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Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation":

where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides.

Although it is often argued that knowledge of the theorem predates him, the theorem is named after the ancient Greek mathematician Pythagoras (c. 570 – c. 495 BC) as it is he who, by tradition, is credited with its first recorded proof.There is some evidence that Babylonian mathematicians understood the formula, although little of it indicates an application within a mathematical framework.Mesopotamian, Indian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases.

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This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Pythagorean_theorem

Pythagorean expectation

Pythagorean expectation is a formula invented by Bill James to estimate how many games a baseball team "should" have won based on the number of runs they scored and allowed. Comparing a team's actual and Pythagorean winning percentage can be used to evaluate how lucky that team was (by examining the variation between the two winning percentages). The name comes from the formula's resemblance to the Pythagorean theorem.

The basic formula is:

where Win is the winning ratio generated by the formula. The expected number of wins would be the expected winning ratio multiplied by the number of games played.

Empirical origin

Empirically, this formula correlates fairly well with how baseball teams actually perform. However, statisticians since the invention of this formula found it to have a fairly routine error, generally about three games off. For example, in 2002, the New York Yankees scored 897 runs and allowed 697 runs. According to James' original formula, the Yankees should have won 62.35% of their games.

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This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Pythagorean_expectation

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• views: 297370

This video covers how to use Pythagoras' Theorem, which helps us to find the length of a missing side in a right-angle triangle. This video is suitable for ma...

This video covers how to use Pythagoras' Theorem, which helps us to find the length of a missing side in a right-angle triangle. This video is suitable for maths courses around the world. KS3 - All on your course GCSE Foundation - All on your course GCSE Higher - All on your course A-level - All on your course Maths Playlist: https://www.youtube.com/playlist?list=PLidqqIGKox7XPh1QacLRiKto_UlnRIEVh GCSE Chemistry playlist: https://www.youtube.com/watch?v=fN8kH9Vvqo0&list=PLidqqIGKox7WeOKVGHxcd69kKqtwrKl8W GCSE Biology Playlist: https://www.youtube.com/watch?v=--dIBinUdeU&list=PLidqqIGKox7X5UFT-expKIuR-i-BN3Q1g GCSE Physics Playlist: https://www.youtube.com/watch?v=aHVJfRxeAxo&list=PLidqqIGKox7UVC-8WC9djoeBzwxPeXph7

https://wn.com/Gcse_Maths_Pythagoras'_Theorem_And_How_To_Use_It_120

This video covers how to use Pythagoras' Theorem, which helps us to find the length of a missing side in a right-angle triangle. This video is suitable for maths courses around the world. KS3 - All on your course GCSE Foundation - All on your course GCSE Higher - All on your course A-level - All on your course Maths Playlist: https://www.youtube.com/playlist?list=PLidqqIGKox7XPh1QacLRiKto_UlnRIEVh GCSE Chemistry playlist: https://www.youtube.com/watch?v=fN8kH9Vvqo0&list=PLidqqIGKox7WeOKVGHxcd69kKqtwrKl8W GCSE Biology Playlist: https://www.youtube.com/watch?v=--dIBinUdeU&list=PLidqqIGKox7X5UFT-expKIuR-i-BN3Q1g GCSE Physics Playlist: https://www.youtube.com/watch?v=aHVJfRxeAxo&list=PLidqqIGKox7UVC-8WC9djoeBzwxPeXph7

• published: 19 Sep 2021
• views: 297370

0:44

Pythagorean theorem water demo

• Order: Reorder
• Duration: 0:44
• Uploaded Date: 14 Apr 2009
• views: 2932831

Wheel with liquid demonstrates the Pythagorean theorem at Brentwood.

Wheel with liquid demonstrates the Pythagorean theorem at Brentwood.

https://wn.com/Pythagorean_Theorem_Water_Demo

Wheel with liquid demonstrates the Pythagorean theorem at Brentwood.

• published: 14 Apr 2009
• views: 2932831

12:55

An Introduction to the Pythagorean Theorem | Math with Mr. J

• Order: Reorder
• Duration: 12:55
• Uploaded Date: 21 Apr 2023
• views: 583544

Welcome to An Introduction to the Pythagorean Theorem with Mr. J! Need help with the Pythagorean Theorem? You're in the right place! Whether you're just starti...

