The kidneys remove from the blood the nitrogenous wastes such as urea, as well as salts and excess water, and excrete them in the form of urine. This is done with the help of millions of nephrons present in the kidney. The filtrated blood is carried away from the kidneys by the renal vein (or kidney vein). The urine from the kidney is collected by the ureter (or excretory tubes), one from each kidney, and is passed to the urinary bladder. The urinary bladder collects and stores the urine until urination. The urine collected in the bladder is passed into the external environment from the body through an opening called the urethra.


title: Excretory system

text: The kidney's primary function is the elimination of waste from the bloodstream by production of urine. They perform several homeostatic functions such as:-


title: Excretory system

text: The way the kidneys do this is with nephrons. There are over 1 million nephrons in each kidney; these nephrons act as filters inside the kidneys. The kidneys filter needed materials and waste. Needed materials go back into the bloodstream; unneeded materials become urine and are expelled through the urethra.


title: Excretory system

text: In some cases, excess wastes crystallize as kidney stones. They grow and can become painful irritants that may require surgery or ultrasound treatments. Some stones are small enough to be forced into the urethra.


title: Excretory system

text: The ureters are muscular ducts that propel urine from the kidneys to the urinary bladder. In the human adult, the ureters are usually 25–30 cm (10–12 in) long. In humans, the ureters arise from the renal pelvis on the medial aspect of each kidney before descending towards the bladder on the front of the psoas major muscle. The ureters cross the pelvic brim near the bifurcation of the iliac arteries (which they run over). This "pelviureteric junction" is a common site for the impaction of kidney stones (the other being the uteterovesical valve). The ureters run posteriorly on the lateral walls of the pelvis. They then curve anteriormedially to enter the bladder through the back, at the vesicoureteric junction, running within the wall of the bladder for a few centimeters. The backflow of urine is prevented by valves known as ureterovesical valves. In the female, the ureters pass through the mesometrium on the way to the bladder.


title: Excretory system

text: The urinary bladder is the organ that collects waste excreted by the kidneys prior to disposal by urination. It is a hollow muscular, and distensible (or elastic) organ, and sits on the pelvic floor. Urine enters the bladder via the ureters and exits via the urethra.


title: Excretory system

text: Embryologically, the bladder is derived from the urogenital sinus, and it is initially continuous with the allantois. In human males, the base of the bladder lies between the rectum and the pubic symphysis. It is superior to the prostate, and separated from the rectum by the rectovesical excavation. In females, the bladder sits inferior to the uterus and anterior to the vagina. It is separated from the uterus by the vesicouterine excavation. In infants and young children, the urinary bladder is in the abdomen even when empty.


title: Excretory system

text: In anatomy, the (from Greek – ourethra) is a tube which connects the urinary bladder to the outside of the body. In humans, the urethra has an excretory function in both genders to pass.


title: Excretory system

text: One of the main functions of the lungs is to diffuse gaseous wastes, such as carbon dioxide, from the bloodstream as a normal part of respiration.


title: Excretory system

text: The large intestine's main function is to transport food particles through the body and expel the indigestible parts at the other end, but it also collects waste from throughout the body. The typical brown colour of mammal waste is due to bilirubin, a breakdown product of normal heme catabolism. The lower part of the large intestine also extracts any remaining usable water and then removes solid waste. At about 10 feet long in humans, it transports the wastes through the tubes to be excreted.


title: Excretory system

text: The liver detoxifies and breaks down chemicals, poisons and other toxins that enter the body. For example, the liver transforms ammonia (which is poisonous) into urea in fish, amphibians and mammals, and into uric acid in birds and reptiles. Urea is filtered by the kidney into urine or through the gills in fish and tadpoles. Uric acid is paste-like and expelled as a semi-solid waste (the "white" in bird excrements). The liver also produces bile, and the body uses bile to break down fats into usable fats and unusable waste.


title: Excretory system

text: Invertebrates lack a liver, but most terrestrial groups, like insects, possesses a number of blind guts that serve the similar functions. Marine invertebrates do not need the ammonia conversion of the liver, as they can usually expel ammonia directly by diffusion through the skin.


title: Excretory system

text: Sweat glands in the skin secrete a fluid waste called sweat or perspiration; however, its primary functions are temperature control and pheromone release. Therefore, its role as a part of the excretory system is minimal. Sweating also maintains the level of salt in the body.


title: Excretory system

text: In mammals, the skin excretes sweat through sweat glands throughout the body. The sweat, helped by salt, evaporates and helps to keep the body cool when it is warm. In amphibians, the lungs are very simple, and they lack the necessary means to the exhale like other tetrapods can. The moist, scale-less skin is therefore essential in helping to rid the blood of carbon dioxide, and also allows for urea to be expelled through diffusion when submerged.


title: Excretory system

text: In small-bodied marine invertebrates, the skin is the most important excretory organ. That is particularly true for acoelomate groups like cnidarians, flatworms and nemerteans, who have no body cavities and hence no body fluid that can be drained or purified by nephrons, which is the reason acoelomate animals are thread-like (nemertans), flat (flatworms) or only consist of a thin layer of cells around a gelatinous non-cellular interior (cnidarians).


title: Excretory system

text: Like sweat glands, eccrine glands allow excess water to leave the body. The majority of eccrine glands are located mainly on the forehead, the bottoms of the feet, and the palms, although the glands are everywhere throughout the body. They help the body to maintain temperature control. Eccrine glands in the skin are unique to mammals.


title: Excretory system

text: Secretions of sweat from the eccrine glands play a large role in controlling the body temperature of humans. Regulation of body temperature, also known as thermoregulation, is very important when it comes to instances that bring the body's temperature outside of the homeostatic temperature such as with a fever or even exercise. Together these glands make up the size of about one kidney and in one day a human can perspire amounts as much as 10 liters. The two functions consist of secretion of a filtrate in response to acetylcholine and reabsorption of sodium near the duct when there is water in excess so that a sweat can be surfacing the skin.


title: Excretory system

text: There are three parts to the eccrine sweat gland and these are the pore, the duct, and the gland. The pore is the portion that goes through the outermost layer of the skin and is typically 5-10 microns in diameter. The duct is the part of the sweat gland that connects dermis cells to the epidermis. It is composed by two layers of cells and is between 10 and 20 microns in diameter. The gland does the actual secretion and it lies deep within the dermis. The cells that make up the gland are larger in size than the duct cells and its lumen is around 20 microns in diameter.


title: Excretory system

text: After bile is produced in the liver, it is stored in the gall bladder. It is then secreted within the small intestine where it helps to emulsify fats in the same manner as a soap. Bile also contains bilirubin, which is a waste product.


title: Excretory system

text: Bile salts can be considered waste that is useful for the body given that they have a role in fat absorption from the stomach. They are excreted from the liver and along with blood flow they help to form the shape of the liver where they are excreted. For instance, if biliary drainage is impaired than that part of the liver will end up wasting away.


title: Excretory system

text: Biliary obstruction is typically due to masses blocking the ducts of the system such as tumors. The consequences of this depend on the site of blockage and how long it goes on for. There is inflammation of the ducts due to the irritation from the bile acids and this can cause infections. If rupture of the duct takes place it is very traumatic and even fatal.


title: Excretory system

text: Within the kidney, blood first passes through the afferent artery to the capillary formation called a glomerulus and is collected in the Bowman's capsule, which filters the blood from its contents—primarily food and wastes. After the filtration process, the blood then returns to collect the food nutrients it needs, while the wastes pass into the collecting duct, to the renal pelvis, and to the ureter and are then secreted out of the body via the urinary bladder.


title: Excretory system

text: Scientifically, masses referred to as a renal calculus or nephrolith, or more commonly, “kidney stones,” are solid masses of crystals that may be a variety of shapes, sizes, and textures, that can reside within one or both of the kidneys. Kidney stones form when the balance is off between the concentration of substances that pass through urine, and the substances that are supposed to dissolve them. When substances are not properly dissolved, they have the ability to build up, and form these kidney stones. These stones are most commonly made up of substances such as calcium, cystine, oxalate, and uric acid, as these are the substances that normally would dissolve within the urine. When they do not dissolve correctly and further build up, they will commonly lodge themselves in the urinary tract and in this case, are usually small enough to pass through urine. In extreme situations, however, these stones may lodge themselves within the tube that connects the kidney and the bladder, called the ureter. In this case, they become very large in size and will most likely cause great pain, bleeding, and possibly even block the flow of urine. These can occur in both men and women, and studies show that around 12% of men, and 8% of women in America will develop kidney stones within their lifetime.


title: Excretory system

text: In those extreme situations, in which kidney stones are too large to pass on their own, patients may seek removal. Most of these treatments involving kidney stone removal are done by a urologist; a physician who specializes in the organs of the Urinary system. A common way of removal is shock wave lithotripsy, in which the urologist will shock the kidney stone into smaller pieces via laser, allowing these pieces to further pass through the urine on their own, as a normal case of kidney stones. Larger, more serious cases may demand Cystoscopy, Ureteroscopy, or Percutaneous Nephrolithotomy, in which the doctor will use a viewing tool or camera to locate the stone, and based on the size or situation, may either chose to continue with surgical removal, or use the shock wave lithotripsy treatment. Once the kidney stone(s) are successfully eliminated, the urologist will commonly suggest medication to prevent future recurrences.


title: Excretory system

text: Pyelonephritis is a type of urinary tract infection that occurs when bacteria enters the body through the urinary tract. It causes an inflammation of the renal parenchyma, calyces, and pelvis. There are three main classifications of pyelonephritis: acute, chronic and xanthogranulomatous.


title: Excretory system

text: In acute pyelonephritis, the patient experiences high fever, abdominal pain and pain while passing urine. Treatment for acute pyelonephritis is provided via antibiotics and an extensive urological investigation is conducted to find any abnormalities and prevent recurrence.


title: Excretory system

text: In chronic pyelonephritis, patients experience persistent abdominal and flank pain, high fever, decreased appetite, weight loss, urinary tract symptoms and blood in the urine. Chronic pyelonephritis can also lead to scarring of the renal parenchyma caused by recurrent kidney infections.


