title: Tom Seaver

text: On December 16, 1982, Seaver was traded back to the Mets, for Charlie Puleo, Lloyd McClendon, and Jason Felice. On April 5, 1983, he tied Walter Johnson's major league record of 14 Opening Day starts, shutting out the Philadelphia Phillies for six innings in a 2–0 Mets win, but had a 9–14 record that season. The Mets exercised an option on Seaver's contract worth $750,000 for the 1984 season. Overall, in 12 seasons with the Mets, Seaver was 198–124 with a 2.57 earned run average in 3,045 innings with 171 complete games, winning three Cy Young awards, the 1969 World Series and the 1967 NL Rookie of the Year Award.


title: Tom Seaver

text: On January 20, 1984, the Chicago White Sox claimed Seaver from the Mets in a free-agent compensation draft. The Mets, especially general manager Frank Cashen, incorrectly assumed that no one would pursue a high-salaried, 39-year-old starting pitcher and left him off the protected list.


title: Tom Seaver

text: Seaver pitched two and a half seasons in Chicago and recorded his last shutout on July 19, 1985, against the visiting Indians. In an anomaly, Seaver won two games on May 9, 1984; he pitched the 25th and final inning of a game suspended the day before, picking up the win in relief against the Milwaukee Brewers, before starting and winning the day's regularly scheduled game, also facing the Brewers.


title: Tom Seaver

text: On August 4, 1985, Seaver recorded his 300th victory at Yankee Stadium over the Yankees, throwing a complete game 4–1 victory, with Mets announcer Lindsey Nelson in the booth.


title: Tom Seaver

text: In three seasons with the White Sox, Seaver was 33–28 with a 3.67 earned run average and 17 complete games in 81 appearances.


title: Tom Seaver

text: Seaver started on Opening Day for the 16th and final time of his career in 1986. The White Sox traded Seaver to the Boston Red Sox for Steve Lyons in mid-season. Seaver's 311th and final win came on August 18, 1986, against the Minnesota Twins.


title: Tom Seaver

text: A knee injury prevented Seaver from appearing against the Mets in the World Series with the Red Sox, but he received among the loudest ovations during player introductions prior to Game 1. Roger Clemens attributes the time he shared with Seaver as teammates in 1986 as instrumental in helping him make the transition from thrower to pitcher. The Red Sox did not offer Seaver a contract to his liking for the 1987 season. His 1986 salary was $1 million; the Red Sox offered $500,000, which Seaver declined. When no new contract agreement was reached, Seaver was granted free agency on November 12, 1986.


title: Tom Seaver

text: In 1987, the Mets starting rotation was decimated by injury and they sought help from Seaver. Though no contract was signed, Seaver joined the club on June 6, and was hit hard in an exhibition game against the Triple-A Tidewater Tides on June 11. After similarly poor outings on June 16 and 20, he announced his retirement, saying that, "there were no more pitches in this 42-year-old arm that were competitive. I've used them all up."


title: Tom Seaver

text: The Mets retired Seaver's uniform number 41 in 1988 in a Tom Seaver Day ceremony, making him the franchise's first player to be so honored.


title: Tom Seaver

text: Seaver was elected to the Baseball Hall of Fame on January 7, 1992, with the then-highest percentage of votes with 98.84%. He was named on 425 out of 430 ballots. Three of the five ballots that had omitted Seaver were blank, cast by writers protesting the Hall's decision to make Pete Rose ineligible for consideration. One ballot was sent by a writer who was recovering from open-heart surgery and failed to notice Seaver's name. The fifth "no" vote was cast by a writer who said he never voted for any player in their first year of eligibility. Seaver is one of two players enshrined in the Hall of Fame with a Mets cap on his plaque, along with Mike Piazza. He was also inducted into the New York Mets Hall of Fame, the Marine Corps Sports Hall of Fame, and the Cincinnati Reds Hall of Fame.


title: Tom Seaver

text: On September 28, 2006, Seaver was chosen as the "Hometown Hero" for the Mets franchise by ESPN. Seaver made a return to Shea Stadium during the "Shea Goodbye" closing ceremony on September 28, 2008, where he threw out the final pitch in the history of the stadium to Piazza. Along with Piazza he opened the Mets' new home, Citi Field with the ceremonial first pitch on April 13, 2009.


title: Tom Seaver

text: The 2013 Major League Baseball All-Star Game was dedicated to Seaver. He concluded the introduction of the starting lineup ceremonies by throwing out the ceremonial first pitch. Mets player David Wright participated. In 2019, the New York City renamed the street outside Citi Field from 126th Street to Seaver Way and changed the ballpark's address to 41 Seaver Way, a salute of the number he wore throughout his career.


title: Tom Seaver

text: Only Seaver and Walter Johnson have 300 wins, 3,000 strikeouts, and an earned run average under 3.00. Seaver's 16 Opening-Day starts are an MLB record. At the time of his retirement, he was third on MLB's all-time strikeout list (3,640), trailing only his former teammate Nolan Ryan and Steve Carlton; he currently ranks sixth all time. Seaver is tied with Ryan for the seventh-most shutouts in MLB history (61). His feat of striking out ten consecutive batters has only been matched once, by Aaron Nola in 2021. He also holds the record for consecutive 200-strikeout seasons with nine (1968–1976). In 1999, Seaver ranked 32nd on "Sporting News" list of the 100 Greatest Baseball Players, the only player to have spent a majority of his career with the Mets to make the list. In 2016, ESPN.com ranked Seaver 34th on its list of the greatest MLB players, while "The Athletic" ranked him the 41st-greatest player in 2020.


title: Tom Seaver

text: Seaver could also help himself at the plate. A decent hitter and proficient bunter, Seaver hit 12 home runs during his career, along with a relatively solid lifetime batting average, for a pitcher, of .154.


title: Tom Seaver

text: Seaver approached Hank Aaron before his first All-Star Game in 1967 and asked Aaron for his autograph. Seaver felt the need to introduce himself to Aaron, as he was certain "Hammerin' Hank" would not know who he was. Aaron replied to Seaver, "Kid, I know who you are, and before your career is over, I guarantee you everyone in this stadium will, too."


title: Tom Seaver

text: At the April 15, 2022 Mets' season home opener, a statue of Seaver was unveiled and permanently installed by the franchise at Citi Field.


title: Tom Seaver

text: Seaver's television broadcasting experience dated back to his playing career, when he was invited to serve as a World Series analyst for ABC in and for NBC in , , and . Also while an active player, Seaver called the 1981 National League Division Series between Montreal and Philadelphia and that year's National League Championship Series alongside Dick Enberg for NBC.


title: Tom Seaver

text: After retiring as a player, Seaver worked as a television color commentator for the Mets, the New York Yankees, and with Vin Scully in 1989 for NBC. Seaver replaced Joe Garagiola as NBC's lead baseball color commentator, which led to him calling the 1989 All-Star Game and National League Championship Series. He worked as an analyst for Yankees' telecasts on WPIX from 1989 to 1993 and for Mets' telecasts on WPIX from 1999 to 2005, making him one of three sportscasters to be regular announcers for both teams; the others are Fran Healy and Tim McCarver.


title: Tom Seaver

text: Seaver married Nancy Lynn McIntyre on June 9, 1966. They were the parents of two daughters, Sarah and Annie. They lived in Calistoga, California, where Seaver started his own 3.5-acre (1.4 ha) vineyard, Seaver Family Vineyards, on his 116-acre (47 ha) estate, in 2002. His first vintage was produced in 2005. He presented his two cabernets, "Nancy's Fancy" and "GTS," at an April 2010 wine-tasting event in SoHo, to positive reviews.


title: Tom Seaver

text: His media nickname referred to the cartoon character Tom Terrific. In 2019, NFL quarterback Tom Brady was denied the trademark "Tom Terrific", when the United States Patent and Trademark Office said it "may falsely suggest a connection with Tom Seaver".


title: Tom Seaver

text: In 2013, it was reported that Seaver suffered from memory loss, not even remembering long-term acquaintances and experiencing symptoms of "sleep disorder, nausea, and a general overall feeling of chemical imbalance". According to former teammate Bud Harrelson, Seaver was "otherwise doing well". On March 7, 2019, Seaver's family announced that he had dementia and was retiring from public life.


title: Tom Seaver

text: Seaver died in his sleep as a result of complications from Lewy body dementia and COVID-19 on August 31, 2020, during the COVID-19 pandemic in California. He was 75.


title: Silencer (firearms)

text: A silencer, also known as a sound suppressor, suppressor, or sound moderator, is a muzzle device that reduces the acoustic intensity of the muzzle report (sound of a gunshot) and muzzle rise when a gun (firearm or air gun) is discharged, by modulating the speed and pressure of the propellant gas from the muzzle and hence suppressing the muzzle blast. Like other muzzle devices, a silencer can be a detachable accessory mounted to the muzzle, or an integral part of the barrel.


title: Silencer (firearms)

text: A typical silencer is a metallic (usually stainless steel or titanium) cylinder containing internal sound baffles, with a hollow bore to allow the projectile (bullet) to exit normally. During firing, the bullet flies through the bore with little hindrance, but most of the expanding gas ejecta behind it is retained through a longer and convoluted escape path created by the baffles, prolonging the release time. This slows down the gas and dissipates its kinetic energy into a larger surface area, reducing the blast intensity, thus lowering the loudness.


title: Silencer (firearms)

text: Silencers can also reduce the recoil during shooting, but unlike a muzzle brake or a recoil compensator, which reduce recoil by vectoring the muzzle blast sideways, silencers release almost all the gases towards the front. However, the internal baffles significantly prolong the time of the gas release and therefore decrease the rearward thrust generated — as for the same impulse, force is inversely proportional to time. The weight of the silencer itself and the leverage of its mounting location (at the far front end of the barrel) will also help counter muzzle rise.


