alibayram/wikipedia-40-langs huggingface dataset:
Microsoft PowerPoint

Microsoft Office PowerPoint is a presentation program developed for the Microsoft Windows and Mac OS computer operating systems. Businesspeople, educators, and trainers use it often. It is a component of the Microsoft Office system.

Operation 
In PowerPoint, as in most other presentation software, text, graphics, movies, and other objects are positioned on individual pages or "slides". The "slide" analogy is a reference to the slide projector. Slides can be printed, or (more often) displayed on-screen and navigated through at the command of the presenter. Slides can also form the basis of webcasts.

Versions 
Versions for Microsoft Windows include:

 1993 PowerPoint 4.0 (Office 4.x)
 1995 PowerPoint 7 for Windows 95 (Office '95)
 1997 PowerPoint 97 (Office '97)
 1999 PowerPoint 2000 (Office 2000)
 2001 PowerPoint 2002 (Office XP)
 2003 PowerPoint 2003 (Office 2003)
 2006-2007 PowerPoint 2007 (Office 2007)
 2010 PowerPoint 2010 (Office 2010)
 2016 PowerPoint 2016 (Office 2016)
 2018 PowerPoint 2019 (Office 2019)

Note: There is no PowerPoint 5.0 or 6.0, because the Windows 95 version was launched with Word 7. All of the Office 95 products have OLE 2  - moving data between many programs - and PowerPoint 7 shows that it was as new as Word 7.

Related pages
 LibreOffice Impress, a free, open source alternative to Microsoft PowerPoint
 Apple Keynote

Other websites 
 Official website of PowerPoint at Microsoft
 flashgeek PowerPoint tutorials and community, especially in regards to using PowerPoint in combination with Macromedia Flash.
 PowerPoint Heaven — The Power to Animate Contains PowerPoint movies, showcases, PowerPoint games, animation templates and tutorials on creating animations for your PowerPoint Presentations.
 PowerPoint FAQ pages Compilation of Frequently Asked Questions in the Microsoft Office PowerPoint Discussion Groups.
 Microsoft PowerPoint Viewer 2003 Download (freeware, 1.9 MiB.) Free PowerPoint Viewer provided by Microsoft, supports presentations from PowerPoint 97 to 2003. (only Windows)
 Microsoft PowerPoint Viewer 2007 Download (freeware, 25.8 MiB.) Free PowerPoint Viewer provided by Microsoft, supports presentations from PowerPoint 97 to 2007. (only Windows)
 pdfonline.com Upload a .ppt and get a .pdf via email

Discussion Groups 
 Microsoft Office PowerPoint Discussion Group
 Microsoft Office PowerPoint Yahoo! Group — Help and advice for users of PowerPoint

Articles 
 
 
 
 
  (Astronauts using PowerPoint to replace paper checklists.)
 
 

Microsoft Office
Presentation software
Anna Nicole Smith

Anna Nicole Smith (November 28, 1967 – February 8, 2007) was an American model, actress and celebrity. She first became popular as Playboy magazine's 1993 Playmate of the Year.

Early life
She was born Vicki Lynn Hogan in Houston, Texas.

Death
On February 8, 2007, Smith was found in a hotel room in Hollywood, Florida. At 1:38 p.m. (18:38 UTC) a nurse called 911. At 1:45 p.m. a bodyguard gave her CPR before she was taken to a local hospital and pronounced dead at 2:49 p.m. Her death was caused by an accidental overdose.

Smith was addicted to prescription medications. A psychiatrist said in court in 2010 that she was a member of hospital staff in 2006, when Smith was a patient. The psychiatrist said Smith had borderline personality disorder.

References

Other websites 
AnnaNicole.com Official website

Actors from Houston
American movie actors
American television actors
Drug-related accidental deaths in the United States
Models from Houston
People with borderline personality disorder
1967 births
2007 deaths
Ciao (magazine)

is a Japanese shōjo manga magazine published by Shogakukan for young girls (about 9-13 years old). It has been published since 1977.

Famous works
Slow step (Mitsuru Adachi)
Alpen Rose (Michiyo Akaishi)
Mizuiro jidai (Yuu Yabuuchi)
Dr.Rin ni kiitemite! (Kiyoko Arai)
Mirumo de pon! (Hiromu Shinozuka)
Kirarin revolution (Ann Nakahara)

Cartoonists
Yuu Yabuuchi (1983–)
Kiyoko Arai (1984–)
Masumi shimizu (1989–)
Takemaru SaSaki (1992–)
Tomoko Nishimura (1992–)
Yukino Miyawaki (1992–)
Yumi Tsukirino (1996–)
Mai Jinna (1997–)
Kaoru Igarashi (1999–)
Hiromu Shinozuka (1999–)
Chikako Mori (2000–)
Jun Kawamura (2000–)
Ann Nakahara (2000–)
Ryoko Mizoguchi (2000–)
Chitose Yagami (2001–)
Itsuru Minase (2001–)
Meme Iwaoka (2001–)
Nozomi Shiratori (2002–)
Yūko Kohara (2002–)
Shou Obara (2003–)
Maki Sugawa (2003–)
Mayuki Anan (2004–)
Miru Akino (2004–)
Akira Wao (2005–)
Mariko Kosaka (2005–)
Yayoi Tsukamoto (2005–)
Yūmi Rink (2005–)
Michiru Aoi (2005–)
Aya Misaki (2006–)
Eri Nasubi (2006–)

Manga
Sorting algorithm

A sorting algorithm is an algorithm that puts the elements of a collection into a certain order. Most commonly, numbers are sorted by their value, and words are sorted by their alphabetical order (as they would appear in a dictionary or phone book). Efficient sorting is important for other things: finding an element in a sorted collection is easier, and merging a new element may also be easier if the collection is sorted.