title: Excretory system

text: Xanthogranulomatous pyelonephritis is an unusual form of chronic pyelonephritis. It results in severe destruction of the kidney and causes granulomatous abscess formation. Patients infected with Xanthogranulomatous pyelonephritis experience recurrent fevers, anemia, kidney stones and loss of function in the affected kidney.


title: Excretory system

text: A urine culture and antibiotics sensitivity test is issued for patients who are believed to have pyelonephritis. Since most cases of pyelonephritis are caused from bacterial infections, antibiotics are a common treatment option. Depending on the species of the infecting organism and the antibiotics sensitivity profile of the organism, treatments may include fluoroquinolones, cephalosporins, aminoglycosides, or trimethoprim individually or in combination. For patients with xanthogranulomatous pyelonephritis, treatment might include antibiotics as well as surgery. Nephrectomy is the most common surgical treatment for a majority of cases involving xanthogranulomatous pyelonephritis.


title: Excretory system

text: In men, roughly 2-3 cases per 10,000 are treated as outpatients and 1 in 10,000 cases require admission to the hospital. In women, approximately 12–13 in 10,000 cases are treated as outpatients and 3-4 cases are admitted to a hospital. The most common age group affected by Xanthogranulomatous pyelonephritis is middle-aged women. Infants and elderly are also at an increased risk because of hormonal and anatomical changes.


title: Jason X

text: Jason X is a 2001 American science fiction slasher film directed by Jim Isaac, written by Todd Farmer and starring Lexa Doig, Lisa Ryder, Chuck Campbell, and Kane Hodder in his fourth and final cinematic appearance as Jason Voorhees. It is the tenth installment in the "Friday the 13th" franchise, the first one since 1993's "". In the film, Jason is cryogenically frozen for 445 years and awakens in 2455, after being found by a group of students, whom he subsequently stalks and kills one by one.


title: Jason X

text: While other films of the franchise approach Jason as a human serial killer or undead monster, this movie views him through a science-fiction lens (referring to his inability to die as a "regenerative" power that can be studied and perhaps replicated) and then has him transformed by future-technology into a cyborg. This cyborg incarnation has been called Jason X in tie-in media, but is also often referred to by fans as "Uber Jason", a nickname the art design team and production crew used and which appeared in later comic books "Jason X Special" and "Friday the 13th: Jason vs. Jason X". When conceiving the film, Todd Farmer came up with the idea of sending Jason into space, suggesting to the studio that it was the only direction left for the series. Kane Hodder called into the Howard Stern Show on May 1, 2002 and shared "I was a little hesitant about (the plot) the first time I heard the story too."


title: Jason X

text: "Jason X" was theatrically released in the U.S. on April 26, 2002. It received mostly negative reviews from critics and was a box office bomb, grossing only $17 million on a budget of $11–14 million. The next film in the series, "Freddy vs. Jason", was released in 2003; it is a crossover with the "A Nightmare on Elm Street" franchise, set between the events of "The Final Friday" and "Jason X".


title: Jason X

text: In 2008, mass murderer Jason Voorhees is captured by the United States government and held at the Crystal Lake Research Facility. After numerous failed attempts to kill Jason over the following two years, government scientist Rowan LaFontaine suggests putting him in cryogenic stasis. Dr. Wimmer and Sergeant Marcus arrive with soldiers, hoping to further research Jason's ability to heal from lethal wounds, as they believe it involves rapid cellular regeneration that can be replicated. Jason breaks free of his restraints and kills the soldiers and Dr. Wimmer. Rowan lures him into a cryogenic pod and activates it, but he ruptures the pod with his machete, stabbing her in the abdomen. Cryogenic fluid spills into the sealed room, freezing them both.


title: Jason X

text: 455 years later, Earth has become too polluted to support life and humans have moved to a new planet, Earth II. On a field trip to Earth, Professor Brandon Lowe, his android companion KM-14, intern Adrienne Thomas, and students Tsunaron, Janessa, Azrael, Kinsa, Waylander, and Stoney explore the abandoned Crystal Lake Research Facility, finding the frozen Jason and Rowan. They bring them aboard their spaceship, the "Grendel", and revive Rowan while leaving Jason in the morgue, believing him dead.


title: Jason X

text: Adrienne is ordered to dissect Jason's body but Rowan warns them of the danger, revealing Jason's nature and superhuman abilities. Lowe, who is in serious debt, calls his financial backer Dieter Perez on nearby space station "Solaris". Perez recognizes Jason's name and notes his body could interest a collector. While Stoney and Kinsa have sex, Jason awakens and attacks Adrienne, freezing her face with liquid nitrogen before smashing her head to pieces on a counter. Jason takes a machete-shaped surgical tool and kills Stoney in front of Kinsa. Sergeant Brodski leads a group of soldiers to attack Jason. Jason interrupts a projected holographic game, breaking Azrael's back and bashing in Dallas's skull. He tries to attack Crutch, but Brodski and his soldiers arrive. After Brodski splits up his team, Jason kills them one by one.


title: Jason X

text: Lowe orders pilot Lou to dock at "Solaris". Jason kills Lou and the ship crashes through "Solaris", destroying it and killing everyone aboard. Jason breaks into the lab, reclaims his machete and decapitates Lowe. With the "Grendel" crippled, the survivors head for a shuttle while Tsunaron upgrades KM-14. After crew member Crutch is electrocuted by Jason, Kinsa panics and attempts to escape on her own, but forgets to release the shuttle's fuel line, causing it to crash into the ship and explode. Tsunaron reappears with an upgraded KM-14 who wields weapons and combat skills to stand a better chance against Jason. After having his right arm, left leg, right ribs, and part of his head blasted off by KM-14, his body is knocked into a nanite-equipped medical station. The survivors send a distress call, then set explosive charges to separate the ship's undamaged pontoon from the main section.


title: Jason X

text: The medical station nanites rebuild Jason, who becomes a cyborg. With his new strength, Jason easily defeats KM-14 by punching her head off. As Tsunaron recovers her still-functioning head, Jason is stopped by Waylander, who sacrifices himself by setting off the charges while the others escape. Jason survives and punches a hole through the hull, causing Janessa to die in the vacuum. A power failure with the docking door forces Brodski to go outside in an EVA suit to fix it.


title: Jason X

text: To distract Jason, a holographic simulation of Camp Crystal Lake is created with two virtual teenage girls. After killing them, Jason realizes the deception just as the door is fixed. Still in his EVA suit, Brodski confronts Jason so the rest can escape. As they leave, the pontoon explodes, propelling Jason at high speed towards the survivors; Brodski intercepts Jason's space flight and maneuvers them both toward Earth II's atmosphere, where they are both incinerated on atmospheric entry. Tsunaron, Rowan, and KM-14 escape as Tsunaron assures KM-14 she will have a new body.


title: Jason X

text: On Earth II, a pair of teenagers are by a lake when they see what they believe is a falling star. The teenagers go to investigate as Jason's charred mask sinks to the bottom of the lake.


title: Jason X

text: Development of "Jason X" began in the late 1990s while "Freddy vs. Jason" was still in development hell. With "Freddy vs. Jason" not moving forward, Jim Isaac and Sean S. Cunningham decided that they wanted another "Friday the 13th" film made to retain audience interest in the character. The film was conceived by Todd Farmer, who plays "Dallas" in the film, and was the only pitch he gave to the studio for the movie, having suggested sending Jason into space as a means to advance the film series.


title: Jason X

text: The movie was filmed March 6, 2000 through May 2000 in Toronto. The film score was composed and performed by Harry Manfredini. It was released by Varèse Sarabande on May 14, 2002.


title: Jason X

text: "Jason X" premiered in November 2001 in Spain, and was released on April 26, 2002, in the United States. A theatrical trailer was released on November 9, 2001.


title: Jason X

text: The film was released on VHS and DVD on October 8, 2002. It was released on Blu-ray in 2013, with all of the films in the "Friday the 13th: The Complete Collection" set.


title: Jason X

text: The film made $13.1 million in the U.S. and $3.8 million internationally for a worldwide gross of $16.9 million, becoming one of the worst-performing films in the series, after "" and "", which made $14.3 million and $15.9 million, respectively.


title: Jason X

text: On review aggregator website Rotten Tomatoes "Jason X" has an approval rating of 19% based on 108 reviews, and an average rating of 3.8/10. The site's critical consensus reads: "Jason goes to the future, but the story is still stuck in the past." On Metacritic the film has a weighted average score of 25 out of 100, based on 23 critics, indicating "generally unfavorable reviews". Audiences polled by CinemaScore gave the film an average grade of "C" on an A+ to F scale.


title: Jason X

text: Roger Ebert gave the film 0.5 stars out of 4, quoting one of the film's lines: "This sucks on so many levels."


title: Jason X

text: However, the film was better received in the United Kingdom, gaining positive reviews from the country's two major film magazines, "Total Film" and "Empire". "Empire"s review by Kim Newman in particular praised "Jason X" as "Wittily scripted, smartly directed and well-played by an unfamiliar cast, this is a real treat for all those who have suffered through the story so far."


title: Jason X

text: Despite the initially negative reception from critics, the film has recently seen a retrospective growth in popularity, particularly among younger fans of the series. Praise has been directed at the film's ability to poke fun at itself and the film series as a whole, as well as inventive death scenes; Adrienne's death in particular (head frozen in liquid nitrogen, and then shattered against a table) is often singled out as a highlight, and was even tested on an episode of "MythBusters" in 2009.


title: Jason X

text: In 2005, Avatar Press published the comic book "Jason X Special" as a direct sequel to the movie, written by Brian Pulido, with art by Sebastian Fumara and coloring by Mark Sweeney. The comic reveals that a scientist named Kristen intercepted the Grendel's communications and became interested in learning the secrets of Jason's regenerative abilities so she could save her lover Neil as well as the human race, which is still an endangered species barely surviving. To trick the Grendel survivors into bringing Jason to her, she faked the rescue transmission and hacked into their system, using their own holographic technology to convince them they were escaping to Earth II. This resulted in the deaths of all aboard the "Grendel". Aboard her own ship, Kristen then attempts to study Jason X, referring to him as "Uber-Jason." Jason X's new cyborg abilities allow him to take control of Kristen's technology. When she attempts to pass on his regenerative abilities to Neil, the nanites in Jason X's blood corrupt's the man's mind and he stabs her. Kristen's ship then comes across a hedonistic pleasure spaceship called "Fun Club". After docking, Jason boards the "Fun Club" and begins killing the hedonists, ending the story.