title: Silencer (firearms)

text: Because the internal baffles will slow and cool the released gas and contain gunpowder that is still burning upon exit from the muzzle, silencers also reduce or even eliminate the muzzle flash. This is different from a flash suppressor, which reduces the amount of flash by dispersing burning gases that are already released "outside" the muzzle, without necessarily reducing sound or recoil. A flash hider, or muzzle shroud, on the other hand, conceals visible flashes by screening them from the direct line of sight, rather than reducing the intensity of the flash.


title: Silencer (firearms)

text: In 1892 a Swiss inventor called Jakob Stahel patented a silencer intended for killing cattle though he claimed it could be adapted to other firearms too.


title: Silencer (firearms)

text: American inventor Hiram Percy Maxim, son of Maxim gun inventor Hiram Stevens Maxim, and co-founder of the American Radio Relay League, is usually credited with inventing and selling the first commercially successful silencer around 1902. He received his patent on March 30, 1909. Maxim gave his device the popularly trademarked name "Maxim Silencer," and it was regularly advertised in sporting goods magazines. The muffler for internal combustion engines was developed in parallel with the firearm silencer by Maxim in the early 20th century, using many of the same techniques to provide quieter-running engines, and in many English-speaking countries automobile mufflers are called silencers.


title: Silencer (firearms)

text: Former president of the United States Theodore Roosevelt was known to purchase and use Maxim Silencers.


title: Silencer (firearms)

text: Silencers were regularly used by agents of the United States Office of Strategic Services, who favored the newly designed High Standard HDM .22 LR pistol during World War II. OSS Director William Joseph "Wild Bill" Donovan demonstrated the pistol for President Franklin D. Roosevelt at the White House. According to OSS research chief Stanley Lovell, Donovan, an old and trusted friend of the President, was waved into the Oval Office, where Roosevelt was dictating a letter. When Roosevelt finished, Donovan turned his back and fired ten shots into a sandbag he had brought with him, announced what he had done and handed the smoking gun to the astonished president. The British Special Operations Executive (SOE) Welrod pistol with an integral silencer was also used by the American OSS on clandestine operations in Nazi-occupied Europe.


title: Silencer (firearms)

text: In 2020, the United States Marine Corps began to field suppressors in its combat units, citing improved communication on a squad and platoon level because of the reduced sound. The USMC purchased 7,000 suppressors in 2020, and plan to have a total of 30,000 by the end of 2023, making them the first armed service to issue suppressors for general usage.


title: Silencer (firearms)

text: "Silencer" is the earlier, more traditional term for such noise reduction devices. Recently, however, "suppressor" has gained currency in connection to American gun rights organizations.


title: Silencer (firearms)

text: The US National Firearms Act (NFA) of 1934 defined silencers and established regulations limiting their sale and ownership. Both the US Department of Justice and the Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF) use the term "silencer". Hiram Percy Maxim, the original inventor of the device, marketed them as "Maxim Silencers".


title: Silencer (firearms)

text: The earliest use of the technical term "suppressor" to refer to firearm noise reduction is in US Patent 4530417, July 23, 1985, "A suppressor for reducing the muzzle blast of firearms or the like". In UK English, "silencer" is the common term for either a motor vehicle muffler or for a gun silencer. "Sound moderator" has been used in UK English for silencers on high-powered rifles used for hunting or at ranges.


title: Silencer (firearms)

text: The Oxford, American Heritage, and other dictionaries apply the term "suppressor" to such contexts as electromagnetic shielding devices, genetics, and censorship, but not firearms. These dictionaries define both "silencer" and "suppressor" as essentially equivalent and interchangeable, neither applying exclusively or primarily to sound, and both being applicable as much to complete and total quiet or to partial reduction of sound.


title: Silencer (firearms)

text: In 2011, the National Rifle Association of America began a campaign to increase the civilian use of silencers for hunting and sport shooting in the US, setting the goals of easing the restrictions in the Federal NFA of 1934, and in various state laws, regulating the sale and ownership of firearm silencers. In the same year, the American Silencer Association (ASA) was founded by US manufacturers of silencers, with the same goals of moving silencers into the mainstream. Along with state and federal legislative lobbying efforts, the NRA and ASA began public information campaigns designed to change the perception of silencers from their association with espionage, assassination, crime or military special operation use, to instead show that silencers can have health and safety benefits, primarily protecting the hearing of shooters and people in the vicinity, and to debunk the perceived myth in popular television, film and video game media that silencers are so effective that gunshot sounds can go totally unnoticed, such as by people in the next room of a building.


title: Silencer (firearms)

text: In 2014, the ASA changed its name to American Suppressor Association "in a continuing effort to dispel myths about suppressors". Gun control advocates have said that changing the name from "silencer" to "suppressor" is semantic propaganda similar to the efforts to avoid terms like "assault rifle" or "assault weapon" in favor of friendlier-sounding language like "modern sporting rifle", while gun-rights advocates make essentially the opposite argument, and also that the widespread term "silencer" reflects technical ignorance and is poorly defined.


title: Silencer (firearms)

text: Gun rights advocates and gun media generally say that the word "silencer" is defined as meaning "total" silence, while "suppressor" is defined as only meaning reduced sound intensity.


title: Silencer (firearms)

text: While using subsonic ammunitions can negate the sonic boom, mechanical noise can be reduced but is nearly impossible to eliminate. For these reasons, it is difficult to completely silence any firearm, or achieve an acceptable level of noise suppression in revolvers. Revolvers have a looser gas seal between the barrel and the cylinder that emits noise from escaping gases. Some revolver designs attempt to overcome this, such as the Russian Nagant M1895 and OTs-38, and the US S&W QSPR.


title: Silencer (firearms)

text: Muzzle blast generated by firearm discharge is directly proportional to the amount of propellant to be combusted within the cartridge. Therefore, the greater the case capacity (e.g. a magnum cartridge), the louder the muzzle blast, and consequently a more efficient or larger silencer system is required. A gunshot (the combination of the sonic boom, the vacuum release, and hot gases) will almost always be louder than the sound of the action cycling of an autoloading firearm. Alan C. Paulson, a renowned firearms specialist, claimed to have encountered an integrally suppressed .22 LR gun that had such a quiet report , although this is somewhat uncommon. Properly evaluating the sound generated by a firearm can only be done using a decibel meter in conjunction with a frequency spectrum analyzer during live tests.


title: Silencer (firearms)

text: A silencer is typically a hollow metal tube made from steel, aluminum, or titanium and contains expansion chambers. It is usually cylindrical in shape, and attaches to the muzzle of a pistol, submachine gun, or rifle. Some can-type silencers, named for their resemblance to beverage cans, are detachable, and can be attached to a different firearm. In contrast, integral silencers consist of an expansion chamber or chambers surrounding the barrel. The barrel has openings or ports that bleed off-gases into the chambers. This type of silencer is part of the firearm, and maintenance of the suppressor requires that the firearm be at least partially disassembled.


title: Silencer (firearms)

text: Both types of silencers reduce noise by allowing the rapidly expanding gases from the firing of the cartridge to be decelerated and cooled through a series of hollow chambers. The trapped gas exits the suppressor over a longer period of time and at a greatly reduced speed, producing less noise signature. The chambers are divided by either "baffles" or "wipes". There are typically at least four and up to perhaps fifteen chambers in a suppressor, depending on the intended use and design details. Often, a single, larger expansion chamber is located at the muzzle end of a can-type silencer, which allows the propellant gas to expand considerably and slow down before it encounters the baffles or wipes. This larger chamber may be "reflexed" toward the rear of the barrel to minimize the overall length of the combined firearm and silencer, especially with longer weapons such as rifles.


title: Silencer (firearms)

text: Silencers vary greatly in size and efficiency. One disposable type developed in the 1980s by the U.S. Navy for 9×19mm pistols was long and in outside diameter, and was designed for six shots with standard ammunition or up to thirty shots with subsonic (slower than the speed of sound) ammunition. In contrast, one suppressor designed for rifles firing the powerful .50 caliber (BMG) cartridge is long and in diameter.


title: Silencer (firearms)

text: Two ancillary advantages of the silencer are recoil reduction and flash suppression. Muzzle flash is reduced both by being contained in the suppressor and by the arresting of unburned powder that would ordinarily burn in the air and intensify the flash. Recoil reduction results from the slowing of propellant gases that contribute 30–50% of recoil velocity. However, some suppressors can increase the backpressure produced by the propellant gases. This can cause them to function somewhat like a muzzle booster and thus increase the felt recoil. The weight of the silencer and the location of that additional weight at the muzzle reduces recoil through the basic mass as well as muzzle flip because of the location of this mass.


title: Silencer (firearms)

text: Baffles are usually circular metal dividers that separate the expansion chambers. Each baffle has a hole in its center to permit the passage of the bullet through the silencer and toward the target. The hole is typically at least 1 mm larger than the bullet caliber to minimize the risk of the bullet hitting the baffle, called a baffle strike. Baffles are typically made of stainless steel, aluminum, titanium, or alloys such as Inconel, and are either machined out of solid metal or stamped out of sheet metal. A few silencers for low-powered cartridges such as the .22 Long Rifle have successfully used plastic baffles (certain models by Vaime and others).


title: Silencer (firearms)

text: There are several unique baffle designs. M, K, Z, monolithic core and Ω (Omega) are the most prevalent. M-type, an inverted cone, is the crudest. K forms slanted obstructions diverging from the sidewalls, creating turbulence across the boreline. Z is expensive to machine and includes pockets of dead airspace along the sidewalls which trap expanded gases and hold them thereby lengthening the time that the gases cool before exiting. Omega-type baffles form a series of spaced cones drawing gas away from the borderline and incorporate a scalloped mouth creating cross-bore turbulence, which is in turn directed to a "mouse-hole" opening between the baffle stack and sidewall.


title: Silencer (firearms)

text: Propellant gas heats and erodes the baffles, causing wear, which is worsened by high rates of fire. Aluminum baffles are seldom used with fully automatic weapons because service life is unacceptably short. Some modern suppressors using steel or high-temperature alloy baffles can endure extended periods of fully automatic fire without damage. The highest-quality rifle suppressors available today have a claimed service life of greater than 30,000 rounds. Baffles have not been given any specific angles, a specific size, or weight to meet any standards; they are created on a trial and error basis.