Note that not all sorting algorithms can be applied in all cases. An example might be that the records can only be read one after another (sequentially); they might be stored on a tape. 

Searching and sorting algorithms
Ciao

The word "ciao" is a greeting in Italian. It is used for both "hello" and "goodbye". It is less formal than other greetings in Italian, such as buongiorno or salve.

The word originally comes from the Venetian language. It is also sometimes used by English speakers and speakers of other languages around the world. Other words that mean both "hello" and "goodbye" are shalom in Hebrew, salaam in Arabic, annyeong in Korean, and aloha in Hawaiian. In Vietnamese, the word chào also means "hello" or "goodbye". It sounds similar, but is not related to the Italian word.

Italian language
LaTeX

LaTeX is a computer program used for making articles, books and math formulas look good. LaTeX is well-suited for expressing mathematical formulas on electronic devices in a more human readable format, by showing them in a way similar to how they would be written by hand. 

LaTeX is used for making mathematical formulas for some articles on Wikipedia, in addition to being used within academic circles.

The writer types their article into a plain text document. A plain text document cannot have styled text, like bold or italic. When the writer wants to write styled text, they use special LaTeX commands that start with a backslash (\). For example, the command for bold text is \textbf{This text is bold}.

After the writer is finished writing the article, they tell LaTeX to read the document. After LaTeX is done, LaTeX makes a file that can be printed. The command \textbf{This text is bold} would print as This text is bold.
 
LaTeX was first made in the early 1980s by Leslie Lamport at SRI International, who published its first manual in 1986. The current version is LaTeX2e (styled ), which has been active since 1994.

Example 
The example below shows the LaTeX input and its corresponding output:

Academic contributions to LaTeX
In order to support mathematical typesetting, the American Mathematical Society (AMS) has made the AMS-LaTeX package. AMS also founded MathJax, a Javascript extension to display mathematical formulas on web browsers, with the Society for Industrial and Applied Mathematics.

Related pages
 Acaric (Developer of Cloud LaTeX)
 Beamer (LaTeX-based presentation software)
 CTAN (One of the largest LaTeX-related website)
 KaTeX (LaTeX for web browsers)
 SATySFi (A computer program expected to be an alternative to LaTeX)

References

Further reading
 Van Dongen, M. R. (2012). LATEX and Friends. Springer Science & Business Media.
 Grätzer, G. (2014). Practical LaTeX. Springer.
 Datta, D. (2017). LaTeX in 24 Hours: A Practical Guide for Scientific Writing. Springer.

Programming languages
Mathematical tools
Cross-platform software
First War of Scottish Independence

The First War of Scottish Independence lasted from the outbreak of the war in 1296 until 1328.

The Scots were defeated at Dunbar on 27 April 1296. John Balliol abdicated in Montrose castle on 10 July 1296. John was imprisoned in the Tower of London at first, but then released into the custody of Pope Boniface VIII on condition that he remain in a papal residence. He was later released around the summer of 1301 and lived the rest of his life on his family's estates in Picardy.

But his supporters argued that he was still the rightful King of Scotland. Therefore, the Scots rose in rebellion in 1297 under William Wallace and Andrew de Moray and said they  were acting on behalf of King John. But in fact Scotland had no monarch until the accession of Robert the Bruce in 1306.

Related pages
 Wars of Scottish Independence
 Second War of Scottish Independence

History of the British Isles
Wars of independence
Wars involving England
13th century in Scotland
14th century in Scotland
John of Scotland

|children=Edward Balliol.

John King of Scots (c. 1248 - 1314) is usually known as John Balliol or, correctly, John de Balliol. He was born in 1248. 

After the death of Margaret of Scotland in 1290, John Balliol was one of three major competitors for the throne. King Edward concluded that he was going to pick Balliol as king of Scotland at Scone, 30th November, 1292, St. Andrew's Day.

Edward I steadily undermined the authority of King John. He treated Balliol like a 'Puppet King' and the Scots were not happy. At the Battle of Dunbar King Edward's men slaughtered and wiped out the town of Berwick killing around 8000 people in the brutal killing.

He was stripped of his authority as king and was sent away to France by King Edward. He later died there. 

His son Edward Balliol would later claim the Scottish throne from 1332 until 1356.

1248 births
1314 deaths
Kings and Queens of Scotland
14th century in Scotland
13th century in Scotland
Soul patch

A soul patch is a style of facial hair in which hair is only found below the lower lip and above the chin.

Famous wearers

Living business personalities
 
Ted Yost 
Adam McClellan

Living musicians, actors, and television personalities
 
Gregg Allmjan 
Jack Black
Billy Ray Cyrus
Aamir Khan (Bollywood)
Geddy Lee
Howie Mandel
Ty Pennington
Trent Reznor
Bruce Springsteen
Eddie Vedder
Stevie Wonder
Creig Mabbit
Tom Waits

Deceased musicians

Ray Charles
Dizzy Gillespie
Stevie Ray Vaughan
Frank Zappa

Athletes

Fernando Alonso
Phil Jackson
David Villa

Facial hair
Wars of Scottish Independence

The Wars of Scottish Independence were a series of military campaigns fought between Scotland and England in the late 13th and early 14th centuries.