title: Jason X

text: In 2006, Avatar Press released a licensed two-issue comic book mini-series called "Friday the 13th: Jason vs. Jason X", written and illustrated by Mike Wolfer, with Andrew Dalhouse as colorist. Advertised as a fight between Jason and "Uber-Jason," the mini-series is a continuation of the comic "Jason X Special." While Jason X is aboard the "Fun Club," the story returns to the "Grendel" drifting in space where a malfunctioning medical station attempts to revive the half of Jason's head that KM-14 shot off in the movie. Since the nanites cannot revive only "13%" of Jason's body mass into a full living being, it collects the remains of other dead bodies aboard the ship and uses them as raw material. As a result, another version of Jason is resurrected, one who resembles the traditional version. When scavengers board the "Grendel," the traditional Jason attacks and then uses their shuttle to reach the nearest ship, the "Fun Club" pleasure cruiser. There, the revived Jason finds the cyborg Jason X and the two fight while also killing all passengers they come across. Each killer is revealed to have only part of the mind and memory of the original Jason. The battle ends when Jason X defeats and rips out the brain matter of the traditional Jason, merging it with his own and restoring his full memories and personality. The ship crashes on Earth II and Jason X leaves the wreckage to explore a nearby forest.


title: Jason X

text: After the 2017 release of "", it was teased that the cyborg Jason X incarnation would be playable in the game the following year. However, Victor Miller, screenwriter of the original film "Friday the 13th", exercised his legal creative rights and served a lawsuit regarding residual profits he felt he was owed by the film franchise and tie-in media that resulted from the original movie. As a result, the game halted the release of new characters and features. Although a partial version of Jason X already existed in the game's files and could be activated with a hack, the fully playable version of Jason X was never released for the game.


title: NACA airfoil

text: The NACA airfoils are airfoil shapes for aircraft wings developed by the National Advisory Committee for Aeronautics (NACA). The shape of the NACA airfoils is described using a series of digits following the word "NACA". The parameters in the numerical code can be entered into equations to precisely generate the cross-section of the airfoil and calculate its properties.


title: NACA airfoil

text: NACA initially developed the numbered airfoil system which was further refined by the United States Air Force at Langley Research Center. According to the NASA website:


title: NACA airfoil

text: For example, the NACA 2412 airfoil has a maximum camber of 2% located 40% (0.4 chords) from the leading edge with a maximum thickness of 12% of the chord.


title: NACA airfoil

text: The NACA 0015 airfoil is symmetrical, the 00 indicating that it has no camber. The 15 indicates that the airfoil has a 15% thickness to chord length ratio: it is 15% as thick as it is long.


title: NACA airfoil

text: The formula for the shape of a NACA 00xx foil, with "xx" being replaced by the percentage of thickness to chord, is


title: NACA airfoil

text: Note that in this equation, at "x" = 1 (the trailing edge of the airfoil), the thickness is not quite zero. If a zero-thickness trailing edge is required, for example for computational work, one of the coefficients should be modified such that they sum to zero. Modifying the last coefficient (i.e. to −0.1036) will result in the smallest change to the overall shape of the airfoil. The leading edge approximates a cylinder with a chord-normalized radius of


title: NACA airfoil

text: Now the coordinates formula_4 of the upper airfoil surface and formula_5 of the lower airfoil surface are


title: NACA airfoil

text: Symmetrical 4-digit series airfoils by default have maximum thickness at 30% of the chord from the leading edge.


title: NACA airfoil

text: The simplest asymmetric foils are the NACA 4-digit series foils, which use the same formula as that used to generate the 00xx symmetric foils, but with the line of mean camber bent. The formula used to calculate the mean camber line is


title: NACA airfoil

text: For example, a NACA 2412 airfoil uses a 2% camber (first digit) 40% (second digit) along the chord of a 0012 symmetrical airfoil having a thickness 12% (digits 3 and 4) of the chord.


title: NACA airfoil

text: For this cambered airfoil, because the thickness needs to be applied perpendicular to the camber line, the coordinates formula_4 and formula_5, of respectively the upper and lower airfoil surface, become


title: NACA airfoil

text: For example, the NACA 23112 profile describes an airfoil with design lift coefficient of 0.3 (0.15 × 2), the point of maximum camber located at 15% chord (5 × 3), reflex camber (1), and maximum thickness of 12% of chord length (12).


title: NACA airfoil

text: where the chordwise location formula_14 and the ordinate formula_15 have been normalized by the chord. The constant formula_16 is chosen so that the maximum camber occurs at formula_17; for example, for the 230 camber line, formula_18 and formula_19. Finally, constant formula_20 is determined to give the desired lift coefficient. For a 230 camber-line profile (the first 3 numbers in the 5-digit series), formula_21 is used.


title: NACA airfoil

text: Camber lines such as 231 makes the negative trailing edge camber of the 230 series profile to be positively cambered. This results in a theoretical pitching moment of 0.


title: NACA airfoil

text: Four- and five-digit series airfoils can be modified with a two-digit code preceded by a hyphen in the following sequence:


title: NACA airfoil

text: For example, the NACA 1234-05 is a NACA 1234 airfoil with a sharp leading edge and maximum thickness 50% of the chord (0.5 chords) from the leading edge.


title: NACA airfoil

text: A new approach to airfoil design pioneered in the 1930s, in which the airfoil shape was mathematically derived from the desired lift characteristics. Prior to this, airfoil shapes were first created and then had their characteristics measured in a wind tunnel. The 1-series airfoils are described by five digits in the following sequence:


title: NACA airfoil

text: For example, the NACA 16-123 airfoil has minimum pressure 60% of the chord back with a lift coefficient of 0.1 and maximum thickness of 23% of the chord.


title: NACA airfoil

text: An improvement over 1-series airfoils with emphasis on maximizing laminar flow. The airfoil is described using six digits in the following sequence:


title: NACA airfoil

text: For example, the NACA 61-315 a=0.5 has the area of minimum pressure 10% of the chord back, maintains low drag 0.2 above and below the lift coefficient of 0.3, has a maximum thickness of 15% of the chord, and maintains laminar flow over 50% of the chord.


title: NACA airfoil

text: Further advancement in maximizing laminar flow achieved by separately identifying the low-pressure zones on upper and lower surfaces of the airfoil. The airfoil is described by seven digits in the following sequence:


title: NACA airfoil

text: For example, the NACA 712A315 has the area of minimum pressure 10% of the chord back on the upper surface and 20% of the chord back on the lower surface, uses the standard "A" profile, has a lift coefficient of 0.3, and has a maximum thickness of 15% of the chord.


title: NACA airfoil

text: Supercritical airfoils designed to independently maximize laminar flow above and below the wing. The numbering is identical to the 7-series airfoils except that the sequence begins with an "8" to identify the series.


title: Rensselaer Polytechnic Institute

text: Rensselaer Polytechnic Institute () (RPI) is a private research university in Troy, New York, with an additional campus in Hartford, Connecticut. A third campus in Groton, Connecticut closed in 2018. RPI was established in 1824 by Stephen Van Rensselaer and Amos Eaton for the "application of science to the common purposes of life" and is the oldest technological university in the English-speaking world and the Western Hemisphere.


title: Rensselaer Polytechnic Institute

text: Built on a hillside, RPI's campus overlooks the city of Troy and the Hudson River, and is a blend of traditional and modern architecture. The institute operates an on‑campus business incubator and the Rensselaer Technology Park.


title: Rensselaer Polytechnic Institute

text: RPI is organized into six main schools which contain 37 departments, with emphasis on science and technology. It is classified among "R1: Doctoral Universities: Very High Research Activity" and many of its engineering programs are highly ranked. As of 2017, RPI's faculty and alumni included 6 members of the National Inventors Hall of Fame, 6 National Medal of Technology winners, 5 National Medal of Science winners, 8 Fulbright Scholarship recipients, and a Nobel Prize winner in Physics; in addition, 86 faculty or alumni are members of the National Academy of Engineering, 17 of the National Academy of Sciences, 25 of the American Academy of Arts and Sciences, 8 of the National Academy of Medicine, 1 of the National Academy of Public Administration, and 9 of the National Academy of Inventors.


title: Rensselaer Polytechnic Institute

text: Stephen Van Rensselaer established the Rensselaer School on 5 November 1824 with a letter to the Reverend Dr. Samuel Blatchford, in which Van Rensselaer asked Blatchford to serve as the first president. Within the letter he set down several orders of business. He appointed Amos Eaton as the school's first senior professor and appointed the first board of trustees. The school opened on Monday, 3 January 1825 at the Old Bank Place, a building at the north end of Troy. Tuition was around $40 per semester (equivalent to $800 in 2012). The fact that the school attracted students from as far as Ohio and Pennsylvania is attributed to the reputation of Eaton. Fourteen months of successful trial led to the incorporation of the school on 21 March 1826 by the state of New York. In its early years, the Rensselaer School strongly resembled a graduate school more than it did a college, drawing graduates from many older institutions.


title: Rensselaer Polytechnic Institute

text: Under Eaton, the Rensselaer School, renamed the Rensselaer Institute in 1832, was a small but vibrant center for technological research. The first civil engineering degrees in the United States were granted by the school in 1835, and many of the best remembered civil engineers of that time graduated from the school. Important visiting scholars included Joseph Henry, who had previously studied under Amos Eaton, and Thomas Davenport, who sold the world's first working electric motor to the institute.


title: Rensselaer Polytechnic Institute

text: In 1847 alumnus Benjamin Franklin Greene became the new senior professor. Earlier he had done a thorough study of European technical schools to see how Rensselaer could be improved. In 1850 he reorganized the school into a three-year polytechnic institute with six technical schools. In 1861 the name was changed to Rensselaer Polytechnic Institute. A severe conflagration of 10 May 1862, known as "The Great Fire", destroyed more than 507 buildings in Troy and gutted in the heart of the city. The "Infant School" building that housed the Institute at the time was destroyed in this fire. Columbia University proposed that Rensselaer leave Troy altogether and merge with its New York City campus. Ultimately, the proposal was rejected and the campus left the crowded downtown for the hillside. Classes were temporarily held at the Vail House and in the Troy University building until 1864, when the Institute moved to a building on Broadway on 8th Street, now the site of the Approach.