title: Silencer (firearms)

text: Spacers separate baffles and keep them aligned at a specified distance from one another inside the silencer. Many baffles and spacers are manufactured as a single assembly and several suppressor designs have all the baffles attached together with spacers as a one-piece helical baffle stack. Modern baffles are usually carefully shaped to divert the propellant gases effectively into the chambers. This shaping can be a slanted flat surface, canted at an angle to the bore, or a conical or otherwise curved surface. One popular technique is to have alternating angled surfaces through the stack of baffles.


title: Silencer (firearms)

text: Wipes are inner dividers intended to touch the bullet as it passes through the silencer, and are typically made of rubber, plastic, or foam. Each wipe may either have a hole drilled in it before use, a pattern stamped into its surface at the point where the bullet will strike it, or it may simply be punched through by the bullet. Wipes typically last for a small number of firings (perhaps no more than five) before their performance is significantly degraded. While many suppressors used wipes in the Vietnam War era, most modern suppressors do not use them as anything that touches the projectile has significant accuracy implications. All wipes deteriorate quickly and require disassembly and spare parts replacement.


title: Silencer (firearms)

text: Wet silencers or wet cans use a small quantity of water, oil, grease, or gel in the expansion chambers to cool the propellant gases and reduce their volume (see Ideal gas law). The coolant lasts only a few shots before it must be replenished, but can greatly increase the effectiveness of the suppressor. Water is most effective, because of its high heat of vaporization, but it can run or evaporate out of the silencer. Grease, while messier and less effective than water, can be left in the suppressor indefinitely without losing effectiveness. Oil is the least effective and least preferable, as it runs while being as messy as grease, and leaves behind a fine mist of aerosolized oil after each shot. Water-based gels, such as wire-pulling lubricant gel, are a good compromise; they offer the efficacy of water with less mess, as they do not run or drip. However, they take longer to apply, as they must be cleared from the bore of the suppressor to ensure a clear path for the bullet (grease requires this step as well). Generally, only pistol silencers are shot wet, as rifle silencers handle such high pressure and heat that the liquid is gone within 1–3 shots. Many manufacturers will not warranty their rifle suppressors for wet fire, as some feel this may even result in a dangerous over-pressurization of the silencer.


title: Silencer (firearms)

text: Packing materials such as metal mesh, steel wool, or metal washers may be used to fill the chambers and further dissipate and cool the gases. These are somewhat more effective than empty chambers but less effective than wet designs. Metal mesh, if properly used, may last for hundreds or thousands of shots of spaced semi-automatic fire; however, steel wool usually degrades within ten shots, with stainless steel wool lasting longer than regular steel wool. Like wipes, packing materials are rarely found in modern silencers.


title: Silencer (firearms)

text: Wipes, packing materials, and purpose-designed wet cans have been generally abandoned in 21st-century suppressor design because they decrease overall accuracy and require excessive cleaning and maintenance. The instructions from several manufacturers state that their suppressors need not be cleaned at all. Furthermore, legal changes in the United States during the 1980s and 1990s made it much more difficult for end-users to legally replace internal silencer parts, and the newer designs reflect this reality.


title: Silencer (firearms)

text: Apart from integral silencers that are integrated as a part of the firearm's barrel, most suppressors have a female threaded end, which attaches to male threads cut into the exterior of the barrel. These types of silencers are mostly used on handguns and rifles chambered in .22LR. More powerful rifles may use this type of attachment, but harsh recoil may cause the suppressor to over-tighten to the barrel and the suppressor can become difficult to remove. SilencerCo's Salvo silencer for shotguns attaches via internal barrel threading normally used to mount removable chokes.


title: Silencer (firearms)

text: Military rifles such as the M16 or M14 often use quick-detach suppressors that use coarser than normal threads and are installed over an existing muzzle device such as a flash suppressor and can include a secondary locking mechanism to allow the shooter to quickly and safely add or remove a sound suppressor based on individual needs.


title: Silencer (firearms)

text: In addition to containing and slowly releasing the gas pressure associated with muzzle blast or reducing pressure through the use of coolant mediums, advanced silencer designs attempt to modify the properties of the sound waves generated by the muzzle blast. In these designs, effects known as frequency shifting and phase cancellation (or destructive interference) are used in an attempt to make the suppressor quieter. These effects are achieved by separating the flow of gases and causing them to collide with one another or by venting them through precision-made holes. The intended effect of frequency shifting is to shift audible sound waves frequencies into ultrasound (above 20 kHz), beyond the range of human hearing. The Russian AN-94 assault rifle has a muzzle attachment that claims apparent noise reduction by venting some gases through a "dog-whistle" type channel. Phase cancellation occurs when similar sound waves encounter one another 180° out of phase, cancelling the amplitude of the wave and eliminating the pressure variations perceived as sound.


title: Silencer (firearms)

text: An alternate method under development is called an "anti-phase destructive interference generator." The process duplicates the sound waves generated by the muzzle blast and then uses them to create an anti-phase auditory signal. Currently, this is a muzzle attached device and is only being tested to cancel out the gunshot sound of the firearm. The devices tested incorporate multiple microphones, speakers, and an auditory processor. The first shot fired is recorded, and then played back precisely out of sync(180 degrees out of phase) with each subsequent shot. This has proven successful with small caliber(.17-.22) rifles, but the amplitude has not been matched efficiently with larger cartridges. With the use of subsonic ammunition, the resultant sound waves effectively cancel out one another, and with the exception of the sound of the action cycling, completely eliminate any gunshot sound. In the current development stage, this has worked only in close proximity to the shooter, and the pressure wave (p-wave) can still be felt. Each time a different type of ammunition or firearm is used, the device needs recalibration.


title: Silencer (firearms)

text: Taking advantage of either property requires that the silencer be designed within the specification of the muzzle blast in mind. For example, the velocity of the sound waves is a major factor. This figure can change significantly between different cartridges and barrel lengths.


title: Silencer (firearms)

text: However, these concepts are controversial because a muzzle blast creates broadband noise rather than pure tones, and phase cancellation in particular is therefore extremely difficult (if not impossible) to achieve. Some suppressor manufacturers claim to use phase cancellation in their designs.


title: Silencer (firearms)

text: From a physics standpoint, supersonic cartridge loads are impractical to suppress past the levels that are merely hearing-safe for the shooter due to the sonic boom emitted by the bullet, and cartridges such as .22 LR and .45 ACP have long been recognized as the easiest to suppress even if using technology dating back to the 1940s.


title: Silencer (firearms)

text: Another silencer technology uses a captive piston cartridge; examples are the Smith & Wesson Quiet Special Purpose Revolver (QSPR) and the Soviet and Russian PSS silent pistol, OTs-38 Stechkin silent revolver and the MTs-116M suppressed sniper rifle, a 12.7 mm silenced development of the 7.62mm MTs-116M. The large calibre allows the bullet to be fired at subsonic speed, eliminating a major source of noise, while retaining accuracy, range, and effectiveness. All of these weapons use special, very expensive, captive-piston ammunition; QSPR ammunition resembled metal-cased .410-bore shotgun shells. The cartridge case internally works as a piston to trap the gases; the piston pushes the bullet, but the gases are retained in the cartridge case instead of being expelled noisily; in tests of the PSS the sound pressure level was 124.6 dB, similar to a suppressed .22 rimfire pistol. The ammunition itself, rather than the weapon, is silent; in the US each individual round is considered to be a silencer, subject to regulations on silencers.


title: Silencer (firearms)

text: Improvised silencers have been made from a variety of materials. In 2015, Los Angeles County sheriff deputies recovered a Sa vz. 26 submachine gun with an automobile oil filter attached. PVC pipes, plastic water bottles, and foam-filled pillows are also used. In the United States, improvised silencers are governed by the same laws as manufactured ones.


title: Silencer (firearms)

text: Functionally, a suppressor is meant to diminish the report of a discharged round, or make its sound unrecognizable. Other sounds emanating from the weapon remain unchanged. Even subsonic bullets make distinct sounds by their passage through the air and striking targets, and supersonic bullets produce a small sonic boom, resulting in a ballistic crack. Semi-automatic and fully automatic firearms also make distinct noises as their actions cycle, ejecting the fired cartridge case and loading a new round.


title: Silencer (firearms)

text: Aside from reductions in volume, suppressors tend to alter the sound to something that is not identifiable as a gunshot. This reduces or eliminates attention drawn to the shooter. A Finnish expression dating from the Winter War says that "A silencer does not make a soldier silent, but it does make him invisible." Silencers are particularly useful in enclosed spaces where the sound, flash and pressure effects of a weapon being fired are amplified. Such effects may disorient the shooter, affecting situational awareness, concentration and accuracy, and can permanently damage hearing very quickly.


title: Silencer (firearms)

text: As the suppressed sound of firing is overshadowed by ballistic crack, observers can be deceived as to the location of the shooter, often from 90 to 180 degrees from his actual location. However, counter-sniper tactics can include gunfire locators, such as the U.S. Boomerang system, where sensitive microphones are coupled to computers running algorithms, and use the ballistic crack to detect and localize the origin of the shot.


title: Silencer (firearms)

text: Hunters using centerfire rifles find silencers bring various important benefits that outweigh the extra weight and resulting change in the firearm's center of gravity. The most important advantage of a suppressor is the hearing protection for the shooter as well as their companions. Many hunters have suffered permanent hearing damage due to someone else firing a high-caliber gun too closely without warning. By reducing noise, recoil and muzzle-blast, it also enables the firer to follow through calmly on their first shot and fire a further carefully aimed shot without delay if necessary. Wildlife of all kinds are often confused as to the direction of the source of a well-suppressed shot. In the field, however, the comparatively large size of a centerfire rifle suppressor can cause unwanted noise if it bumps or rubs against vegetation or rocks, so many users cover them with neoprene sleeves.