The First War (1296–1328) began with the English invasion of Scotland in 1296, and ended with the signing of the Treaty of Edinburgh-Northampton in 1328. The Second War (1332–1357) began with the English-supported invasion of Edward Balliol and the 'Disinherited' in 1332, and ended around 1357 with the signing of the Treaty of Berwick. 

The wars were part of a great national crisis for Scotland and the period became one of the most important moments in the nation's history. At the end of both wars, Scotland still was a free and independent nation, which was her main aim throughout the conflict. The wars were also important for other reasons, such as the emergence of the longbow as a key weapon in mediaeval warfare.

Important Figures
Scotland
King David II
King John Balliol
King Robert I the Bruce
William Wallace

England
King Edward I
King Edward II
King Edward III

Battles

Battle of Bannockburn

The Battle of Bannockburn (23–24 June 1314) was an important Scottish victory. It was the decisive battle in the First War of Scottish Independence. In this battle, the Scottish king Robert the Bruce defeated the English king Edward II.

Related pages
First War of Scottish Independence
Second War of Scottish Independence

Other websites 
 Wars of Independence

History of the British Isles
Wars involving England
Rebellions in Europe
13th century in Scotland
14th century in Scotland
Wars of independence
1314



Deaths 
 John of Scotland – King of Scotland

Events 
 June 23 – June 24 – Battle of Bannockburn during the Wars of Scottish Independence.
 Gabra Masqal I becomes Emperor of Ethiopia
Autotroph

An autotroph (from Greek autos = self and trophe = nutrition) is an organism that makes organic compounds from simple molecules.

Uses 
Autotrophs are needed in every food chain in all ecosystems. They take energy from the environment (sun light or inorganic sources) and use it to make other organic molecules that are used to carry out various biological functions such as cell growth or repairing broken tissue.

Types 
Plants and other organisms that carry out photosynthesis are phototrophs (or photoautotrophs). Bacteria that use inorganic compounds like hydrogen sulfide, phosphorus or iron are called chemoautotrophs. Other organisms, called heterotrophs, eat autotrophs. 

There are some species that need organic compounds as a source of food, but are able to use light as a source of energy. These are not autotrophic, but heterotrophic. A mixotroph is a (micro)organism that can use a mix of different sources of energy and carbon. 

Botany
Air France

Air France is one of the largest airlines in the world. It is based in France. It is owned by Air France-KLM. Before it merged with KLM, it employed 71,654 people. Its headquarters are at Charles de Gaulle International Airport near Paris.

History 
The airline can be traced back to 1933, when four other French airlines were combined to create Air France.  Air France hired its first flight attendants in 1946.  The airline started flying between Paris and New York City on July 1, 1946. In 1957, the airline bought its first jet aircraft.  Air France was one of 4 airlines that flew the Concorde.  It used it from 1976 until 2003. In 1988, the airline became the first to fly the Airbus A320.  In 2003, KLM Royal Dutch Airlines and Air France announced they were going to be combining. The combination ended in 2004.  As of 2016, Air France is going through many financial problems.

Fleets

Gallery

References 

1933 establishments in France
Airlines of France
Companies based in Paris
IATA members
Air Dolomiti

Air Dolomiti L.A.R.E. S.p.A is a regional airline from Verona in Italy. It is named after a section of the Alps known as The Dolomites. It is part of Lufthansa Regional connecting medium-size Italian airports to other European cities through Munich and Frankfurt am Main airports. The airline employs 550 people.

References 

Airlines of Italy
Verona
Hampshire

Hampshire is a county in the south of the UK. The county has an area of 1,455 square miles (3,769 km²). At its widest points, the county is about 55 miles (90 km) east-west and 40 miles (65 km) north-south. The county town is Winchester. About 1.6 million people live in Hampshire.

 
Ceremonial counties of England
Manuel Pereira da Silva

Manuel Pereira da Silva (7 December 1920 – 2003) was a Portuguese sculptor. He was born in Oporto, Portugal. 

The workmanship of Manuel Pereira da Silva has an abstract formal orientation inspired in the human figure, in particularly the man and the woman. In 2000, the Medal of Cultural Merit was attributed to Manuel Pereira da Silva for the City Council of Vila Nova de Gaia.

Education
In 1939, he entered the Oporto University's College of Arts. In 1953, he finished his coursework with the final classification of 18 values. During his coursework he was distinguished with two awards, "Teixeira Lopes" and "Soares dos Reis".

In 1946 and 1947, he studied in Paris, France, at the Paris College of Arts.

Selected works
I Exposition of the Independents, in the Oporto University's College of Arts. (1943)
II Exposition of the Independents, in the Atheneum Commercial of Oporto. (1944)
III Exposition of the Independents, in the Coliseum of Oporto. (1945)
Low-relives in Stone in the Rivoli Theatre and in the Coliseum, in Oporto. (1945)
Exposition of the Portuguese Life and the Art in Lourenço Marques, Moçambique (1946)
Exposition of Modern Art in the city of Caldas da Rainha. (1954)
Sculpture in Bronze of General Ulysses S. Grant, 18º President of the United States of America between 1868 and 1876. This monument was ordered by the Portuguese Government to Pereira da Silva for the capital of Guiné-Bissau. (1955)
Paintings in the Church of Saint Luzia, in the city of Viana do Castelo. (1956)
Paintings of the "Snow White" in the Street of Saint Catarina, in Oporto. (1957)
Sculpture in Bronze in the Square Marquis do Pombal, in Oporto. (1958)
II Exposition of Modern Art in the city of Viana do Castelo. (1959)
Low-relief in Ceramics in the capital of Angola. (1960)
Low-relief in Stone of "D. Pedro Pitões exhorting the Crusades" in the Courthouse, in Oporto. (1961)
II Exposition of Plastic Arts of the Foundation Calouste Gulbenkian, in the city of Lisbon. (1962)
Retrospective Exposition in Homage to the workmanship of Pereira da Silva by the Artists Association of Vila Nova de Gaia. (1987)