title: Rensselaer Polytechnic Institute

text: One of the first Latino student organizations in the United States was founded at RPI in 1890. The Club Hispano Americano was established by the international Latin American students that attended the institute at this time.


title: Rensselaer Polytechnic Institute

text: In 1904 the institute was for the fourth time devastated by fire, when its main building was completely destroyed. However, RPI underwent a period of academic and resource expansion under the leadership of President Palmer Ricketts. Named president in 1901, Ricketts liberalized the curriculum by adding the Department of Arts, Science, and Business Administration, in addition to the Graduate School. He also expanded the university's resources and developed RPI into a true polytechnic institute by increasing the number of degrees offered from two to twelve; these included electrical engineering, mechanical engineering, biology, chemistry, and physics. During Rickett's tenure, enrollment increased from approximately 200 in 1900 to a high of 1,700 in 1930.


title: Rensselaer Polytechnic Institute

text: Another period of expansion occurred following World War II as returning veterans used their GI Bill education benefits to attend college. The "Freshman Hill" residence complex was opened in 1953 followed by the completion of the Commons Dining Hall in 1954, two more halls in 1958, and three more in 1968. In this same time frame (1966) Herta Regina Leng was appointed as RPI's first female full professor. She is now honored there with an annual lecture series. In 1961, there was major progress in academics at the institute with the construction of the Gaerttner Linear Accelerator, then the most powerful in the world, and the Jonsson-Rowland Science Center. The current Student Union building was opened in 1967.


title: Rensselaer Polytechnic Institute

text: The next three decades brought continued growth with many new buildings (see 'Campus' below), and growing ties to industry. The "H-building", previously used for storage, became the home for the RPI incubator program, the first such program sponsored solely by a university. Shortly after this, RPI decided to invest $3 million in pavement, water and power on around of land it owned south of campus to create the Rensselaer Technology Park. In 1982 the New York State legislature granted RPI $30 million to build the George M. Low Center for Industrial Innovation, a center for industry-sponsored research and development.


title: Rensselaer Polytechnic Institute

text: In 1999, RPI gained attention when it was one of the first universities to implement a mandatory laptop computer program. This was also the year of the arrival of Shirley Ann Jackson, a former chairperson of the Nuclear Regulatory Commission under U.S. President Bill Clinton, as the eighteenth president of RPI. She instituted "The Rensselaer Plan" (discussed below), an ambitious plan to revitalize the institute. Many advances have been made under the plan, and Jackson has enjoyed the ongoing support of the RPI Board of Trustees. However, her leadership style did not sit well with many faculty; on 26 April 2006, RPI faculty voted 149 to 155 in a failed vote of no-confidence in Jackson. In September 2007, RPI's Faculty Senate was suspended for over four years over conflict with the administration. On 3 October 2008, RPI celebrated the opening of the $220 million Experimental Media and Performing Arts Center. That same year the national economic downturn resulted in the elimination of 98 staff positions across the institute, about five percent of the workforce. Campus construction expansion continued, however, with the completion of the $92 million East Campus Athletic Village and opening of the new Blitman Commons residence hall in 2009. As of 2015, all staff positions had been reinstated at the institute, experiencing significant growth from pre-recession levels and contributing over $1 billion annually to the economy of the Capital District. That same year, renovation of the North Hall, E-Complex, and Quadrangle dormitories began and was later completed in 2016 to house the largest incoming class in Rensselaer's history.


title: Rensselaer Polytechnic Institute

text: In July 2022, Martin A. Schmidt, formerly provost of Massachusetts Institute of Technology, became RPI's nineteenth president.


title: Rensselaer Polytechnic Institute

text: RPI's campus sits upon a hill overlooking Troy and the Hudson River. The surrounding area is mostly residential neighborhoods, with the city of Troy lying at the base of the hill. The campus is bisected by 15th Street, with most of the athletic and housing facilities to the east, and the academic buildings to the west. A footbridge spans the street, linking the two halves. Much of the campus features a series of Colonial Revival style structures built in the first three decades of the 20th century. Overall, the campus has enjoyed four periods of expansion.


title: Rensselaer Polytechnic Institute

text: RPI was originally located in downtown Troy, but gradually moved to the hilltop that overlooks the city. Buildings that remain from this time include Winslow Chemical Laboratory, a building on the National Register of Historic Places. Located at the base of the hill on the western edge of campus, it currently houses the Social and Behavioral Research Laboratory.


title: Rensselaer Polytechnic Institute

text: President Palmer Ricketts supervised the construction of the school's "Green Rooftop" Colonial Revival buildings that give much of the campus a distinct architectural style. Buildings constructed during this period include the Carnegie Building (1906), Walker Laboratory (1907), Russell Sage Laboratory (1909), Pittsburgh Building (1912), Quadrangle Dormitories (1916–1927), Troy Building (1925), Amos Eaton Hall (1928), Greene Building (1931) and Ricketts Building (1935). Also built during this period was "The Approach" (1907), a massive ornate granite staircase found on the west end of campus. Originally linking RPI to the Troy Union Railroad station, it again serves as an important link between the city and the university. In 1906 the '86 Field, home field of the football team until 2008, was completed with support of the Class of 1886.


title: Rensselaer Polytechnic Institute

text: After World War II, the campus again underwent major expansion. Nine dormitories were built at the east edge of campus bordering Burdett Avenue, a location that came to be called "Freshman Hill". The Houston Field House (1949) was reassembled, after being moved in pieces from its original Rhode Island location. West Hall, which was originally built in 1869 as a hospital, was acquired by the Institute in 1953. The ornate building is an example of French Second Empire architecture. It was listed on the National Register of Historic Places in 1973.


title: Rensselaer Polytechnic Institute

text: Another unique building is the Voorhees Computing Center (VCC). Originally the St. Joseph's Seminary chapel, it was built in 1933 and acquired by Rensselaer in 1958, and after renovation served as the institute's library from 1960 until the completion of the new Folsom Library, in 1976. The Folsom Library, located adjacent to the computing center, has a concrete exterior that was designed to harmonize with the light gray brick of the chapel; architecturally, it is an example of the modern brutalist style. Subsequently, the university was unsure of what to do with the chapel, or whether to keep it at all, but in 1979 decided to preserve it and renovate it to house computer labs and facilities to support the institute's computing initiatives. Today the VCC serves as the backbone for the institute's data and telephony infrastructure.


title: Rensselaer Polytechnic Institute

text: The modern campus features the Jonsson-Rowland Science Center (J-ROWL) (1961), Materials Research Center (MRC) (1965), Rensselaer Union (1967), Cogswell Laboratory (1971), Darrin Communications Center (DCC) (1973), Jonsson Engineering Center (JEC) (1977), Low Center for Industrial Innovation (CII) (1987), a public school building which was converted into Academy Hall (1990), and the Center for Biotechnology and Interdisciplinary Studies (2004). Tunnels connect the Low Center, DCC, JEC and Science Center. A tenth dormitory named Barton Hall was added to Freshman Hill in August 2000, featuring the largest rooms available for freshmen.


title: Rensselaer Polytechnic Institute

text: On 3 October 2008, the university celebrated the grand opening of the Experimental Media and Performing Arts Center (EMPAC) situated on the west edge of campus. The building was constructed on the precipice of the hill, with the main entrance on top. Upon entering, elevated walkways lead into a 1,200-seat concert hall. Most of the building is encased in a glass exoskeleton, with an atrium-like space between it and the "inner building". Adjacent to and underneath the main auditorium there is a 400-seat theater, offices, and two black-box studios with to ceilings. Originally budgeted for $50 million, the EMPAC construction costs ballooned to over $200 million due to difficulty of anchoring the foundation in the soft clay of the hill.


title: Rensselaer Polytechnic Institute

text: In 2008, RPI announced the purchase of the former Rensselaer Best Western Inn, located at the base of the hill, along with plans to transform it into a new residence hall. After extensive renovations, the residence hall was dedicated on 15 May 2009, as the Howard N. Blitman, P.E. '50 Residence Commons. It houses about 300 students in 148 rooms and includes a fitness center, dining hall, and conference area. The new residence hall is part of a growing initiative to involve students in the Troy community and help revitalize the downtown. RPI owns and operates three office buildings in downtown Troy, the Rice and Heley buildings and the historic W. & L.E. Gurley Building. RPI also owns the Proctor's Theater building in Troy which was purchased in 2004, with the intention of converting it into office space. As of 2011, Rensselaer had signed an agreement with Columbia Development Companies to acquire both Proctor's Theatre and Chasan Building in Troy and launch a redevelopment.


title: Rensselaer Polytechnic Institute

text: The Institute runs a campus in Hartford, Connecticut, and a distance learning center in Groton, Connecticut. These centers are used by graduates and working professionals and are managed by the Hartford branch of RPI, Rensselaer at Hartford. At Hartford, graduate degrees are offered in business administration, management, computer science, computer and systems engineering, electrical engineering, engineering science, mechanical engineering and information technology. There are also a number of certificate programs and skills training programs for working professionals.


title: Rensselaer Polytechnic Institute

text: Rensselaer Polytechnic Institute has five schools: the School of Architecture, the School of Engineering, the School of Humanities, Arts, and Social Sciences, the Lally School of Management & Technology, and the School of Science. The School of Engineering is the largest by enrollment, followed by the School of Science, the School of Management, the School of Humanities, Arts, and Social Sciences, and the School of Architecture. There also exists an interdisciplinary program in Information Technology that began in the late 1990s, programs in prehealth and prelaw, Reserve Officers' Training Corps (ROTC) for students desiring commissions as officers in the armed forces, a program in cooperative education (Co-Op), and domestic and international exchange programs. All together, the university offers over 145 degree programs in nearly 60 fields that lead to bachelor's, master's, and doctoral degrees. In addition to traditional majors, RPI has around a dozen special interdisciplinary programs, such as Games and Simulation Arts and Sciences (GSAS), Design, Innovation, and Society (DIS), Minds & Machines, and Product Design and Innovation (PDI). RPI is a technology-oriented university; all buildings and residence hall rooms have hard-wired and wireless high speed internet access, and all incoming freshmen have been required to have a laptop computer since 1999.