title: Silencer (firearms)

text: Silencers reduce firing recoil significantly, primarily by diverting and trapping the propellant gas. The gas generally has much less mass than the projectile, but it exits the muzzle at multiples of the projectile velocity, so reducing the speed and quantity of the gas expelled can significantly reduce the total momentum of the matter (gas and projectile) leaving the barrel, the negation of which, because momentum is conserved, is transferred to the gun as recoil. Paulson "et al.", discussing low-velocity pistol calibers, suggest the recoil reduction is around 15%. With high-velocity calibers, recoil reduction runs in the range of 20–30%. The added mass of the suppressor—normally 300 to 500  grams—also helps to manage the recoil.


title: Silencer (firearms)

text: A suppressor also cools the hot gases coming out of the barrel enough that most of the lead-laced vapor that leaves the barrel condenses inside the silencer, reducing the amount of lead that might be inhaled by the shooter and others around them. However, in auto-loading actions, this might be offset by increased back pressure, which results in propellant gas blowing back into a shooter's face through the chamber during case ejection.


title: Silencer (firearms)

text: In weapons firing supersonic ammunition, the bullet itself produces a loud and very sharp sound as it leaves the muzzle in excess of the speed of sound and gradually reducing speed as it travels downrange. This is a small sonic boom, and is referred to in the firearm field as ballistic crack or sonic signature. Subsonic ammunition eliminates this sound, but at the cost of lower velocity, resulting in decreased range and much decreased muzzle energy, thus lessening effectiveness on the target; this can be compensated for by increasing bullet weight. For example, if the muzzle velocity is reduced from (common for the .308 Winchester, for example) to a subsonic , the muzzle energy is reduced by a factor of 8. Military marksmen and police units may use subsonic ammunition in suppressed rifles when minimal noise is more important than range and energy.


title: Silencer (firearms)

text: However, the numeric effectiveness of subsonic rounds is, again, misrepresented by media. Independent testing of commercially available firearm suppressors with commercially available subsonic rounds has found that .308 subsonic rounds decreased the volume at the muzzle by 10 to 12 dB when compared to the same caliber of suppressed supersonic ammunition. When combined with silencers, the subsonic .308 rounds metered between 121 and 137 dB.


title: Silencer (firearms)

text: The ballistic crack depends on the speed of sound, which in turn depends mainly on air temperature. At sea level, an ambient temperature of , and under normal atmospheric conditions, the speed of sound is approximately . Bullets that travel near the speed of sound are considered transonic, which means that the airflow over the surface of the bullet, which at points travels faster than the bullet itself, can break the speed of sound. Pointed bullets, which gradually displace air, can get closer to the speed of sound than round- or snub-nosed bullets before becoming transonic.


title: Silencer (firearms)

text: Special cartridges have been developed for use with a silencer. These cartridges use very heavy bullets to make up for the energy lost by keeping the bullet subsonic. A good example of this is the .300 Whisper cartridge, which is formed from a necked-up .221 Remington Fireball cartridge case. The subsonic .300 Whisper fires up to a , .30 caliber bullet at about , generating about of energy at the muzzle. While this is similar to the energy available from the .45 ACP pistol cartridge, the reduced diameter, and streamlined shape of the heavy .30 caliber bullet provides far better external ballistic performance, improving range substantially.


title: Silencer (firearms)

text: 9×19 mm Parabellum, a very popular caliber for suppressed shooting, can use almost any factory-loaded weight round to achieve subsonic performance. These 147 gr weight bullets typically have a velocity of , which is less than the speed of sound.


title: Silencer (firearms)

text: The Soviet/Russian armor-piercing 9×39mm ammunition used in rifles such as the AS Val has a high subsonic ballistic coefficient, high retained downrange energy, high sectional density, and moderate recoil.


title: Silencer (firearms)

text: Without using subsonic ammunition, the muzzle velocity of a supersonic bullet can be lowered by other means, before it leaves the barrel. Some silencer designs, called integrals, do this by allowing gas to bleed off along the length of the barrel before the projectile exits. The MP5SD is an example of this, with holes right after the chamber of the barrel used to reduce a regular 115 or 124 gr ammunition to subsonic velocities.


title: Silencer (firearms)

text: Live tests by independent reviewers of numerous commercially available suppressors find that even low-power, unsuppressed .22 LR handguns produce gunshots over 160 decibels. A recent study of various suppressors reported peak sound pressure level reductions between 17 dB and 24 dB. Another study evaluated two calibers of rifle and nine suppressors, .223 caliber AR-15 (five suppressors) and .300 caliber AAC Blackout (four suppressors), and reported noise reduction of the peak sound level pressure between 7 dB and 32 dB. The De Lisle carbine, a British World War II suppressed rifle used in small numbers by Special Forces, was recorded at 85.5 dB in official firing tests.


title: Silencer (firearms)

text: Comparatively, ear protection commonly used while shooting provides 18 to 32 dB of sound reduction at the ear. For additional comparison, chainsaws, rock concerts, rocket engines, pneumatic drills, small firecrackers, and ambulance sirens are rated between 100 and 140 dB.


title: Silencer (firearms)

text: While some consider the noise reduction of a suppressor significant enough to permit safe shooting without hearing protection ("hearing safe"), noise-induced hearing loss may occur at 85 time-weighted-average decibels or above if exposed for a prolonged period, and suppressed gunshots regularly meter above 130 dB. However, the U.S. Occupational Safety and Health Administration uses 140 dB as the safety cutoff for impulsive noise, which has led most U.S. manufacturers to advertise sub-140 dB silencers as hearing safe. Current OSHA standards would allow no more than sub-single-second exposure to impact noise over 130 dB per 24 hours. That would equate to a single .308 round fired through a very efficient suppressor. This result effectively requires all users of silencers to wear additional ear protection.


title: Silencer (firearms)

text: The United States Department of Veterans Affairs has stated that the most prominent disability in former servicemen is reduced and damaged hearing, and that the United States Marine Corps' decision to purchase and use suppressors would solve this problem.


title: Silencer (firearms)

text: Decibel testing measures only the peak sound pressure level, i.e. the overall quantity of noise at the loudest moment, and does not account for duration or frequency. Limitations of dB testing become apparent in a comparison of sound between a .308 caliber rifle and a .300 Winchester Magnum rifle. The dB meter will show that both rifles produce the same decibel level of noise. When hearing these two rifles, however, it is clear that to human perception the .300 Winchester Magnum is much louder. What a dB meter does not show is that, although both rifles produce the same peak sound pressure level (SPL), the .300 Winchester Magnum remains at that peak level for a longer time, while the .308 peaks and falls off more quickly. Decibel meters are not adequate in this and other regards to be used as the principal means of determining silencer capability. Described mathematically, dB meters take a short-time average, called the root mean square (RMS) intensity, of a sonic signal or impulse over a specified period of time (sampling rate), and do not take into account the rate of increase of the sound wave packet (first derivative of packet envelope), which would in practice provide a better sense of the human perception of sound for this purpose.


title: Silencer (firearms)

text: The legal regulation of silencers varies widely around the world. In some nations, such as Finland, France, and New Zealand some or all types of suppressors are essentially unregulated and are sold through retail stores or by mail-order. In other countries, their possession or use is more restricted.


title: Conic section

text: In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties.


title: Conic section

text: The conic sections in the Euclidean plane have various distinguishing properties, many of which can be used as alternative definitions. One such property defines a non-circular conic to be the set of those points whose distances to some particular point, called a "focus", and some particular line, called a "directrix", are in a fixed ratio, called the "eccentricity". The type of conic is determined by the value of the eccentricity. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2; that is, as the set of points whose coordinates satisfy a quadratic equation in two variables which can be written in the form formula_1 The geometric properties of the conic can be deduced from its equation.


title: Conic section

text: In the Euclidean plane, the three types of conic sections appear quite different, but share many properties. By extending the Euclidean plane to include a line at infinity, obtaining a projective plane, the apparent difference vanishes: the branches of a hyperbola meet in two points at infinity, making it a single closed curve; and the two ends of a parabola meet to make it a closed curve tangent to the line at infinity. Further extension, by expanding the real coordinates to admit complex coordinates, provides the means to see this unification algebraically.


title: Conic section

text: The conic sections have been studied for thousands of years and have provided a rich source of interesting and beautiful results in Euclidean geometry.


title: Conic section

text: A conic is the curve obtained as the intersection of a plane, called the "cutting plane", with the surface of a double cone (a cone with two "nappes"). It is usually assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice. Planes that pass through the vertex of the cone will intersect the cone in a point, a line or a pair of intersecting lines. These are called "degenerate" conics and some authors do not consider them to be conics at all. Unless otherwise stated, "conic" in this article will refer to a non-degenerate conic.


title: Conic section

text: There are three types of conics: the ellipse, parabola, and hyperbola. The circle is a special kind of ellipse, although historically Apollonius considered it a fourth type. Ellipses arise when the intersection of the cone and plane is a closed curve. The circle is obtained when the cutting plane is parallel to the plane of the generating circle of the cone; for a right cone, this means the cutting plane is perpendicular to the axis. If the cutting plane is parallel to exactly one generating line of the cone, then the conic is unbounded and is called a "parabola". In the remaining case, the figure is a "hyperbola": the plane intersects "both" halves of the cone, producing two separate unbounded curves.


title: Conic section

text: Compare also spheric section (intersection of a plane with a sphere, producing a circle or point), and spherical conic (intersection of an elliptic cone with a concentric sphere).


title: Conic section

text: Alternatively, one can define a conic section purely in terms of plane geometry: it is the locus of all points whose distance to a fixed point (called the "focus") is a constant multiple (called the "eccentricity" ) of the distance from to a fixed line (called the "directrix").


title: Conic section

text: A circle is a limiting case and is not defined by a focus and directrix in the Euclidean plane. The eccentricity of a circle is defined to be zero and its focus is the center of the circle, but its directrix can only be taken as the line at infinity in the projective plane.


title: Conic section

text: The eccentricity of an ellipse can be seen as a measure of how far the ellipse deviates from being circular.