Other websites 
Twitter
Facebook
Blogspot
Instagram
Flickr
 Youtube

1920 births
2003 deaths
Portuguese artists
Sculptors
Yeti

The Yeti (also called the abominable snowman) is an animal said to live in the Himalaya mountain range made of ice. People say they have seen it, but none have ever been caught. It is supposed to look like an ape that walks upright. Some body parts, said to be of a yeti, are kept in a few monasteries in the area. There no real evidence that it exists, but there have been reports of footprints in the snow which could have been made by a yeti.

Description
The yeti has been described as having white shaggy fur and a lean muscular body like an ape. This "creature" could also live in the Asian mountains near the Himalayan snow line. Stories about the Yeti and another similar creature, Bigfoot, suggest that if they are real, they could be the same, or similar species. The yeti can stand at least 6 – 10 foot tall, not as tall as the Bigfoot. It has also been said the Yeti can weigh at least 200 - 400 pounds. The yeti is shy, which is why it has never been found. In 2010 an unsuccessful exhibition, some hunters found a hairless four legged creature, they said was a Yeti. It was a small hairless cat that lost it's hair from a disease.

Popular culture
The yeti has been shown in couple of movies including Monsters, Inc. The Yeti has also been a WWE wrestler name. Toys and games using creatures like yetis have been made including Lego Cards (Lego).

Related pages
 Bigfoot

Cryptozoology
Primality test

A primality test is a method (or algorithm) to find out if a certain number is a prime number. Cryptography uses prime numbers, and needs to test if a certain number is prime.  The official proof of a prime is through its primality certificate.

Simple methods
Sieve of Eratosthenes: Determine if there is a number (between 2 and n, the number to test) that divides n, without a rest
 Wilson's theorem (inefficient):  evaluates to -1 mod p where p is the candidate prime number

Better methods
Fermat's primality test
Miller-Rabin primality test

Prime numbers
.
Padding (cryptography)

Padding is a term used in cryptography. Very often, messages (to be encrypted) start or end in a well-known way (Dear Bob, ..., Yours, Alice). This is a problem, because that knowledge could be used to break (or start to break) encryption. To prevent this, a number of random characters are added at the beginning or the end of the message.

This procedure may also be necessary because many cryptographic methods operate on blocks of code. If a block is not full, additional characters need to be filled in. Filling in random text has proven very useful.

Cryptography
Dictionary attack

A dictionary attack is a method used in cryptography to find a key (or username, or password). A large number of words are tried. These words usually come from a special collection, called a "dictionary". 

The attack is based on trying all the strings in a pre-arranged listing. The listing is usually derived from a list of words, such as in a dictionary (hence the phrase dictionary attack).

References 

Cryptography
Rocky Marciano

Rocco Francis Marchegiano, better known as Rocky Marciano (September 1, 1923 – August 31, 1969), was an American boxer (1946-1956). Marciano was the World Heavyweight Boxing Champion from 9/23/1952 until 11/30/1956. He had the shortest reach of any heavyweight champion at only 68 inches (173 cm). He was also short for a champion, standing 5'10 1/2" (179 cm). Marciano is the only heavyweight champion in professional boxing history who never lost or drew (tied) in a professional match. He won 43 fights by a way of knockout or technical knockout, an 87.76% knockout rate.

Early life 
His parents were Italian immigrants.

Professional career 
Before becoming a professional fighter, Marciano had an amateur record of 10-4 (8KOs). Marciano's first professional fight was in March 1947. He won the championship from Jersey Joe Walcott on September 23, 1952.

Marciano was named fighter of the year by Ring Magazine three times. His three championship fights between 1952 and 1954 were named fights of the year by that magazine. Marciano's last title fight was against Archie Moore on September 21, 1955. Marciano was knocked down in the fight, but he got up and knocked out Moore in the 9th round. Marciano announced his retirement in a press conference on April 27, 1956.

Retirement 
Marciano considered a comeback in 1959 when Ingemar Johansson won the heavyweight championship from Floyd Patterson on June 26, 1959. However, Floyd Patterson's contract demanded a rematch with Ingemar within one year. After a period in training and thinking about a comeback, Marciano decided against it and never seriously considered a comeback again.

Death 
In 1969, on the eve of his 46th birthday, Marciano was a passenger in a small private plane, a Cessna 172, headed to Des Moines, Iowa. It was at night and bad weather set in. The pilot tried to land the plane on a small airfield outside Newton, Iowa, but the plane hit a tree two miles short of the runway. The passengers died almost instantly. He is entombed in a crypt at Forest Lawn Memorial Cemetery in Fort Lauderdale, Florida. His widow, who died five years after him at the age of 46, is entombed next to him.