title: Rensselaer Polytechnic Institute

text: Nationally, RPI is a member of the National Association of Independent Colleges and Universities (NAICU) and the NAICU's University and College Accountability Network (U-CAN).


title: Rensselaer Polytechnic Institute

text: With the arrival of President Shirley Ann Jackson came the "Rensselaer Plan", announced in 1999. Its goal is to achieve greater prominence for Rensselaer as a technological research university. Various aspects of the plan include bringing in a larger graduate student population and new research faculty, and increasing participation in undergraduate research, international exchange programs, and "living and learning communities". So far, there have been a number of changes under the plan: new infrastructure such as the Center for Biotechnology and Interdisciplinary Studies, Experimental Media and Performing Arts Center, and Computational Center for Nanotechnology Innovations (CCNI) have been built to support new programs, and application numbers have increased. In 2018, Rensselaer received a record number of applications: 20,337. According to Jared Cohon in 2006, then president of Carnegie Mellon University, "Change at Rensselaer in the last five years has occurred with a scope and swiftness that may be without precedent in the recent history of American higher education."


title: Rensselaer Polytechnic Institute

text: The ability to attract greater research funds is needed to meet the goals of the plan, and the university has set a goal of $100 million annually. Fourteen years later, in FY2013, research expenditures reached this goal. To help raise money the university mounted a $1 billion capital campaign, of which the public phase began in September 2004 and was expected to finish by 2008. In 2001, a major milestone of the campaign was the pledging of an unrestricted gift of $360 million by an anonymous donor, believed to be the largest such gift to a U.S. university at the time. The university had been a relative stranger to such generosity as the prior largest single gift was $15 million. By September 2006, the $1 billion goal has been exceeded much in part to an in-kind contribution of software commercially valued at $513.95 million by the Partners for the Advancement of Collaborative Engineering Education (PACE). In light of this, the board of trustees increased the goal of the $1 billion capital campaign to $1.4 billion by 30 June 2009. The new goal was met by 1 October 2008.


title: Rensselaer Polytechnic Institute

text: In anticipation of RPI's 200th anniversary, an updated version called the "Rensselaer Plan 2024" was announced in 2012.


title: Rensselaer Polytechnic Institute

text: In 2016, Jackson announced during the Fall Town Hall Meeting that the institute was in the final stages of organizing a new capital campaign which it would launch in 2017 to meet the goals of the Rensselaer Plan 2024. The goal of the campaign was cited as being primarily for the support of financial aid for undergraduate students and the expansion of on-campus research facilities to accommodate planned increases in doctoral and graduate enrollment. The fundraising goal of the capital campaign was $1 billion, with over $400 million raised prior to the campaign going public.


title: Rensselaer Polytechnic Institute

text: Ambitious spending on the Rensselaer Plan has led the university into financial difficulties, with its credit rating lowered by several agencies.


title: Rensselaer Polytechnic Institute

text: For 2021, "U.S. News & World Report" ranked Rensselaer tied for 53rd among national universities in the U.S., 40th out of 180 for "Best Value" in undergraduate education, and tied for 68th out of the top 83 in "Most Innovative Schools". The same rankings placed Rensselaer's undergraduate engineering program tied at 32nd among schools whose highest degree is a doctorate, and its graduate program is ranked tied for 43rd out of 218 engineering schools.


title: Rensselaer Polytechnic Institute

text: The Leiden Ranking (2016) placed RPI at 127 among the top 900 world universities and research institutions according to the proportion of the top 1% most frequently cited publications of a university. In 2016, "The Economist" ranked Rensselaer No. 18 among four-year non-vocational colleges and universities and Times Higher Education–QS World University Rankings placed Rensselaer among the top 50 universities for technology in the world. In 2016, Rensselaer was listed among the top ten universities for highest median earnings.


title: Rensselaer Polytechnic Institute

text: Civil liberties organization FIRE gave RPI its 2020 "Lifetime Censorship Award" "For its unashamed, years-long record of censoring its critics and utter disinterest in protecting students’ rights".


title: Rensselaer Polytechnic Institute

text: One of the major departments at RPI is the ECSE department, or Electrical and Computer Systems Engineering department. The department offers students the ability to gain bachelors, masters, and doctoral degrees in Electrical Engineering, or Computer Systems Engineering. While the school itself was founded in 1824, Electrical Engineering was first introduced to Rensselaer Polytechnic in 1907 with the class of 1911, long before the invention of the first computers but twenty eight years after the invention of the lightbulb. The department was listed as Physics and Electrical Engineering in 1924 while under President Palmer Ricketts. Computer system engineering was added later. Today Computer Systems Engineering and Electrical Engineering are in many ways similar, with many of the core classes being shared between the two. Electrical Engineering, however tends to focus more on hardware, while computer systems engineering tends to focus on algorithms and systems. Many students take dual majors, the common ones being Electrical Engineering and Computer Systems Engineering, Electrical Engineering and Mechanic Engineering, Electrical Engineering and Applied Physics, and Computer Systems Engineering and Computer Science. Many students in the ECSE department often do minors in other fields such as economics or psychology. The ECSE department currently does research in the areas of information science and systems, communication and network, control and autonomy, energy and power systems, electronics and photonics, and computer systems design. Notable alumni from the ECSE department include James A. Parsons, B. Jayant Baliga, Alan Borck, founder of RLC Electronics, Bruce Carlson, Mukesh Chatter, Allen B. Du Mont, Nariman Farvardin, Peter HArt, inventor of the A* search algorithm Herman A. Haus, Marcian E. Hoff, creator of the microprocessor, Doug Mercer, who was influential in the field of analog to digital converters, Sean O’Sullivan, Curtis P. Priem, founder of NVIDIA, George Saridis, Steven J. Sassoon, inventor of digital camera, Chauncey Starr, Raymond S. Tomlinson, inventor of e-mail, and Eitan Yudilevich.


title: Rensselaer Polytechnic Institute

text: Rensselaer is classified among ". Rensselaer has established six areas of research as institute priorities: biotechnology, energy and the environment, nanotechnology, computation and information technology, and media and the arts. Research is organized under the Office of the Vice President for Research, Jonathan Dordick. In 2018, Rensselaer operated 34 research centers and maintained annual sponsored research expenditures of $100.8 million.


title: Rensselaer Polytechnic Institute

text: One of the most recent of Rensselaer's research centers is the Center for Biotechnology and Interdisciplinary Studies, a 218,000 square-foot research facility and a national pacesetter for fundamental and applied research in biotechnology. The primary target of the research center is biologics, a research priority based on data-driven understanding of proteomics, protein regulation, and gene regulation. It involves using biocatalysis and synthetic biology tools to block or supplement the actions of specific cells or proteins in the immune system. Over the past decade, CBIS has produced over 2,000 peer-reviewed publications with over 30,000 citations and currently employs over 200 scientists and engineers. The center is also used primarily to train undergraduate and graduate students, with over 1,000 undergraduates and 200 doctoral students trained. The center also has numerous academic and industry partners including the Icahn School of Medicine at Mount Sinai. These partnerships have resulted in numerous advances over the last decade through new commercial developments in diagnostics, therapeutics, medical devices, and regenerative medicine which are a direct result of research at the center. Examples of advancements include the creation of synthetic heparin, antimicrobial coatings, detoxification chemotherapy, on-demand bio-medicine, implantable sensors, and 3D cellular array chips.


title: Rensselaer Polytechnic Institute

text: Rensselaer also hosts the Tetherless World Constellation, a multidisciplinary research institution focused on theories, methods, and applications of the World Wide Web. Research is carried out in three inter-connected themes: Future Web, Semantic Foundations and Xinformatics. At Rensselaer, a constellation is a multidisciplinary team composed of senior and junior faculty members, research scientists, and postdoctoral, graduate, and undergraduate students. The faculty experts for the TWC constellation are James Hendler, Deborah McGuinness and Peter Fox. Faculty alumni of TWC includes Heng Ji (Natural Language Processing). In 2016, the Constellation received a one million dollar grant from the Bill & Melinda Gates Foundation for continuing work on a novel data visualization platform that will harness and accelerate the analysis of vast amounts of data for the foundation's Healthy Birth, Growth, and Development Knowledge Integration initiative.


title: Rensselaer Polytechnic Institute

text: In conjunction with the constellation, Rensselaer operates the Center for Computational Innovations which is the result of a $100 million collaboration between Rensselaer, IBM, and New York State to further nanotechnology innovations. The center is currently home to the most powerful private-university based supercomputer in the world and its supercomputer is consistently ranked among the most powerful in the world, capable of performing over 1.1 peta-FLOPS. The center's main focus is on reducing the cost associated with the development of nanoscale materials and devices, such as used in the semiconductor industry. The university also utilizes the center for interdisciplinary research in biotechnology, medicine, energy, and other fields. Rensselaer additionally operates a nuclear reactor and testing facility – the only university-run reactor in New York State – as well as the Gaerttner Linear Accelerator, which is currently being upgraded under a $9.44 million grant from the US Department of Energy.


title: Rensselaer Polytechnic Institute

text: In 2018, Rensselaer's enrollment was 7,442 total resident students, including 6,590 undergraduate and 1,329 graduate. Over 71% of Rensselaer's students are from out of state. More than 20% of students are international. Rensselaer students represent all 50 U.S. states and over 60 countries. The undergraduate student to faculty ratio is 13:1. Among the class of 2020, 66% are in the top 5 percent of their high school class, 93% in the top quarter, and 99% in the top half. The average unweighted high school GPA for enrolled students was 3.88 on a 4.0 scale, with 65% having a 3.75 GPA or higher and 99% having at least a 3.0.