title: Conic section

text: If the angle between the surface of the cone and its axis is formula_2 and the angle between the cutting plane and the axis is formula_3 the eccentricity is formula_4


title: Conic section

text: A proof that the above curves defined by the focus-directrix property are the same as those obtained by planes intersecting a cone is facilitated by the use of Dandelin spheres.


title: Conic section

text: Alternatively, an ellipse can be defined in terms of two focus points, as the locus of points for which the sum of the distances to the two foci is ; while a hyperbola is the locus for which the difference of distances is . (Here is the semi-major axis defined below.) A parabola may also be defined in terms of its focus and latus rectum line (parallel to the directrix and passing through the focus): it is the locus of points whose distance to the focus plus or minus the distance to the line is equal to ; plus if the point is between the directrix and the latus rectum, minus otherwise.


title: Conic section

text: In addition to the eccentricity (), foci, and directrix, various geometric features and lengths are associated with a conic section.


title: Conic section

text: The "principal axis" is the line joining the foci of an ellipse or hyperbola, and its midpoint is the curve's "center". A parabola has no center.


title: Conic section

text: The "latus rectum" is the chord parallel to the directrix and passing through a focus; its half-length is the "semi-latus rectum" ().


title: Conic section

text: The "major axis" is the chord between the two vertices: the longest chord of an ellipse, the shortest chord between the branches of a hyperbola. Its half-length is the "semi-major axis" (). When an ellipse or hyperbola are in standard position as in the equations below, with foci on the -axis and center at the origin, the vertices of the conic have coordinates and , with non-negative.


title: Conic section

text: The "minor axis" is the shortest diameter of an ellipse, and its half-length is the "semi-minor axis" (), the same value as in the standard equation below. By analogy, for a hyperbola the parameter in the standard equation is also called the semi-minor axis.


title: Conic section

text: After introducing Cartesian coordinates, the focus-directrix property can be used to produce the equations satisfied by the points of the conic section. By means of a change of coordinates (rotation and translation of axes) these equations can be put into "standard forms". For ellipses and hyperbolas a standard form has the -axis as principal axis and the origin (0,0) as center. The vertices are and the foci . Define by the equations for an ellipse and for a hyperbola. For a circle, so , with "radius" . For the parabola, the standard form has the focus on the -axis at the point and the directrix the line with equation . In standard form the parabola will always pass through the origin.


title: Conic section

text: For a "rectangular" or "equilateral" hyperbola, one whose asymptotes are perpendicular, there is an alternative standard form in which the asymptotes are the coordinate axes and the line is the principal axis. The foci then have coordinates and .


title: Conic section

text: The first four of these forms are symmetric about both the -axis and -axis (for the circle, ellipse and hyperbola), or about the -axis only (for the parabola). The rectangular hyperbola, however, is instead symmetric about the lines and .


title: Conic section

text: In the Cartesian coordinate system, the graph of a quadratic equation in two variables is always a conic section (though it may be degenerate), and all conic sections arise in this way. The most general equation is of the form


title: Conic section

text: This form is a specialization of the homogeneous form used in the more general setting of projective geometry (see below).


title: Conic section

text: The conic sections described by this equation can be classified in terms of the value formula_22, called the discriminant of the equation.


title: Conic section

text: In the notation used here, and are polynomial coefficients, in contrast to some sources that denote the semimajor and semiminor axes as and .


title: Conic section

text: The discriminant of the conic section's quadratic equation (or equivalently the determinant of the 2 × 2 matrix) and the quantity (the trace of the 2 × 2 matrix) are invariant under arbitrary rotations and translations of the coordinate axes, as is the determinant of the 3 × 3 matrix above. The constant term and the sum are invariant under rotation only.


title: Conic section

text: the eccentricity can be written as a function of the coefficients of the quadratic equation. If the conic is a parabola and its eccentricity equals 1 (provided it is non-degenerate). Otherwise, assuming the equation represents either a non-degenerate hyperbola or ellipse, the eccentricity is given by


title: Conic section

text: where again formula_27 This has precisely one positive solution—the eccentricity— in the case of a parabola or ellipse, while in the case of a hyperbola it has two positive solutions, one of which is the eccentricity.


title: Conic section

text: where formula_32 and formula_33 are the eigenvalues of the matrix formula_34 — that is, the solutions of the equation


title: Conic section

text: — and formula_36 is the determinant of the 3 × 3 matrix above, and formula_37 is again the determinant of the 2 × 2 matrix. In the case of an ellipse the squares of the two semi-axes are given by the denominators in the canonical form.


title: Conic section

text: In polar coordinates, a conic section with one focus at the origin and, if any, the other at a negative value (for an ellipse) or a positive value (for a hyperbola) on the -axis, is given by the equation


title: Conic section

text: As above, for , the graph is a circle, for the graph is an ellipse, for a parabola, and for a hyperbola.


title: Conic section

text: The polar form of the equation of a conic is often used in dynamics; for instance, determining the orbits of objects revolving about the Sun.


title: Conic section

text: Just as two (distinct) points determine a line, five points determine a conic. Formally, given any five points in the plane in general linear position, meaning no three collinear, there is a unique conic passing through them, which will be non-degenerate; this is true in both the Euclidean plane and its extension, the real projective plane. Indeed, given any five points there is a conic passing through them, but if three of the points are collinear the conic will be degenerate (reducible, because it contains a line), and may not be unique; see further discussion.


title: Conic section

text: Four points in the plane in general linear position determine a unique conic passing through the first three points and having the fourth point as its center. Thus knowing the center is equivalent to knowing two points on the conic for the purpose of determining the curve.


title: Conic section

text: Furthermore, a conic is determined by any combination of "k" points in general position that it passes through and 5 – "k" lines that are tangent to it, for 0≤"k"≤5.


title: Conic section

text: Any point in the plane is on either zero, one or two tangent lines of a conic. A point on just one tangent line is on the conic. A point on no tangent line is said to be an "interior point" (or inner point) of the conic, while a point on two tangent lines is an "exterior point" (or outer point).


title: Conic section

text: All the conic sections share a "reflection property" that can be stated as: All mirrors in the shape of a non-degenerate conic section reflect light coming from or going toward one focus toward or away from the other focus. In the case of the parabola, the second focus needs to be thought of as infinitely far away, so that the light rays going toward or coming from the second focus are parallel.


title: Conic section

text: Pascal's theorem concerns the collinearity of three points that are constructed from a set of six points on any non-degenerate conic. The theorem also holds for degenerate conics consisting of two lines, but in that case it is known as Pappus's theorem.


title: Conic section

text: Non-degenerate conic sections are always "smooth". This is important for many applications, such as aerodynamics, where a smooth surface is required to ensure laminar flow and to prevent turbulence.


title: Conic section

text: It is believed that the first definition of a conic section was given by Menaechmus (died 320 BC) as part of his solution of the Delian problem (Duplicating the cube). His work did not survive, not even the names he used for these curves, and is only known through secondary accounts. The definition used at that time differs from the one commonly used today. Cones were constructed by rotating a right triangle about one of its legs so the hypotenuse generates the surface of the cone (such a line is called a generatrix). Three types of cones were determined by their vertex angles (measured by twice the angle formed by the hypotenuse and the leg being rotated about in the right triangle). The conic section was then determined by intersecting one of these cones with a plane drawn perpendicular to a generatrix. The type of the conic is determined by the type of cone, that is, by the angle formed at the vertex of the cone: If the angle is acute then the conic is an ellipse; if the angle is right then the conic is a parabola; and if the angle is obtuse then the conic is a hyperbola (but only one branch of the curve).


title: Conic section

text: Euclid (fl. 300 BC) is said to have written four books on conics but these were lost as well. Archimedes (died BC) is known to have studied conics, having determined the area bounded by a parabola and a chord in "Quadrature of the Parabola". His main interest was in terms of measuring areas and volumes of figures related to the conics and part of this work survives in his book on the solids of revolution of conics, "On Conoids and Spheroids".


title: Conic section

text: The greatest progress in the study of conics by the ancient Greeks is due to Apollonius of Perga (died BC), whose eight-volume "Conic Sections" or "Conics" summarized and greatly extended existing knowledge. Apollonius's study of the properties of these curves made it possible to show that any plane cutting a fixed double cone (two napped), regardless of its angle, will produce a conic according to the earlier definition, leading to the definition commonly used today. Circles, not constructible by the earlier method, are also obtainable in this way. This may account for why Apollonius considered circles a fourth type of conic section, a distinction that is no longer made. Apollonius used the names 'ellipse', 'parabola' and 'hyperbola' for these curves, borrowing the terminology from earlier Pythagorean work on areas.


title: Conic section

text: Pappus of Alexandria (died AD) is credited with expounding on the importance of the concept of a conic's focus, and detailing the related concept of a directrix, including the case of the parabola (which is lacking in Apollonius's known works).


title: Conic section

text: An instrument for drawing conic sections was first described in 1000 AD by the Islamic mathematician Al-Kuhi.


title: Conic section

text: Apollonius's work was translated into Arabic, and much of his work only survives through the Arabic version. Persians found applications of the theory, most notably the Persian mathematician and poet Omar Khayyám, who found a geometrical method of solving cubic equations using conic sections.


title: Conic section

text: Johannes Kepler extended the theory of conics through the "principle of continuity", a precursor to the concept of limits. Kepler first used the term 'foci' in 1604.


title: Conic section

text: Girard Desargues and Blaise Pascal developed a theory of conics using an early form of projective geometry and this helped to provide impetus for the study of this new field. In particular, Pascal discovered a theorem known as the hexagrammum mysticum from which many other properties of conics can be deduced.


title: Conic section

text: René Descartes and Pierre Fermat both applied their newly discovered analytic geometry to the study of conics. This had the effect of reducing the geometrical problems of conics to problems in algebra. However, it was John Wallis in his 1655 treatise who first defined the conic sections as instances of equations of second degree. Written earlier, but published later, Jan de Witt's starts with Kepler's kinematic construction of the conics and then develops the algebraic equations. This work, which uses Fermat's methodology and Descartes' notation has been described as the first textbook on the subject. De Witt invented the term 'directrix'.