References

Other websites 
 
 Rocky Marciano Biography
 Official Record 
 Official Website 
 

1923 births
1969 deaths
American boxers
Aviation deaths in the United States
Sportspeople from Massachusetts
International Boxing Hall of Fame inductees
Exponentiation by squaring

Exponentiating by squaring is an algorithm. It is used for quickly working out large integer powers of a number. It is also known as the square-and-multiply algorithm or binary exponentiation. It uses the binary expansion of the exponent. It is of quite general use, for example in modular arithmetic. 

The algorithm is believed to have first been documented in the Sanskrit book Chandah-sûtra, about 200 BC.

Squaring algorithm

The following recursive algorithm computes xn for a positive integer n where n > 0:

This algorithm is much faster than the ordinary method to compute such a value. Multiplying x by itself, n operations are needed to calculate x n. With the method shown above, only log2(n) operations are needed. 

The following algorithm computes modular exponentiation xn mod m where x is the base, n is the exponent and m is the modulus.

#include <stdio.h>
#include <stdlib.h>

unsigned long long exponentiation_by_squaring(int base, int exponent, int modulus)
{
    unsigned long long result = 1;
    while (exponent > 0)
    {
        if (exponent % 2 == 1)
        {
            result = (result * base) % modulus;
        }
        base = (base * base) % modulus;
        exponent = exponent / 2;
    }
    return result;
}

int main()
{
    int x, n, m;
    scanf("%d %d %d", &x, &n, &m);
    // x : base
    // n : exponent
    // m : modulus
    unsigned long long result = exponentiation_by_squaring(x, n, m);
    printf("%llu", result);

    return 0;
}

Algorithms
Smart card

A smart card is a card with a microchip in it. Such cards are used as a method of identification and authentication. 

Plastic cards that allow to take out money from a automated teller machine (ATM) often are smart cards nowadays (Some of them still have a magnetic stripe which holds the same information). Very often the user is identified with a PIN. If the PIN is entered correctly, money can be withdrawn. If the PIN is not entered correctly, the card is blocked (after a number of false attempts).

At first, smart cards were used in public telephones in France, in 1983. There, the card simply stored a pre-paid credit. This credit was reduced when calls were made. Another way to solve the problem is that the balance is stored in a remote database. To make calls, a (usually toll-free number) is first called. From there, additional calls can be made. This eliminates the need for cards with chips on them.

Smart cards also have many other uses, such as for making payments. These kinds of cards are used a lot in Japan, Singapore, and the Octopus card in Hong Kong.

Kinds
There are two basic kinds of smart cards:
 Simple cards only contain memory that can be read and written to. Examples of this model are phone cards, or cards for health insurance. All the processing of the data is done outside the cards
 Complex cards contain an integrated microchip. In addition to being able to store data, they can also do some of the data processing. Unlike with the simple cards, there is generally no way to directly access the memory of the card. Examples of such cards include the bank cards that can be used for withdrawing money, or the SIM cards used in mobile phones.
Both kind of cards contain a controller for managing the I/O.

Many smart cards have RFID technology that allows them to be used without inserting them into a machine. They just need to be placed on a reader. These are called "contactless smart cards" and many credit and debit cards in the 21st century are this kind.

References

Other websites
What is a smart card? (from HowStuffWorks)

Money
Authentication methods
Coprime

In mathematics, two integers (a and b) are co-prime (or relatively prime) if they share no common factors. This is sometimes written as . In other words, there is no number, other than 1, that divides both a and b evenly. In which case, the greatest common divisor (GCD, or highest common factor) of these numbers is 1.

As an example, 6 and 35 are coprime, because the factors of 6, 2 and 3, do not divide 35 evenly. On the other hand, 6 and 27 are not coprime, because 3 divides both 6 and 27. Another example is 4 and 5:
4 = 2*2*1; 
5 = 5*1 (Prime). The only common factor is 1, so they are coprime.

On the other hand, 10 and 5:
10 = 5*2 
5 = 5*1 (Prime). The common factors are 5 and 1, so they are not coprime.

Prime numbers are always coprime to each other.

 Any two consecutive integers are always coprime.
 Sum of any two coprime numbers is always coprime to their product.
 1 is trivially coprime with all numbers.
 if out of two numbers, any one number is a prime number while the other number is not a multiple of first one, then both are coprime.
 This is not applicable to negative numbers

Related pages 

 Chinese remainder theorem
 Euler's totient function
 Euler's totient theorem

References 

Number theory
Euler's totient function

In number theory, the totient of a positive integer n is the number of positive integers smaller than n which are coprime to n (they share no factors except 1). It is often written as .

For example, , because there are four numbers (1, 3, 5 and 7) which do not share any factors with 8.
The function  used here is the totient function, usually called the Euler totient or Euler's totient, after the Swiss mathematician Leonhard Euler, who studied it.
The totient function is also called Euler's phi function or simply the phi function, since the Greek letter Phi () is so commonly used for it. The cototient of n is defined as .

The totient function is important mainly because it gives the size of the multiplicative group of integers modulo n. More precisely,  is the order of the group of units of the ring . This fact, together with Lagrange's theorem, provides a proof for Euler's theorem. 

A common use of the totient function is in the RSA algorithm. The RSA algorithm is a popular method of encryption used worldwide.

For any prime number, p, .

Related pages 

 Euler's totient theorem

References 
  

Number theory
Key (cryptography)

In cryptography, a key (or cryptographic key) is a piece of information that allows control over the encryption or decryption process.