title: Rensselaer Polytechnic Institute

text: Rensselaer's yield rate for the Class of 2021 surpassed 20 percent in the year 2018 with over 20,000 applications received by Rensselaer's Office of Admissions. The average SAT score range was 1330-1500 for the mid-50% range with a median SAT score of 1420 on a scale of 1600. The average ACT score range was 29-33 for the mid-50% range with a median ACT score of 31. In 2016, Rensselaer's freshman retention rate was 94% and admissions selectivity rating was 35th in the nation according to "U.S. News & World Report". Since 2000, undergraduate enrollment grew by over 1,700 students, from 4,867 to 6,590 during calendar year 2018, and the full-time graduate enrollment declined from 1500 to 1,188.


title: Rensselaer Polytechnic Institute

text: Roughly 12% of students received the Rensselaer medal, a merit scholarship with a cumulative value of $100,000 for exceptional high school students in science and mathematics. 95% of full-time domestic undergraduate students receive either need-based or merit-based financial aid, averaging 85% of total financial need met per student. In 2018, Rensselaer invested over $140 million in financial aid and scholarships for students.


title: Rensselaer Polytechnic Institute

text: RPI became coeducational in 1942. In 1966, the male-to-female ratio was 19:1, in the 1980s it reached as low as 8:1, and in the early 1990s the ratio was around 5:1. In 2009, RPI had a ratio of 2.5:1 (72% male / 28% female), In 2016, the ratio for the incoming freshman class had fallen to 2.1:1 (68% male / 32% female), the lowest in the history of the institute.


title: Rensselaer Polytechnic Institute

text: In the fall of 2016, more than 1,000 women enrolled in Rensselaer Polytechnic Institute's undergraduate engineering programs for the first time in its history. These women represented 30 percent of the student body in engineering at the university, and 32 percent of the university's total gender composition. Shekhar Garde, Rensselaer's dean of engineering, claims he wants to increase the female composition of the institute to 50 percent before 2030.


title: Rensselaer Polytechnic Institute

text: The positions of Grand Marshal and President of the Union at Rensselaer Polytechnic Institute are typically awarded (by student vote) to the students who are respected by the student body and are represented by a top hat and a derby hat respectively. While Rensselaer Polytechnic Institute has had the position of Grand Marshal (GM) since 1865,  the position of President of the Union did not come about until 1890 when the union was developed. However, between 1890 and 1894, there was only a President of the Union, no Grand Marshal. Starting with the 1894–1895 school year, the President of the Union and Grand Marshal ran side by side. The week of voting for said positions is called GM Week, and typically has events on campus for students to do to promote the voting.


title: Rensselaer Polytechnic Institute

text: The Grand Marshal position is elected by the student body (typically in the spring) and is the highest position a student can hold at RPI. The GM plays a big role in the student government by doing projects, appointing officers, and aiding the general campus community. The first GM was Albert M. Harper, and the current GM as of 2021-2022 is Cait Bennet (156th).


title: Rensselaer Polytechnic Institute

text: The President of the Union is elected by the student body (typically in the spring). Their main responsibility is to appoint an Executive Board of 15–20 students (responsible for the Rensselaer Union's budget). The Executive Board is the chief financial body of the Rensselaer Union. They are responsible for preparing and approving the budget for the following fiscal year, keeping track of and distributing union funds, and managing the business affairs with other facilities. In addition to appointing the Executive Board, they also work closely with the union's staff, athletics staff, and student clubs. The first PU was W.C.H. Slagle, and the current as of 2021-2022 is Colleen Corrigan (133th).


title: Rensselaer Polytechnic Institute

text: Rensselaer Polytechnic Institute has an extensive history of Greek community involvement on campus, including past presidents, honorary academic building dedications, and philanthropic achievements. The overall Greek system at Rensselaer stresses Leadership, Fortitude, Innovation, and Evolution. RPI currently has 29 active fraternities as well as 6 sororities, with 32 percent involvement of all males and 18 percent involvement of all females, organized under the Interfraternal Council and Panhellenic Council. Of those Greek organizations, three were founded at Rensselaer including the Theta Xi national engineering fraternity, the Sigma Delta Hispanic-interest local sorority, and the Rensselaer Society of Engineers local engineering fraternity. Theta Xi fraternity was established by RPI students on 29 April 1864, the only national fraternity founded during the Civil War. The Theta Xi Fraternity Chapter House is listed on the National Register of Historic Places. Additionally, Rensselaer is home to the Epsilon Zeta chapter of the Alpha Phi Omega, or "APO," national service fraternity, which operates a test-bank and office at the top floor of the Student Union. The organization also hosts a campus lost & found, universal can tab collection, and a public 3D printing service.


title: Rensselaer Polytechnic Institute

text: In 2017, Chi Phi and Theta Chi at Rensselaer co-hosted an event called "Brave A Shave For Kids With Cancer," along with several other Greek organizations - raising over $22,000 for pediatric cancer research with dozens of participants shaving their heads to spread awareness of pediatric cancers. Many fraternities and sororities also engage in Adopt-a-Highway and host events in the local community. Since its inception, all members of Greek Life have also participated in Navigating Rensselaer & Beyond - RPI's official continuation of student orientation through hosting annual events open to all students such as Beach Day/Hike with Greek Life, a day of hiking and team building activities for incoming freshmen, and Saratoga Therapeutic Equine Program, a day of service focused on horse rehabilitation programs.


title: Rensselaer Polytechnic Institute

text: Greek Life organizations also operate Greek-affiliated groups including the Alumni Inter-Greek Council, Greek Greeks - a student-run venture which aims to promote sustainability and safe environmental practices in Greek chapter houses, Greek Spectrum - an LGBTQIA support and advocacy group, and the undergraduate Greek leadership society Order of Omega.


title: Rensselaer Polytechnic Institute

text: The RPI Engineers are the athletic teams for the university. RPI currently sponsors 23 sports, 21 of which compete at the NCAA Division III level in the Liberty League; men's and women's ice hockey compete at the Division I level in ECAC Hockey. The official nickname of some of the school's Division III teams was changed in 1995 from the Engineers to the Red Hawks. However, the hockey, football, cross-country, tennis and track and field teams all chose to retain the Engineers name. The Red Hawks name was, at the time, very unpopular among the student body; a Red Hawk mascot was frequently taunted with thrown concessions and chants of "kill the chicken!". In 2009 the nickname for all teams has since been changed back to Engineers. In contrast, the official ice hockey mascot, known as Puckman, has always been very popular. Puckman is an anthropomorphic hockey puck with an engineer's helmet.


title: Rensselaer Polytechnic Institute

text: RPI has a competitive Division I hockey team who won NCAA national titles in 1954 and 1985. Depending on how the rules are interpreted, the RPI men's ice hockey team may have the longest winning streak on record for a Division I team; in the 1984–85 season it was undefeated for 30 games, but one game was against the University of Toronto, a non-NCAA team. Continuing into the 1985–86 season, RPI continued undefeated over 38 games, including two wins over Toronto. The streak ended at Boston University against the Terriers. Adam Oates and Daren Puppa, two players during that time, both went on to become stars in the NHL. Joé Juneau, who played from 1987 to 1991, and Brian Pothier, who played from 1996 to 2000, also spent many years in the NHL. Graeme Townshend, who also played in the late 1980s, had a brief NHL career. He is the first man of Jamaican ancestry to play in the National Hockey League.


title: Rensselaer Polytechnic Institute

text: The ice hockey team plays a significant role in the campus's culture, drawing thousands of fans each week to the Houston Field House during the season. The team's popularity even sparked the tradition of the hockey line, where students lined up for season tickets months in advance of the on-sale date. Today, the line generally begins a week or more before ticket sales. Another tradition since 1978 has been the "Big Red Freakout!" game held close to the first weekend of February. Fans usually dress in the schools colors red (cherry) and white, and gifts such as T-shirts are distributed en masse. In ice hockey, the RPI's biggest rival has always been the upstate engineering school Clarkson University. In recent years RPI has also developed a spirited rivalry with their conference travel partner Union College, with whom they annually play a nonconference game in Albany for the Mayor's Cup.


title: Rensselaer Polytechnic Institute

text: The women's ice hockey team moved to the NCAA Division I level in 2005. During the 2008–09 season the team set the record for most wins in one season (19-14-4). On 28 February 2010, Rensselaer made NCAA history. The Engineers beat Quinnipiac, 2–1, but it took five overtimes. It is now the longest game in NCAA Women's Ice Hockey history. Senior defenseman Laura Gersten had the game-winning goal. She registered it at 4:32 of the fifth overtime session to not only clinch the win, but the series victory.


title: Rensselaer Polytechnic Institute

text: The lacrosse team represented the United States in the 1948 Olympics in London. It won the Wingate Memorial Trophy as national collegiate champions in 1952. Future NHL head coach Ned Harkness coached the lacrosse and ice hockey teams, winning national championships in both sports.


title: Rensselaer Polytechnic Institute

text: The Engineers baseball squad is perennially atop the Liberty League standings, and has seen 8 players move on to the professional ranks, including 4 players selected in the MLB draft. The team is coached by Keith Glasser. The Engineers play their home games at the historic Robison Field.


title: Rensselaer Polytechnic Institute

text: American rugby was played on campus in the late 1870s. Intercollegiate football begin as late as 1886 when an RPI team first played a Union College team on a leased field in West Troy (Watervliet). Since 1903, RPI and nearby Union have been rivals in football, making it the oldest such rivalry in the state. The teams have played for the Dutchman's Shoes since 1950. RPI Football had their most successful season in 2003, when they finished 11-2 and lost to St. Johns (Minn.) in the NCAA Division III semi final game.


title: Rensselaer Polytechnic Institute

text: The Houston Field House is a 4,780‑seat multi-purpose arena located on the RPI campus. It opened in 1949 and is home to the RPI Engineers men's and women's ice hockey teams. The Field House was renovated starting in 2007 as part of the major campus improvement project to build the East Campus Athletic Village. The renovations included locker rooms upgrades, addition of a new weight room, and a new special reception room dedicated to Ned Harkness. Additionally, as part of the renovations through a government grant, solar panels were installed on the roof to supply power to the building.