title: Conic section

text: Conic sections are important in astronomy: the orbits of two massive objects that interact according to Newton's law of universal gravitation are conic sections if their common center of mass is considered to be at rest. If they are bound together, they will both trace out ellipses; if they are moving apart, they will both follow parabolas or hyperbolas. See two-body problem.


title: Conic section

text: The reflective properties of the conic sections are used in the design of searchlights, radio-telescopes and some optical telescopes. A searchlight uses a parabolic mirror as the reflector, with a bulb at the focus; and a similar construction is used for a parabolic microphone. The 4.2 meter Herschel optical telescope on La Palma, in the Canary islands, uses a primary parabolic mirror to reflect light towards a secondary hyperbolic mirror, which reflects it again to a focus behind the first mirror.


title: Conic section

text: The conic sections have some very similar properties in the Euclidean plane and the reasons for this become clearer when the conics are viewed from the perspective of a larger geometry. The Euclidean plane may be embedded in the real projective plane and the conics may be considered as objects in this projective geometry. One way to do this is to introduce homogeneous coordinates and define a conic to be the set of points whose coordinates satisfy an irreducible quadratic equation in three variables (or equivalently, the zeros of an irreducible quadratic form). More technically, the set of points that are zeros of a quadratic form (in any number of variables) is called a quadric, and the irreducible quadrics in a two dimensional projective space (that is, having three variables) are traditionally called conics.


title: Conic section

text: The Euclidean plane is embedded in the real projective plane by adjoining a line at infinity (and its corresponding points at infinity) so that all the lines of a parallel class meet on this line. On the other hand, starting with the real projective plane, a Euclidean plane is obtained by distinguishing some line as the line at infinity and removing it and all its points.


title: Conic section

text: In a projective space over any division ring, but in particular over either the real or complex numbers, all non-degenerate conics are equivalent, and thus in projective geometry one speaks of "a conic" without specifying a type. That is, there is a projective transformation that will map any non-degenerate conic to any other non-degenerate conic.


title: Conic section

text: The three types of conic sections will reappear in the affine plane obtained by choosing a line of the projective space to be the line at infinity. The three types are then determined by how this line at infinity intersects the conic in the projective space. In the corresponding affine space, one obtains an ellipse if the conic does not intersect the line at infinity, a parabola if the conic intersects the line at infinity in one double point corresponding to the axis, and a hyperbola if the conic intersects the line at infinity in two points corresponding to the asymptotes.


title: Conic section

text: As multiplying all six coefficients by the same non-zero scalar yields an equation with the same set of zeros, one can consider conics, represented by as points in the five-dimensional projective space formula_43


title: Conic section

text: Metrical concepts of Euclidean geometry (concepts concerned with measuring lengths and angles) can not be immediately extended to the real projective plane. They must be redefined (and generalized) in this new geometry. This can be done for arbitrary projective planes, but to obtain the real projective plane as the extended Euclidean plane, some specific choices have to be made.


title: Conic section

text: Fix an arbitrary line in a projective plane that shall be referred to as the "absolute line". Select two distinct points on the absolute line and refer to them as "absolute points". Several metrical concepts can be defined with reference to these choices. For instance, given a line containing the points and , the "midpoint" of line segment is defined as the point which is the projective harmonic conjugate of the point of intersection of and the absolute line, with respect to and .


title: Conic section

text: A conic in a projective plane that contains the two absolute points is called a "circle". Since five points determine a conic, a circle (which may be degenerate) is determined by three points. To obtain the extended Euclidean plane, the absolute line is chosen to be the line at infinity of the Euclidean plane and the absolute points are two special points on that line called the circular points at infinity. Lines containing two points with real coordinates do not pass through the circular points at infinity, so in the Euclidean plane a circle, under this definition, is determined by three points that are not collinear.


title: Conic section

text: It has been mentioned that circles in the Euclidean plane can not be defined by the focus-directrix property. However, if one were to consider the line at infinity as the directrix, then by taking the eccentricity to be a circle will have the focus-directrix property, but it is still not defined by that property. One must be careful in this situation to correctly use the definition of eccentricity as the ratio of the distance of a point on the circle to the focus (length of a radius) to the distance of that point to the directrix (this distance is infinite) which gives the limiting value of zero.


title: Conic section

text: A synthetic (coordinate-free) approach to defining the conic sections in a projective plane was given by Jakob Steiner in 1867.


title: Conic section

text: A "perspective" mapping formula_48 of a pencil formula_49 onto a pencil formula_50 is a bijection (1-1 correspondence) such that corresponding lines intersect on a fixed line formula_54, which is called the "axis" of the perspectivity formula_48.


title: Conic section

text: As a projective mapping in a projective plane over a field (pappian plane) is uniquely determined by prescribing the images of three lines, for the Steiner generation of a conic section, besides two points formula_45 only the images of 3 lines have to be given. These 5 items (2 points, 3 lines) uniquely determine the conic section.


title: Conic section

text: By the Principle of Duality in a projective plane, the dual of each point is a line, and the dual of a locus of points (a set of points satisfying some condition) is called an "envelope" of lines. Using Steiner's definition of a conic (this locus of points will now be referred to as a "point conic") as the meet of corresponding rays of two related pencils, it is easy to dualize and obtain the corresponding envelope consisting of the joins of corresponding points of two related ranges (points on a line) on different bases (the lines the points are on). Such an envelope is called a "line conic" (or dual conic).


title: Conic section

text: In the real projective plane, a point conic has the property that every line meets it in two points (which may coincide, or may be complex) and any set of points with this property is a point conic. It follows dually that a line conic has two of its lines through every point and any envelope of lines with this property is a line conic. At every point of a point conic there is a unique tangent line, and dually, on every line of a line conic there is a unique point called a "point of contact". An important theorem states that the tangent lines of a point conic form a line conic, and dually, the points of contact of a line conic form a point conic.


title: Conic section

text: Karl Georg Christian von Staudt defined a conic as the point set given by all the absolute points of a "polarity" that has absolute points. Von Staudt introduced this definition in "Geometrie der Lage" (1847) as part of his attempt to remove all metrical concepts from projective geometry.


title: Conic section

text: A "polarity", , of a projective plane is an involutory bijection between the points and the lines of that preserves the incidence relation. Thus, a polarity associates a point with a line by and . Following Gergonne, is called the "polar" of and the "pole" of . An "absolute point" (or "line") of a polarity is one which is incident with its polar (pole).


title: Conic section

text: No continuous arc of a conic can be constructed with straightedge and compass. However, there are several straightedge-and-compass constructions for any number of individual points on an arc.


title: Conic section

text: One of them is based on the converse of Pascal's theorem, namely, "if the points of intersection of opposite sides of a hexagon are collinear, then the six vertices lie on a conic." Specifically, given five points, and a line passing through , say , a point that lies on this line and is on the conic determined by the five points can be constructed. Let meet in , meet in and let meet at . Then meets at the required point . By varying the line through ,as many additional points on the conic as desired can be constructed.


title: Conic section

text: Another method, based on Steiner's construction and which is useful in engineering applications, is the parallelogram method, where a conic is constructed point by point by means of connecting certain equally spaced points on a horizontal line and a vertical line. Specifically, to construct the ellipse with equation , first construct the rectangle with vertices and . Divide the side into equal segments and use parallel projection, with respect to the diagonal , to form equal segments on side (the lengths of these segments will be times the length of the segments on ). On the side label the left-hand endpoints of the segments with to starting at and going towards . On the side label the upper endpoints to starting at and going towards . The points of intersection, for will be points of the ellipse between and . The labeling associates the lines of the pencil through with the lines of the pencil through projectively but not perspectively. The sought for conic is obtained by this construction since three points and and two tangents (the vertical lines at and ) uniquely determine the conic. If another diameter (and its conjugate diameter) are used instead of the major and minor axes of the ellipse, a parallelogram that is not a rectangle is used in the construction, giving the name of the method. The association of lines of the pencils can be extended to obtain other points on the ellipse. The constructions for hyperbolas and parabolas are similar.


title: Conic section

text: Yet another general method uses the polarity property to construct the tangent envelope of a conic (a line conic).


title: Conic section

text: In the complex plane , ellipses and hyperbolas are not distinct: one may consider a hyperbola as an ellipse with an imaginary axis length. For example, the ellipse formula_57 becomes a hyperbola under the substitution formula_58 geometrically a complex rotation, yielding formula_59. Thus there is a 2-way classification: ellipse/hyperbola and parabola. Extending the curves to the complex projective plane, this corresponds to intersecting the line at infinity in either 2 distinct points (corresponding to two asymptotes) or in 1 double point (corresponding to the axis of a parabola); thus the real hyperbola is a more suggestive real image for the complex ellipse/hyperbola, as it also has 2 (real) intersections with the line at infinity.


title: Conic section

text: Further unification occurs in the complex projective plane : the non-degenerate conics cannot be distinguished from one another, since any can be taken to any other by a projective linear transformation.


title: Conic section

text: It can be proven that in , two conic sections have four points in common (if one accounts for multiplicity), so there are between 1 and 4 intersection points. The intersection possibilities are: four distinct points, two singular points and one double point, two double points, one singular point and one with multiplicity 3, one point with multiplicity 4. If any intersection point has multiplicity > 1, the two curves are said to be tangent. If there is an intersection point of multiplicity at least 3, the two curves are said to be osculating. If there is only one intersection point, which has multiplicity 4, the two curves are said to be "superosculating".


title: Conic section

text: Furthermore, each straight line intersects each conic section twice. If the intersection point is double, the line is a tangent line.


title: Conic section

text: Intersecting with the line at infinity, each conic section has two points at infinity. If these points are real, the curve is a hyperbola; if they are imaginary conjugates, it is an ellipse; if there is only one double point, it is a parabola. If the points at infinity are the cyclic points and , the conic section is a circle. If the coefficients of a conic section are real, the points at infinity are either real or complex conjugate.