There are two basic types of cryptographic algorithms.
Symmetric algorithm: If there is just one key for encrypting and decrypting, the algorithm is called symmetric.
Asymmetric algorithm: If there are two different keys, each of which can be used only to encrypt data or only to decrypt it, the algorithm is called asymmetric.  If an algorithm is asymmetric, one person publishes a key and accepts messages encrypted with that key.  Anyone can encrypt a message, but only the person who owns the other key can decrypt it.  This is how online stores, banks, etc., work.

Key sizes
For symmetric algorithms, a minimum key size of 128 bits is recommended. For applications that need extreme security, such as top secret documents, 256 bits is recommended. Many older ciphers used 40, 56, or 64-bit keys—these have all been cracked by brute force attack because the key was too short.

Asymmetric (public key) algorithms need much longer keys to be secure. For RSA, at least 2048 bits is recommended. The largest publicly-known key that has been cracked was a 768-bit key.

Related pages 
 Key exchange

Cryptography
Hollywood, Florida

Hollywood is a city in Broward County in Florida in the United States.  In 2020, there were 153,067 people living in Hollywood. Joseph W. Young, Jr. first came to south Florida in 1920 from the state of Washington. He had also lived in California and liked what he had seen of Hollywood, California and the burgeoning movie industry in that state. He dreamed of creating a motion picture industry on the east coast, and founded Hollywood, Florida in 1920.

Young originally named his town "Hollywood by the Sea".

Young's own Mediterranean styled mansion was built in 1921 and still stands at 1055 Hollywood Boulevard, the main thoroughfare from downtown Hollywood to Hollywood Beach. The mansion is on the U.S. National Register of Historic Places.

Geography 
Hollywood is located on the coastal plain along the Atlantic Ocean in the south-eastern part of the United States, also of Florida. It is bordered by Pembroke Pines, Fort Lauderdale and Hialeah.

Climate 
In Hollywood, the summers are long, hot, oppressive, wet, and mostly cloudy and the winters are short, comfortable, humid, windy, and mostly clear. Over the course of the year, the temperature typically varies from 61 °F to 89 °F and is rarely below 48 °F or above 92 °F.

References

Other websites 

 City of Hollywood official website
 Hollywood Historical Society
Hollywood-Specific Alcohol Use Stats

Cities in Florida
Magnetic stripe card

A Magnetic stripe card is a plastic card which has a magnetic stripe on it. Different kinds of information can be stored on the magnetic stripe. Such stripes are usually made of small particles of iron (or another metal). Information is stored by changing the magnetism of the particles, as with magnetic tape
Today such cards are widely used for:
 Banking (debit or credit cards)
 Tickets issued for transportation or in parking lots.
 Keys in hotels and other buildings
 Systems to track working hours in companies
There are different ways in which the data is stored on the card. But all of them are read in much the same way, by "swiping" (sliding the card through a slot) on a machine called a reader. These readers can be separate from or built into other machines such as a payment terminal in a cash register or point of sale system.

Similar cards, which can also do calculations themselves, are called smart cards.

Details 
The standard ISO 7811 specifies the format in which information is stored on these cards. A magnetic stripe holds about 1024 bits of information, which is arranged in three tracks. The first track holds 76 alphanumeric characters, encoded in 7 bit per character. The two other tracks  hold 37 and 104 numeric characters, encoded with 5 bits per character. The first two tracks can only be read, the third track can also be written to. 

Cards that are used for banking used to store the PIN as a hash value on the magnetic stripe. Today, the ATM calculates the hash value, and transmits it to the server of the bank, which does the comparison. Storing the PIN in the ATM is no longer allowed.

In many payment cards around the world, magnetic stripes are being replaced with a more secure technology called EMV. Most of these cards, though, still have magnetic stripes to be used in places which do not yet work with EMV.

References

Other websites
 Magnetic Stripe Formats 
 A Brief History of Reprogrammable Card Technology (2012)   

Identification documents
Magnetism
Authentication methods
Payphone

A payphone is a telephone that lets the public make phone calls if they pay for them first.  Many payphones accept coins, but some can accept credit cards, debit cards, and phone cards as well. In the 20th century they were very often used, especially in cities. When people used more mobile phones, payphones quickly became rarer in small towns, and later also in cities.

Related pages
 Telephone box

Telephone
Sápmi

Sápmi (as its name is in Northern Sámi language), in English commonly known as Lapland (), is the most northern part of Fennoscandia. Fennoscandia is a peninsula in northern Europe.

The area of Sápmi is shared between four countries: Norway, Sweden, Finland and Russia. In Norway, as far south as Hedmark county, there are areas with many Sámi people.

The original people of Sápmi are the Sámi. They are now a minority there. The Sámi people are sometimes called Lapps, but this word has a negative association and is something most Sámi dislike being called.

The weather of Sápmi is cold. Summer is short. There are big hills with no trees on top of them. Reindeer live in Sápmi. You can see northern lights in the sky.

Related pages 
 Finnish Lapland
 Swedish Lapland

References
Judah

The Kingdom of Judah was an ancient Jewish kingdom that existed in the southern part of the Levant. It was on the western shore of the Dead Sea. Its main cities were Jerusalem and Hebron. It existed from the 9th or 8th century BC, up until 586 BC.

After the death of Saul, Israel picked David to rule them. (1 Chronicles 11:1) After the death of King Solomon, son of David, ten of the twelve of the tribes of Israel did not want Solomon's son, Rehoboam to lead them. This caused the kingdom to split the Northern Kingdom, the Kingdom of Israel and the Southern Kingdom, the Kingdom of Judah. Jerusalem was the capital of the Kingdom of Judah.