title: Rensselaer Polytechnic Institute

text: As part of the Rensselaer Plan, the Institute recently completed a major project to improve its athletic facilities with the East Campus Athletic Village. The plan included construction of a new and much larger 4,842‑seat football stadium, a basketball arena with seating for 1,200, a new 50-meter pool, an indoor track and field complex, new tennis courts, new weight rooms and a new sports medicine center. The Institute broke ground on 26 August 2007, and construction of the first phase is expected to last two years. The estimated cost of the project is $78 million for phase one and $35–$45 million for phase two. Since the completion of the new stadium, the bleachers on the Class of '86 football field on the central campus have been removed and the field has become an open space. In the future the new space could be used for expansions of the academic buildings, but for now members of the campus planning team foresee a "historic landscape with different paths and access ways for students and vehicles alike".


title: Rensselaer Polytechnic Institute

text: The students of RPI have created and participate in a variety of clubs and organizations funded by the Student Union. About 170 of these organizations are funded by the Student Union, while another thirty, which consist mostly of political and religious organizations, are self-supporting. In 2006 the "Princeton Review" ranked RPI second for "more to do on campus." The Union was the last entirely student-run union at a private university in the United States until September 2017.


title: Rensselaer Polytechnic Institute

text: Phalanx is RPI's Senior Honor Society. It was founded in 1912, when Edward Dion and the Student Council organized a society to recognize those RPI students who had distinguished themselves among their peers in the areas of leadership, service and devotion to the "alma mater". It is a fellowship of the most active in student activities and has inducted more than 1,500 members since its founding.


title: Rensselaer Polytechnic Institute

text: RPI has around twenty intramural sports organizations, many of which are broken down into different divisions based on level of play. Greek organizations compete in them as well as independent athletes. There are also thirty-nine club sports.


title: Rensselaer Polytechnic Institute

text: Given the university's proximity to the Berkshires, Green Mountains and Adirondacks, the Ski Club and the Outing Club are some of the largest groups on campus. The Ski Club offers weekly trips to local ski areas during the winter months, while the Outing Club offers trips on a weekly basis for a variety of activities.


title: Rensselaer Polytechnic Institute

text: "The Rensselaer Polytechnic" is the student-run weekly newspaper. "The Poly" printed about 7,000 copies each week and distributed them around campus until 2018 when the newspaper switched to online-only distribution due to budget concerns. Although it is the Union club with the largest budget, "The Poly" receives no subsidy from the Union, and obtains all funding through the sale of advertisements. There is also a popular student-run magazine called "Statler & Waldorf" which prints on a semesterly basis.


title: Rensselaer Polytechnic Institute

text: RPI has an improvisational comedy group, Sheer Idiocy, which performs several shows a semester. There are also several music groups ranging from "a cappella" groups such as the Rusty Pipes, Partial Credit, the Rensselyrics and Duly Noted, to several instrumental groups such as the orchestra, the jazz band and a classical choral group, the Rensselaer Concert Choir.


title: Rensselaer Polytechnic Institute

text: Another notable organization on campus is WRPI, the campus radio station. WRPI differs from most college radio in that it serves a radius including the greater Albany area. With 10 kW of broadcasting power, WRPI maintains a stronger signal than nearly all college radio stations and some commercial stations. WRPI currently broadcasts on 91.5 FM in the Albany area.


title: Rensselaer Polytechnic Institute

text: The RPI Players is an on‑campus theater group that was formed in 1929. The Players resided in the Old Gym until 1965 when they moved to their present location at the 15th Street Lounge. This distinctive red shingled building had been a USO hall for the U.S. Army before being purchased by RPI. The Players have staged over 275 productions in its history.


title: Rensselaer Polytechnic Institute

text: Another notable aspect of student life at RPI is the "First-Year Experience" (FYE) program. Freshman begin their stay at RPI with a week called "Navigating Rensselaer and Beyond" or NRB week. The Office of the First-Year Experience provides several programs that extend to not only freshman, but to all students. These include family weekend, community service days, the Information and Personal Assistance Center (IPAC), and the Community Advocate Program. The FYE program was awarded the 2006 NASPA Excellence Gold Award, in the category of "Enrollment Management, Orientation, Parents, First-Year, Other-Year and related".


title: Rensselaer Polytechnic Institute

text: Starting in 2008, the Division of Student Life updated the structure of its residential college model based upon the concept of "Clustered Learning Advocacy and Support for Students" (CLASS), which included a planned requirement for all sophomores to live on campus and to live with special "residence cluster deans".


title: Rensselaer Polytechnic Institute

text: The transition to this program began in early 2010 among some resistance from some fraternities and students who had planned to live off campus.


title: Rensselaer Polytechnic Institute

text: RPI NROTC is an officer accession program hosted at RPI with the goal of developing Midshipmen into commissioned officers into the United States Navy and Marine Corps. The unit consists of students from RPI as well as Union College. The program was officially started at RPI in September 1941, just a few months before the US involvement in WWII. RPI NROTC was part of the V-12 training program that was aimed at increasing the number of total commissioned officers during WWII. It focused on developing officers for the military specializing in technical degrees such as engineering, medicine, and foreign languages. The RPI class of 1945 had a large majority of its student body in the NROTC program with around 70% of the 932 students.


title: Rensselaer Polytechnic Institute

text: Since 1926, over 75 Naval Officers have attained flag officer rank with a degree from RPI. Besides the US Naval Academy, this is the largest number of flag officers produced from one single institute. RPI NROTC is home to several notable alumni including NASA Astronaut CDR Reid Wiseman and RDML Lewis Combs. RDML Combs is the founder of the Navy Construction Battalion, commonly referred to as the “Seabees”, which plays a crucial role in creating forward deployed bases as well as humanitarian efforts to bring fresh water to underdeveloped communities.


title: Rensselaer Polytechnic Institute

text: One of the religious clubs that can be found at Rensselaer Polytechnic Institute is RPI-Sage Hillel. This is a Jewish club that incorporates both Rensselaer Polytechnic Institute and Russell Sage College. Hillel club is a club that is part of a much larger international organization called Hillel International. Hillel's purpose is “Enriching the lives of Jewish students so that they may enrich the Jewish people and the world”, and their vision is for “a world where every student is inspired to make an enduring commitment to Jewish life, learning and Israel.” Hillel meets on Fridays at 6:30 for services and has several other activities throughout the week as decided on by the board of Hillel.


title: Rensselaer Polytechnic Institute

text: Another religious club at RPI is Cru, which is a non-denominational Christian club that holds worship on Fridays from 7pm. There are other events throughout the week, such as a men's small group, a women's small group, a Saturday morning small group, and a book club. Cru club is part of an also much larger organization, and there are many such programs in schools across the country. Cru was originally founded in 1951 by Bill and Vonette Bright at Fuller Theological Seminary. Its values are faith, growth, and fruitfulness. Cru holds retreats several times a year and has many resources dedicated to helping people who are curious in the Christian faith.


title: Rensselaer Polytechnic Institute

text: Rensselaer Polytechnic Institute historically has always been a male dominated institute. The first woman to apply to RPI applied in 1873, and her name was Elizabeth R. Bruswell. However, she did not attend as she was the only female to apply and it was suggested that she would not be accepted as it would not be comfortable for her as the only woman on campus. For many years afterwards, the school continued to only allow admission to men. It wasn't until 1942 that women were welcome to enroll in classes at Rensselaer.


title: Rensselaer Polytechnic Institute

text: Camilla (Trent) Cluett (Architecture), Elizabeth English (Biology), Helen Ketchum (Architecture), Lois Graham (Mechanical Engineering), and Mary Ellen Rathbun (Metallurgical Engineering) were the first women to enroll in 1942. Lois Graham and Mary Ellen Rathbun became the first to graduate on April 22, 1945. In addition, Antoinette A. Patti was the first woman to receive a master's degree from RPI in February 1947, in Chemistry. The first Doctoral Degree received by a woman at RPI was Reva R. G. Servoss in June 1954, in Chemistry as well.


title: Rensselaer Polytechnic Institute

text: Miss Hazel Brennan was the first woman assistant instructor in chemistry in 1918. She officially was the first woman to teach at Rensselaer Polytechnic Institute. The following year, 1919, Marie De Pierpont was hired as an instructor in French and was later named professor as well as being named head of the language department in 1928. She was the first woman to hold a full professorship at the institute, and ended her position in 1932. It wasn't for another 11 years (1943) that another woman was hired as an instructor. Herta Leng, who worked in the Physics Department, was given the title of assistant professor in 1945, and became a full professor in 1966, the second woman to be a full professor at Rensselaer Polytechnic Institute.


title: Rensselaer Polytechnic Institute

text: To this day, the percentage of women enrolled at RPI is still significantly lower. The ratio as of 2020 was about 32% women and 68% men.


title: Rensselaer Polytechnic Institute

text: According to the Rensselaer Alumni Association, there are nearly 100,000 RPI graduates currently living in the United States, and another 4,378 living abroad. In 1995, the Alumni Association created the Rensselaer Alumni Hall of Fame.


title: Rensselaer Polytechnic Institute

text: Several notable 19th century civil engineers graduated from RPI. These include the visionary of the transcontinental railroad, Theodore Judah, Brooklyn Bridge engineer Washington Roebling, George Washington Gale Ferris Jr. (who designed and built the original Ferris Wheel) and Leffert L. Buck, the chief engineer of the Williamsburg Bridge in New York City.


title: Rensselaer Polytechnic Institute

text: Many RPI graduates have made important inventions, including Allen B. DuMont ('24), creator of the first commercial television and radar; Keith D. Millis ('38), inventor of ductile iron; Ted Hoff ('58), father of the microprocessor; Raymond Tomlinson ('63), often credited with the invention of e-mail; inventor of the digital camera Steven Sasson<ref name="The Rediff Interview/Steven J Sasson, inventor of the digital camera"></ref> and Curtis Priem ('82), designer of the first graphics processor for the PC, and co-founder of NVIDIA. RPI Prof. Matthew Hunter invented a process to refine titanium in 1910. H. Joseph Gerber pioneered computer-automated manufacturing systems for industry.