title: Conic section

text: What should be considered as a "degenerate" case of a conic depends on the definition being used and the geometric setting for the conic section. There are some authors who define a conic as a two-dimensional nondegenerate quadric. With this terminology there are no degenerate conics (only degenerate quadrics), but we shall use the more traditional terminology and avoid that definition.


title: Conic section

text: In the Euclidean plane, using the geometric definition, a degenerate case arises when the cutting plane passes through the apex of the cone.


title: Conic section

text: The degenerate conic is either: a point, when the plane intersects the cone only at the apex; a straight line, when the plane is tangent to the cone (it contains exactly one generator of the cone); or a pair of intersecting lines (two generators of the cone). These correspond respectively to the limiting forms of an ellipse, parabola, and a hyperbola.


title: Conic section

text: If a conic in the Euclidean plane is being defined by the zeros of a quadratic equation (that is, as a quadric), then the degenerate conics are: the empty set, a point, or a pair of lines which may be parallel, intersect at a point, or coincide. The empty set case may correspond either to a pair of complex conjugate parallel lines such as with the equation formula_60 or to an "imaginary ellipse", such as with the equation formula_61 An imaginary ellipse does not satisfy the general definition of a degeneracy, and is thus not normally considered as degenerated. The two lines case occurs when the quadratic expression factors into two linear factors, the zeros of each giving a line. In the case that the factors are the same, the corresponding lines coincide and we refer to the line as


title: Conic section

text: a "double" line (a line with multiplicity 2) and this is the previous case of a tangent cutting plane.


title: Conic section

text: In the real projective plane, since parallel lines meet at a point on the line at infinity, the parallel line case of the Euclidean plane can be viewed as intersecting lines. However, as the point of intersection is the apex of the cone, the cone itself degenerates to a cylinder, i.e. with the apex at infinity. Other sections in this case are called "cylindric sections". The non-degenerate cylindrical sections are ellipses (or circles).


title: Conic section

text: When viewed from the perspective of the complex projective plane, the degenerate cases of a real quadric (i.e., the quadratic equation has real coefficients) can all be considered as a pair of lines, possibly coinciding. The empty set may be the line at infinity considered as a double line, a (real) point is the intersection of two complex conjugate lines and the other cases as previously mentioned.


title: Conic section

text: To distinguish the degenerate cases from the non-degenerate cases (including the empty set with the latter) using matrix notation, let be the determinant of the 3 × 3 matrix of the conic section—that is, ; and let be the discriminant. Then the conic section is non-degenerate if and only if . If we have a point when , two parallel lines (possibly coinciding) when , or two intersecting lines when .


title: Conic section

text: A (non-degenerate) conic is completely determined by five points in general position (no three collinear) in a plane and the system of conics which pass through a fixed set of four points (again in a plane and no three collinear) is called a "pencil of conics". The four common points are called the "base points" of the pencil. Through any point other than a base point, there passes a single conic of the pencil. This concept generalizes a pencil of circles.


title: Conic section

text: The solutions to a system of two second degree equations in two variables may be viewed as the coordinates of the points of intersection of two generic conic sections.


title: Conic section

text: An efficient method of locating these solutions exploits the homogeneous matrix representation of conic sections, i.e. a 3 × 3 symmetric matrix which depends on six parameters.


title: Conic section

text: The procedure to locate the intersection points follows these steps, where the conics are represented by matrices:


title: Conic section

text: Conics may be defined over other fields (that is, in other pappian geometries). However, some care must be used when the field has characteristic 2, as some formulas can not be used. For example, the matrix representations used above require division by 2.


title: Conic section

text: A generalization of a non-degenerate conic in a projective plane is an oval. An oval is a point set that has the following properties, which are held by conics: 1) any line intersects an oval in none, one or two points, 2) at any point of the oval there exists a unique tangent line.


title: Conic section

text: Generalizing the focus properties of conics to the case where there are more than two foci produces sets called generalized conics.


title: Conic section

text: The intersection of an elliptic cone with a sphere is a spherical conic, which shares many properties with planar conics.


title: Conic section

text: The classification into elliptic, parabolic, and hyperbolic is pervasive in mathematics, and often divides a field into sharply distinct subfields. The classification mostly arises due to the presence of a quadratic form (in two variables this corresponds to the associated discriminant), but can also correspond to eccentricity.


title: Alan Dale

text: Alan Hugh Dale (born 6 May 1947) is a New Zealand actor. As a child, Dale enjoyed theatre and rugby. After retiring from the sport, he took on a number of occupations, before deciding to become a professional actor at age 27. Dale subsequently moved to Australia, where he played Dr. John Forrest in "The Young Doctors" from 1979 to 1982. He later appeared as Jim Robinson in "Neighbours", a part he played from 1985 until 1993. He left the series when he fell out with the producers over the pay he and the rest of the cast received. In 2018, it was revealed that Dale would reprise his role as Jim for one episode of "Neighbours", 25 years after his last appearance.


title: Alan Dale

text: After leaving "Neighbours", Dale found he had become typecast as Jim Robinson in Australia and struggled to find work. His career was revitalised after he relocated to the United States in 2000. Since then, he has had roles in many American series including prominent parts in "The O.C." (as Caleb Nichol) and "Ugly Betty" (as Bradford Meade), as well as recurring and guest roles in "Lost", "24", "NCIS", "ER", "The West Wing", "The X-Files", "Entourage" and "Once Upon a Time". Dale has also appeared in minor roles in films such as "", "Hollywood Homicide", "Indiana Jones and the Kingdom of the Crystal Skull", "The Girl with the Dragon Tattoo" and "", as well as the London West End production of "Spamalot". Dale has been married to former Miss Australia Tracey Pearson since 1990 and has four children. From 2017 to 2021, Dale starred in the soap opera "Dynasty" as Joseph Anders.


title: Alan Dale

text: Dale was born on 6 May 1947 in Dunedin, Otago, New Zealand. One of four children, Dale enjoyed his childhood, but his family was relatively poor. Growing up in New Zealand without televisions, Dale loved the theatre and amateur dramatics. His first performance was for a school concert, at the age of 13, doing an impression of comedian Shelley Berman. After moving northwards, his parents became founding members of an amateur theatre in Auckland called "The Little Dolphin Theatre". Dale often operated the stage equipment used to produce weather effects,


title: Alan Dale

text: Dale was a skilled rugby player, but opted to move into drama instead because "the acting fraternity didn't like footballers and the footballers didn't like actors. [...] Acting gave me the same buzz and there was the chance of a longer career." He gave up rugby at the age of 21 because it was not considered a workable career at the time, and he had to support his family. Acting roles were limited in New Zealand so Dale worked in multiple jobs, including as a male model, a car salesman and a realtor. While working as a milkman he heard the disc jockey at his local radio station resign during a broadcast. Dale went over to the station and told the managers he could do a better job. They gave him a trial and then signed him up for the afternoon show. At the age of 27, he decided to become a professional actor.


title: Alan Dale

text: Dale's first professional acting job was playing an Indian in a production of "The Royal Hunt of the Sun" at the Grafton Theatre in Auckland. His first on-screen role came in the New Zealand television drama "Radio Waves", which although not successful, he described as "nine months of solid work and great fun." In the late 1970s, Dale moved to Australia at the age of 32, due to the limited acting work in New Zealand. He applied to the National Institute of Dramatic Art in Sydney, but was rejected because he "was a lot older than anybody else on the course." He was soon cast as Dr. John Forrest in the Australian soap opera "The Young Doctors", where he remained for three-and-a-half years.


title: Alan Dale

text: In 1985, Dale was cast in the continuing role of Jim Robinson in the Australian soap opera "Neighbours", earning him acclaim across the world. He appeared on the show from the first episode and stayed for eight years before his character was killed off in 1993. He found working on "Neighbours" "exciting" and it enabled him to provide for his sons, but he said: "You were a totally replaceable commodity; [the production company] didn't put any value on any of the people appearing in the show." He expanded: "I didn't like it there, they were not nice people. When we decided that we hated each other, the company and me, one of the things the company did was to market everything they could out of us and pay us nothing." Dale and the company (Grundy Television) parted on "bad terms", although he would later go on to appear on the show again in 2018 and 2019.


title: Alan Dale

text: After "Neighbours", Dale struggled to find work in Australia because he was typecast as Jim Robinson. His only regular sources of income were voice-overs, and publishing magazines about his former show which he "made quite a lot of money out of". He lost most of his profits investing in a failed children's magazine. In 1999, he was cast in the American television film "First Daughter", which was filmed in Australia. After discovering he could perform a convincing American accent, Dale attended the film's premiere, finally moving with his family to the United States permanently in January 2000. Dale, his second wife Tracey, and their then two-year-old son Nick moved into an "awful little flat" in Los Angeles and found an agent. Dale recalled telling his wife in Melbourne that "there's no way this is going to work. But if it does, it proves you can do anything."


title: Alan Dale

text: At the age of 52, he began to revive his career and started taking acting classes, something he had not thought about after being cast in "Neighbours". He described his age, unknown status and willingness to work for a relatively low fee as being his main assets for getting work in America. His drama teacher, whom he has remained with ever since, told him "that you might want to play great roles, but truth is you will get cast as a specific type. Just work out your type. The others in the class said I was a bit Anthony Hopkins and a bit Sean Connery and that went into my head. I thought if I go for roles those guys would go for I'm more likely to get them." The first role he was offered was a part in a series called "Sign of Life", a show about a rock band, which eventually fell through. Dale only received a couple of auditions during his first year in America, but his break came when he was cast as the South African Al Patterson in four episodes of "ER". Since then, Dale has been "busier than ever".