In 586 BC, the king of Babylon, Nebuchadnezzar II, took over Jerusalem and destroyed Judah.

References 

6th-century BC disestablishments
Former monarchies of Asia
Former countries in the Middle East
Ancient Israel and Judah
Gantt chart

A Gantt chart is a type of bar chart. It is a tool of project management invented by the engineer Henry L. Gantt in the 1910s. The chart illustrates a project schedule. 

Gantt charts show the start and finish dates of the elements of a project. Gantt charts show dependency between activities. It means that some activities can begin only after other activities are finished. If activities are independent, they can go on at the same time (though the converse is not necessarily true). Gantt charts can be used to show current schedule status using percent-complete shadings and a vertical "TODAY" line as shown here.

Gantt chart also helps in scheduling, managing, and monitoring specific tasks and resources in a project. The chart shows the project timeline, which includes scheduled and completed work over a period. The Gantt chart aids project managers in communicating project status or plans and also helps ensure the project remains on track.

They are now a common charting technique, but Gantt charts were thought revolutionary when first introduced. The charts are also used in information technology to represent data that has been collected.

Horizontal bars of different lengths represent the project timeline, which can include task sequences, duration, and the start and end dates for each task. The horizontal bar also shows how much of a task requires completion.

References 

Planning
Charts
Mind map

A mind map is a drawing used to show words, ideas, tasks or other things. Everything is written around a word or idea in the middle. This word or idea is the main topic of the mind map, and the things linked to it are related to the main idea. It is used to store and order ideas, and is very useful for study, ordering things, solving problems, and making choices.

Other websites 

Mindmapping for offices, Website 

Diagrams
Learning
Dia

Dia is open source software that is used to make diagrams. It lets people draw many different types of technical drawings, for example flow charts and circuit diagrams. Technical diagrams are needed when doing work in subjects such as electronics and resistant materials. A flow chart can also be used to show how to plan out how to solve a problem, for example, how to bake a cake.

Other websites 
Dia Project Homepage
Free Software Magazine 
Addictive Tips

Diagramming software
Free software
Talent

A talent (or aptitude) is the natural ability to do something better than most people. Talent is often confused with skill. We can develop and improve skill but not talent. Talent is the information written in genes when we are born. That information never changes in our lifetime. It can only be inherited by our children. Talent means only a greater potential for doing something. But talent is not enough. To get good results we need also practice. Even the greatest talent without practice will not give good skill. But on the other hand, even years of practice without talent will not give good results either. If somebody has no talent for music but learns to play piano several hours a day for two years, they will achieve some skill but never become a great musician.

Related pages 
 Genius
 Gifted education
 Mensa

References

Psychology
Giftedness
Human skills
Talent (measurement)

A talent (Latin: talentum, from Ancient Greek:  "scale, balance") is an ancient unit of mass; it corresponded generally to the mass of water in the volume of an amphora, i.e. a one-foot cube.

The Babylonians and Sumerians had a system in which there were 60 shekels in a mina and 60 minas in a talent (in Ancient Greece one talent was 26 kg of silver). The Roman talent consisted of 100 libra (pounds) which were smaller in magnitude than the mina.

When used as a measure of money, it refers to a talent-weight of gold or of silver. The gold talent is reported as weighing roughly the same as a person, and so perhaps 50 kg (>110 lb avoirdupois). Some authorities say that the talent typically weighed about 33 kg (>72 lb) varying from 20 to 40 kg. In June, 2018, the international price of gold was about US $41,155.69 per kilogram. One gram costs about $38. At this price, a talent (33 kg) would be worth about $1,400,116.57. Similarly, in February 2016, the price of silver was about $15 per troy ounce or about 50 cents per gram, so a 33 kg silver talent would be worth about $16,500. Thus when we read that King Auletes of Egypt paid Gaius Julius Caesar the sum of 6,000 talents of gold to grant him the status of a "Friend and Ally of the Roman People," this amount would be worth about US$8,400,000,000 today! These estimates are only rough values, because they are based on modern estimates.The value of silver in comparison to gold drastically changed. This is because of the output of the Spanish silver mines in the New World. In ancient times the same amount of silver was often worth more than gold. The estimates do not account for the less technical mining ability of the time, nor that there were still native deposits available. Later in Roman history, during the medieval Byzantine period, the emperor Basil II was said to have stockpiled the legendary amount of 200,000 talents of gold which, in modern terms, would be worth approximately US$280,023,314,760. At any rate, he did save enough money that the Byzantine government was able to remit all taxes paid during the final two years of his reign.

Another way to calculate the modern equivalent to a talent is from its use in estimating military pay. During the Peloponnesian war in Ancient Greece, a talent was the amount of silver needed to pay the crew of a trireme for one month. Hellenistic mercenaries were commonly paid one drachma for every day of service, which was a good salary in the post-Alexander (III) days. 6,000 drachma made a talent.

The talent as a unit of coinage is mentioned in the New Testament in Jesus' parable of the talents. One talent was an incredible amount of money.

Old units of measurement
Units of mass
Phototroph

Phototrophs (photo = light, troph = nutrition) or photoautotrophs are organisms which carry out photosynthesis. 

With their plastids and the help of energy from sunlight, carbon dioxide and water are converted into sugar by photosynthesis. Sugar is then converted into other organic molecules which can be used in cellular functions. Such a function might be, for example, respiration. 