title: Rensselaer Polytechnic Institute

text: In addition to NVIDIA, RPI graduates have also gone on to found or co-found major companies such as John Wiley and Sons, Texas Instruments, Fairchild Semiconductor, PSINet, MapInfo, Adelphia Communications, Level 3 Communications, Garmin, Bugle Boy and Vacasa. Several RPI graduates have played a part in the U.S. space program: George Low (B.Eng. 1948, M.S. 1950) was manager of the Apollo 11 project and served as president of RPI, and astronauts John L. Swigert, Jr., Richard Mastracchio, Gregory R. Wiseman, and space tourist Dennis Tito are alumni. The Electric Power Research Institute (EPRI) was founded by Dr. Chauncey Starr who graduated from RPI with a PhD in physics in 1935.


title: Rensselaer Polytechnic Institute

text: Political figures who graduated from RPI included federal judge Arthur J. Gajarsa (B.S. 1962), and Major General Thomas Farrell of the Manhattan Project. Edward Burton Hughes, the Acting Commissioner of New York State Department of Transportation in 1969, Executive Deputy Commissioner of New York State Department of Transportation from 1967 to 1970, and Deputy Superintendent of New York State Department of Public Works from 1952 to 1967. Bertram Dalley Tallamy, seventh Federal Highway Administrator under the Federal Aid Highway Act of 1956, in office from February 5, 1957 – January 20, 1961. DARPA director Tony Tether, Representative John Olver of Massachusetts's 1st congressional district, and Senators John Barrasso of Wyoming, Mark Shepard of Vermont, and George R. Dennis of Maryland, Prime Minister Hani Al-Mulki of Jordan.


title: Rensselaer Polytechnic Institute

text: Notable ice hockey players include NHL Hockey Hall of Famer and five-time NHL All Star Adam Oates (1985), Stanley Cup winner and former NHL All Star Mike McPhee (1982), two-time Calder Cup winner Neil Little (1994), former NHL All Rookie Joé Juneau (1991), and former NHL All Star Daren Puppa (1985).


title: Rensselaer Polytechnic Institute

text: Other notable alumni include 1973 Nobel Prize in Physics winner Ivar Giaever (Ph.D. 1964); the first African-American woman to become a thoracic surgeon, Rosalyn Scott (B.S. 1970); director of Linux International Jon Hall (M.S. 1977); NCAA president Myles Brand (B.S. 1964); Lois Graham (B.S.ME 1946), who was the first woman to receive a degree in engineering from RPI, and went on to become the first woman in the US to receive a PhD in engineering; adult stem cell pioneer James Fallon; Michael D. West, gerontologist and stem cell scientist, founder of Geron, now CEO of BioTime (1976); director Bobby Farrelly (1981), David Ferrucci, lead researcher on IBM's Watson/Jeopardy! project; 66th AIA Gold Medal-winning architect Peter Q Bohlin; Matt Patricia, former head coach for the Detroit Lions; Garrettina LTS Brown, founder of Garrett's List, King Breeders and inventor of FreeTV; Luis Acuña-Cedeño, Governor of the Venezuelan Sucre State and former Minister of Universities; Andrew Franks, former placekicker for the Miami Dolphins of the National Football League; Sean Conroy, the first openly gay professional baseball player; Prem Jain (Father of Green Buildings in India); Keith Raniere, an American felon and the founder of NXIVM, a multi-level marketing company and cult.


title: Pimiento

text: A pimiento or pimento (or cherry pepper) is a variety of large, red, heart-shaped chili pepper ("Capsicum annuum") that measures 3 to 4 in (7 to 10 cm) long and 2 to 3 in (5 to 7 cm) wide (medium, elongate).


title: Pimiento

text: Pimientos can have various colours including yellow, green, red, and maroon. Some are green when immature and turn red when they reach maturity.


title: Pimiento

text: The flesh of the pimiento is sweet, succulent, and more aromatic than that of the red bell pepper. Some varieties of the pimiento type are hot, including the Floral Gem and Santa Fe Grande varieties. The fruits are typically used fresh or pickled.


title: Pimiento

text: Spanish and Portuguese both come from Latin ("pigment; coloring") and came to be used for bell peppers. The English borrowed "pimiento" and "pimento" as loanwords for what is distinguished in Spanish as and in Portuguese as .


title: Pimiento

text: "Sweet" (i.e., neither sour nor savory) pimiento peppers are the familiar red stuffing found in prepared Spanish or Greek green olives. Originally, the pimiento was hand-cut into tiny pieces, then hand-stuffed into each olive to balance out the olive's otherwise strong, salty flavor. Despite the popularity of the combination, this production method was very costly and time-intensive. In the industrial era, the cut pimiento was shot by a hydraulic pump into one end of each olive, simultaneously inserting the pimiento in the center while ejecting the pit out the other end.


title: Pimiento

text: More recently, for ease of production, pimientos are often puréed then formed into tiny strips, with the help of a natural gum (such as sodium alginate or guar gum). This allows olive stuffing to be mechanized, speeding the process and lowering production costs.


title: Pimiento

text: Pimientos are commonly used for making pimento cheese. It is also used for making pimento loaf, a type of processed sandwich meat.


title: Category theory

text: Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, category theory is used in almost all areas of mathematics, and in some areas of computer science. In particular, many constructions of new mathematical objects from previous ones, that appear similarly in several contexts are conveniently expressed and unified in terms of categories. Examples include quotient spaces, direct products, completion, and duality.


title: Category theory

text: A category is formed by two sorts of objects: the objects of the category, and the morphisms, which relate two objects called the "source" and the "target" of the morphism. One often says that a morphism is an "arrow" that "maps" its source to its target. Morphisms can be "composed" if the target of the first morphism equals the source of the second one, and morphism composition has similar properties as function composition (associativity and existence of identity morphisms). Morphisms are often some sort of function, but this is not always the case. For example, a monoid may be viewed as a category with a single object, whose morphisms are the elements of the monoid.


title: Category theory

text: The second fundamental concept of category is the concept of a functor, which plays the role of a morphism between two categories formula_1 and formula_2 it maps objects of formula_1 to objects of formula_4 and morphisms of formula_1 to morphisms of formula_4 in such a way that sources are mapped to sources and targets are mapped to targets (or, in the case of a contravariant functor, sources are mapped to targets and "vice-versa"). A third fundamental concept is a natural transformation that may be viewed as a morphism of functors.


title: Category theory

text: Relations among morphisms (such as ) are often depicted using commutative diagrams, with "points" (corners) representing objects and "arrows" representing morphisms.


title: Category theory

text: Every retraction is an epimorphism, and every section is a monomorphism. Furthermore, the following three statements are equivalent:


title: Category theory

text: Functors are structure-preserving maps between categories. They can be thought of as morphisms in the category of all (small) categories.


title: Category theory

text: A contravariant functor is like a covariant functor, except that it "turns morphisms around" ("reverses all the arrows"). More specifically, every morphism in "C" must be assigned to a morphism in "D". In other words, a contravariant functor acts as a covariant functor from the opposite category "C" to "D".


title: Category theory

text: A "natural transformation" is a relation between two functors. Functors often describe "natural constructions" and natural transformations then describe "natural homomorphisms" between two such constructions. Sometimes two quite different constructions yield "the same" result; this is expressed by a natural isomorphism between the two functors.


title: Category theory

text: If "F" and "G" are (covariant) functors between the categories "C" and "D", then a natural transformation η from "F" to "G" associates to every object "X" in "C" a morphism in "D" such that for every morphism in "C", we have ; this means that the following diagram is commutative:


title: Category theory

text: The two functors "F" and "G" are called "naturally isomorphic" if there exists a natural transformation from "F" to "G" such that η is an isomorphism for every object "X" in "C".


title: Category theory

text: Using the language of category theory, many areas of mathematical study can be categorized. Categories include sets, groups and topologies.


title: Category theory

text: Each category is distinguished by properties that all its objects have in common, such as the empty set or the product of two topologies, yet in the definition of a category, objects are considered atomic, i.e., we "do not know" whether an object "A" is a set, a topology, or any other abstract concept. Hence, the challenge is to define special objects without referring to the internal structure of those objects. To define the empty set without referring to elements, or the product topology without referring to open sets, one can characterize these objects in terms of their relations to other objects, as given by the morphisms of the respective categories. Thus, the task is to find "universal properties" that uniquely determine the objects of interest.


title: Category theory

text: Numerous important constructions can be described in a purely categorical way if the "category limit" can be developed and dualized to yield the notion of a "colimit".


title: Category theory

text: It is a natural question to ask: under which conditions can two categories be considered "essentially the same", in the sense that theorems about one category can readily be transformed into theorems about the other category? The major tool one employs to describe such a situation is called "equivalence of categories", which is given by appropriate functors between two categories. Categorical equivalence has found numerous applications in mathematics.


title: Category theory

text: The definitions of categories and functors provide only the very basics of categorical algebra; additional important topics are listed below. Although there are strong interrelations between all of these topics, the given order can be considered as a guideline for further reading.


title: Category theory

text: Many of the above concepts, especially equivalence of categories, adjoint functor pairs, and functor categories, can be situated into the context of "higher-dimensional categories". Briefly, if we consider a morphism between two objects as a "process taking us from one object to another", then higher-dimensional categories allow us to profitably generalize this by considering "higher-dimensional processes".


title: Category theory

text: For example, a (strict) 2-category is a category together with "morphisms between morphisms", i.e., processes which allow us to transform one morphism into another. We can then "compose" these "bimorphisms" both horizontally and vertically, and we require a 2-dimensional "exchange law" to hold, relating the two composition laws. In this context, the standard example is Cat, the 2-category of all (small) categories, and in this example, bimorphisms of morphisms are simply natural transformations of morphisms in the usual sense. Another basic example is to consider a 2-category with a single object; these are essentially monoidal categories. Bicategories are a weaker notion of 2-dimensional categories in which the composition of morphisms is not strictly associative, but only associative "up to" an isomorphism.


title: Category theory

text: This process can be extended for all natural numbers "n", and these are called "n"-categories. There is even a notion of "ω-category" corresponding to the ordinal number ω.


title: Category theory

text: Higher-dimensional categories are part of the broader mathematical field of higher-dimensional algebra, a concept introduced by Ronald Brown. For a conversational introduction to these ideas, see John Baez, 'A Tale of "n"-categories' (1996).