title: Alan Dale

text: He has appeared in many television series including guest appearances on "The West Wing", "Torchwood", "The Lone Gunmen", "Californication", and "The Practice". Many of these have been recurring roles, such as the part of Tom Morrow in "JAG" and its spin-off "NCIS", as well as appearing in three episodes, including the series finale, of "The X-Files", playing the "Toothpick Man". He played the recurring role of Vice President of the United States Jim Prescott for seven episodes of the second season of "24", a part which was originally supposed to be a single scene. Dale had recurring roles in the serial "Midnight Man" and the Australian series "Sea Patrol" in 2008. He also had recurring parts on "Undercovers", "Entourage" as John Ellis, the fictional owner of Warner Bros., and the British series "Moving Wallpaper" as a fictional version of himself. He had a recurring role as King George in the series "Once Upon a Time", and Emmett in "Hot in Cleveland", before joining the main cast of "Dominion" in 2014, playing General Edward Riesen.


title: Alan Dale

text: From 2003 to 2010, Dale appeared in his longest running American roles. He starred in the Fox TV series, "The O.C." playing Caleb Nichol, a wealthy tycoon. The producers saw that the character had further potential, and made his initially recurring role a regular character in the series. After 35 appearances, Caleb was killed off in the second-season episode "The O.Sea" in 2005. Dale was disappointed that Caleb was written out and described it as a mistake by the production staff. In 2006, Dale was cast in the starring role of Bradford Meade, the owner of Meade Publications in the ABC show "Ugly Betty". Although he impressed the producers in his audition, he initially lost the role to a "bigger star". After said star began "causing trouble" and was fired, Dale was given the part. Bradford was killed off during the show's second season. Dale appeared in the second-season finale of "Lost", "Live Together, Die Alone", as Charles Widmore, a businessman and leader of the Others. Dale's publicist was initially worried that Widmore (who was an integral part of the show's mystery) would become a starring role, meaning it would be hard for Dale to appear in both "Lost" and "Ugly Betty" at the same time. The part became a recurring role, with Dale appearing numerous times between seasons two (2006) and six (2010). He enjoyed the role but often found it difficult due to his character's unclear motivation.


title: Alan Dale

text: In March 2008, Dale replaced Peter Davison in the lead role of King Arthur in the London West End production of Monty Python's "Spamalot" at the Palace Theatre. He accepted the role because he was a huge fan of "Monty Python" and considered that "life's too short" for him to have turned down a West End part. Although he has seen all of the Flying Circus sketches and Life Of Brian, Dale had never seen "Monty Python and the Holy Grail" (from which "Spamalot" is "lovingly ripped off") and had to buy a copy to prepare for the role. It was not his first experience in musical theatre because he appeared in a 1984 Australian production of "Applause", but Dale found the comic timing of the part to be the hardest task. "On stage, the battle is to find all of the humorous moments and not skip over them. [...] There's an art to Python humour and I'm aiming to try and get every single joke just right." He was succeeded in the role by Sanjeev Bhaskar on 23 June 2008.


title: Alan Dale

text: Dale has also made several film appearances. He appeared as the Romulan Praetor Hiren in "", a part he got after the actor originally cast fell ill, and had small parts in films such as "Hollywood Homicide", "After the Sunset", and the minor part of General Ross in "Indiana Jones and the Kingdom of the Crystal Skull". Dale said his script for "Kingdom of the Crystal Skull" was printed on tin foil so it was impossible to replicate, in order to keep the film's plot a secret. He appeared in four films released in 2011: "A Little Bit of Heaven", "Priest", "Don't Be Afraid of the Dark", and "The Girl with the Dragon Tattoo", having joined late in the film's production.


title: Alan Dale

text: Despite his mainstream success upon his move to America, Dale remained primarily known for his role as Jim Robinson in "Neighbours" in the United Kingdom and Australia for several years. This was spoofed in a promotional ident for the UK's Channel 4 in 2007 which sees Dale taking part in a mock interview about the sudden upturn in his career, before being accosted by an Australian fan, who recognises him as Jim Robinson. Discussing this association after "Ugly Betty"<nowiki>'</nowiki>s 2007 Golden Globe win, Dale noted: "Every article I read I'm always, 'Ex-soap star Jim Robinson'. Maybe now people will just get to know me as actor Alan Dale." In 2007, Amazon.co.uk reported that they had sold more DVDs of films and television shows featuring Dale than any featuring other ex-"Neighbours" cast members.


title: Alan Dale

text: Dale's characters on most of the American television shows he has appeared on have shared similar character traits, which Dale describes as the "go-to powerful guy". "I either play rulers of the world or the guy who kills the ruler of the world", he said, recalling that his age benefited him after moving to the US, because "A lot of the American middle-aged faces were too familiar, I came along and people were saying 'Who is this great new guy?' And I was cheap". Following his appearance as Senator Eaton in "The Killing" in 2011, reviewers commented on his tendency to play powerful, wealthy and mysterious characters in many shows. Maureen Ryan of "TV Squad" wrote that it was "lovely to see Alan Dale playing a typically Alan Dale-ian character. He's always so great at playing That Sketchy Wealthy Guy With a Hidden Agenda, which he has now played on, I believe, 87 different shows. And he always does it well." Coincidentally, Dale's characters in "Neighbours", "The O.C." and "Ugly Betty" have all been killed off by a fatal heart attack. Christopher Rosen of "The New York Observer" wrote in 2008 that "with his square jaw and seemingly no nonsense attitude, Mr. Dale is the go-to actor when casting directors need a conservative-looking authoritarian. When he comes onto the screen, audiences immediately take him seriously, since he radiates rich, smug and serious. He demands your respect." Rosen says that Dale is "not even...a particularly good actor" but is "fine enough" and "bring[s] a no frills, no gimmicks style to his roles," and "manages to give a consistent performance in every show he appears on."


title: Alan Dale

text: Jayne Nelson, writing in magazine "SFX", named Dale the second most "serial" science-fiction guest star after Mark Sheppard. She wrote: "The thing is, soap-opera origins aside, Dale is always good. Which is why he keeps getting so much work...Dale never lets you down, always (well, usually) summoning up a pitch-perfect accent, too. There's something comforting about his presence on a show, as though the fact he's in it has lent it some weight." In a profile of his work on "cult shows", Ben Rawson-Jones of Digital Spy called Dale an "institution".


title: Alan Dale

text: In 1968, Dale married his girlfriend, Claire. The couple had two children, Simon and Matthew, both of whom are involved in the entertainment industry, Simon as a radio announcer at Kiss 100 and Matthew as a writer, film maker and actor. The marriage ended in divorce in 1979. At the time, Dale lived in Auckland but after the divorce he moved to Sydney with his sons.


title: Alan Dale

text: On 8 April 1990, he married Tracey Pearson, the 1986 Miss Australia, whom he met at the 1986 Australian Grand Prix, when she was 21 and he was 39. Dale described it as "the most appropriate relationship I've ever had." Dale also has two children from this marriage, Daniel and Nick.


title: Alan Dale

text: He and his family now live in Manhattan Beach, California and also owns property in Australia. Dale sold his holiday home in New Zealand in 2011 for $1.25m. Both of Dale's parents died in 2007. Dale describes his life philosophy as being Winston Churchill's quote "Never, never, never give up", and counts Gene Hackman as his "big acting hero".


title: Host and hostess clubs

text: A hostess club is a type of night club found primarily in Japan. They employ primarily female staff and cater to men seeking drinks and attentive conversation. The modern host club is a similar type of establishment where primarily male staff attend to women. Host and hostess clubs are considered part of "mizu shōbai" (literally "water trade"), the night-time entertainment business in Japan.


title: Host and hostess clubs

text: In Japan, two types of bars are hostess clubs: , a portmanteau of ; and . Kyabakura hostesses are known as ("cabaret girl"), and many use professional names, called . They light cigarettes, provide beverages for men, offer flirtatious conversation, and sing karaoke to entertain customers. They can be seen as the modern counterpart of geishas, providing entertainment to groups of salarymen after work. The clubs also often employ a female bartender usually well-trained in mixology, and who may also be the manager or "mamasan". Hostess clubs are distinguished from strip clubs in that there is no dancing, prostitution or nudity.


title: Host and hostess clubs

text: Hostesses often drink with customers each night, and alcohol problems are fairly common. These problems can be the result of frequent consumption of alcohol, from which many consequences may arise. Most bars use a commission system by which hostesses receive a percentage of sales. For example, a patron purchases a $20 drink for the hostess, these are usually non-alcoholic concoctions like orange juice and ginger ale, and the patron has purchased the hostess's attention for the subsequent 30–45 minutes. The hostess then splits the proceeds of the sale with the bar 50/50. The light or no alcohol content of the drinks maximizes profits and ensures that the hostess does not become intoxicated after only a short time at work.


title: Host and hostess clubs

text: Businesses may pay for tabs on company expense with the aim of promoting trust among male co-workers or clients. At one establishment, about 90% of all tabs were reportedly paid for by companies.


title: Host and hostess clubs

text: Patrons are generally greeted comfortably at the door and seated as far away from other customers as possible. In some instances, a customer is able to choose with whom he spends time, while most often that is decided by the house. In either case, the hostess will leave after a certain amount of time or number of drinks, offering the customer a chance to see a fresh face. While most establishments have male touts outside to bring in customers, it may also fall upon a (usually new) hostess to do so. While hostess clubs are clearly gendered in the way that women serve men, research has also revealed the complexity of intra-gender dynamics and sometimes tension among hostesses as well, and the ways that male customers often work to mitigate problems among hostesses as well as between hostesses and Mama-san.


title: Host and hostess clubs

text: Hostess clubs have a strict "no touching" policy, and patrons who try to initiate private or sexual conversation are removed. However a red-light district version of the host/hostess club exists, called "seku-kyabakura" or "ichya-kyabakura", where patrons are permitted to touch their host/hostess above the waist and engage in sexual conversation topics or kissing, although this type of establishment is not common. Normal hostess clubs are classified as food and entertainment establishments and regulated by the Businesses Affecting Public Morals Regulation Act, prohibiting any form of sexual contact between employees and customers. Normal hostess clubs also need a permit to allow dancing. Clubs are inspected often by the Public Safety Commission. Any club found violating its permitted activities can have its business license suspended, until corrections are made.