Botany
NTFS

NTFS is a file system developed by Microsoft. NTFS stands for New Technology File System. A file system is a way of storing computer files. Microsoft introduced it with the Windows NT operating system. 

It was made to replace the old file-system used by earlier versions of Windows, like Windows 95, Windows 98, and Windows 98SE. That file system was also used by MS-DOS and is called FAT.

A newer version of NTFS (v3.1) was used in Windows XP, Windows Server 2003, Windows Vista, and the most recent version of operating system, Windows 10. NTFS can be accessed from non-Windows operating systems such as Linux using the NTFS-3G driver.

Software
Microsoft
File system

A File system (or filesystem) is a way of storing all data on a data storage device. The data is usually organized in computer files in directories. Below the file system there is usually a physical device where the files are stored.  This might be a hard disk, USB flash drive, compact disc, or DVD. The file system might also talk to a remote server over a network where the file is stored. The file system might also only use RAM to store the files. 

The underlying storage mechanism usually has no concept of a file. A hard disk knows of disk blocks, which are numbered in a certain way. These disk blocks contain binary data (usually: large numbers). 

The file system does the translation between the large numbers, and the view the users see, that is that of files, organized in a certain way.

More recently, concepts from databases have been used to develop file systems. That way, there are two different kinds of data:
Data that holds the files
Data that is used to describe what state the files are in. This is called metadata.
It then becomes possible to always keep the file system in a consistent state. With databases, this is known as ACID. That way, an operation on a file is either done, or it is not done. There are however, no states in between. The file being written to the filesystem is no longer visible. This is usually done using transactions. But with filesystems, it is called journaling.

References 
software
Systems
David II of Scotland

David II (5 March 1324 – 22 February 1371) King of Scots, son of King Robert the Bruce by his second wife, Elizabeth de Burgh (d. 1327), was born at Dunfermline Palace, Fife.

He was married on 17 July 1328, aged only four, to Joan of the Tower (d. 1362), daughter of Edward II of England and Isabella of France. Joan was only seven years old.

At the age of five, David became King of Scotland after the death of his father on 7 June 1329. He was crowned at Scone in November 1331. 

Edward Balliol, with support from Edward III of England fought against David, so that he could become king. He defeated David at the Battle of Dupplin on 12 August 1332. Balliol was crowned king, and in July 1333, the nine year old David and his queen were sent to France for their safety. In June 1341 he came back and began to rule. In 1346 he invaded England, but was defeated and taken prisoner at the Battle of Neville's Cross on 17 October 1346, and remained in England for eleven years, living mainly in London and at Odiham in Hampshire. In October 1357 he was allowed to go back to Scotland for a payment of 100,000 marks. The money was never paid completely. 
In 1371 David died in Edinburgh Castle.

References

 Andrew of Wyntoun, The orygynale cronykil of Scotland, edited by D. Laing (Edinburgh, 1872–1879)
 John of Fordun, Chronica gentis Scotorum, edited by W. F. Skene (Edinburgh, 1871–1872)
 J. H. Burton, History of Scotland, vol. ii. (Edinburgh, 1905)
 Andrew Lang, History of Scotland, vol. i. (Edinburgh, 1900)

Further reading
 Michael Brown, The Wars of Scotland, 1214–1371. The New Edinburgh History of Scotland, volume 4. Edinburgh: Edinburgh University Press, 2004.
 Ranald Nicholson, Scotland. The Later Middle Ages. Edinburgh: Mercat Press, 1975.
 Michael Penman, David II, 1329–71: The Bruce Dynasty in Scotland. East Linton: Tuckwell Press, 2003.

1324 births
1371 deaths
Kings and Queens of Scotland
14th century in Scotland
Aurora

An aurora, also called polar light, northern light or southern light, is a natural light display in the sky. They are usually seen in the high latitudes (Arctic and Antarctic) regions. Auroras are produced when the Earth's magnetosphere is disturbed by the solar wind.

 

An aurora around the North Pole is called the Aurora borealis or 'northern lights'. Around the South Pole is the Aurora australis or 'dawn of the south' or 'southern lights'. It can be seen from long distances, stretching in the sky many hundreds of miles.

Auroras can happen at any time, however, they can only be seen at night because their light is not as intense as the light of day. Faint stars can even be seen through the aurora.

Many legends are associated with the aurora in all countries where this phenomenon regularly occurs.

How it happens 
An aurora occurs when the Sun sends off small particles into space. These particles are mainly electrons, with charge and energy, which means they contribute to electricity. Earth has a protective shield of energy around it. This is called the "magnetic field" and forms an elongated sphere around the Earth called the "magnetosphere". The Earth’s magnetic field keeps off most solar wind. 

At high-latitude areas (polar areas), the magnetic field is vertical. It does not keep off particles of the solar wind which can come from the magnetosphere and hit the particles of the air (Earth's atmosphere). When they hit, the atmosphere is heated and excited and the excess gets away, a phenomenon which we see as moving lights in the sky above 100 km altitude typically. An aurora can be especially bright following a solar flare and coronal mass ejection (CME) when the charged particles rips through the electromagnetic field because of their power.

On other planets 

Auroral phenomena have been observed on other planets that have a magnetic field, such as Jupiter, and Saturn. It is believed to be a widespread phenomenon in the Solar System and beyond.

References 

Earth sciences
Meteorology