Welcome to An Introduction to the Pythagorean Theorem with Mr. J! Need help with the Pythagorean Theorem? You're in the right place! Whether you're just starting out, or need a quick refresher, this is the video for you if you're looking for help with the Pythagorean Theorem. Mr. J will go through examples of right triangles and explain the Pythagorean Theorem. About Math with Mr. J: This channel offers instructional videos that are directly aligned with math standards. Teachers, parents/guardians, and students from around the world have used this channel to help with math content in many different ways. All material is absolutely free. #MathWithMrJ Click Here to Subscribe to the Greatest Math Channel On Earth: https://goo.gl/XHTrfY Follow Mr. J on Twitter: @MrJMath5 Email: [email protected] Music: https://www.bensound.com/royalty-free-music Hopefully this video is what you're looking for when it comes to the Pythagorean Theorem. Have a great rest of your day and thanks again for watching! ✌️✌️✌️ ✅ Thanks to Aloud, this video has been dubbed into Spanish and Portuguese. #DubbedWithAloud English This video has been dubbed into Spanish (United States) and Portuguese (Brazil) using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu. Spanish Este video ha sido doblado al español con voz artificial con https://aloud.area120.google.com para aumentar la accesibilidad. Puede cambiar el idioma de la pista de audio en el menú Configuración. Portuguese Este vídeo foi dublado para o português usando uma voz artificial via https://aloud.area120.google.com para melhorar sua acessibilidade. Você pode alterar o idioma do áudio no menu Configurações.

https://wn.com/An_Introduction_To_The_Pythagorean_Theorem_|_Math_With_Mr._J

Welcome to An Introduction to the Pythagorean Theorem with Mr. J! Need help with the Pythagorean Theorem? You're in the right place! Whether you're just starting out, or need a quick refresher, this is the video for you if you're looking for help with the Pythagorean Theorem. Mr. J will go through examples of right triangles and explain the Pythagorean Theorem. About Math with Mr. J: This channel offers instructional videos that are directly aligned with math standards. Teachers, parents/guardians, and students from around the world have used this channel to help with math content in many different ways. All material is absolutely free. #MathWithMrJ Click Here to Subscribe to the Greatest Math Channel On Earth: https://goo.gl/XHTrfY Follow Mr. J on Twitter: @MrJMath5 Email: [email protected] Music: https://www.bensound.com/royalty-free-music Hopefully this video is what you're looking for when it comes to the Pythagorean Theorem. Have a great rest of your day and thanks again for watching! ✌️✌️✌️ ✅ Thanks to Aloud, this video has been dubbed into Spanish and Portuguese. #DubbedWithAloud English This video has been dubbed into Spanish (United States) and Portuguese (Brazil) using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu. Spanish Este video ha sido doblado al español con voz artificial con https://aloud.area120.google.com para aumentar la accesibilidad. Puede cambiar el idioma de la pista de audio en el menú Configuración. Portuguese Este vídeo foi dublado para o português usando uma voz artificial via https://aloud.area120.google.com para melhorar sua acessibilidade. Você pode alterar o idioma do áudio no menu Configurações.

• published: 21 Apr 2023
• views: 583544

3:56

Field Dimensions and the Pythagorean Theorem - A word Problem

• Order: Reorder
• Duration: 3:56
• Uploaded Date: 07 Dec 2024
• views: 80

https://wn.com/Field_Dimensions_And_The_Pythagorean_Theorem_A_Word_Problem

• published: 07 Dec 2024
• views: 80

5:17

How many ways are there to prove the Pythagorean theorem? - Betty Fei

• Order: Reorder
• Duration: 5:17
• Uploaded Date: 11 Sep 2017
• views: 3701839

Check out our Patreon page: https://www.patreon.com/teded View full lesson: https://ed.ted.com/lessons/how-many-ways-are-there-to-prove-the-pythagorean-theorem...

Check out our Patreon page: https://www.patreon.com/teded View full lesson: https://ed.ted.com/lessons/how-many-ways-are-there-to-prove-the-pythagorean-theorem-betty-fei What do Euclid, 12-year-old Einstein, and American President James Garfield have in common? They all came up with elegant proofs for the famous Pythagorean theorem, one of the most fundamental rules of geometry and the basis for practical applications like constructing stable buildings and triangulating GPS coordinates. Betty Fei details these three famous proofs. Lesson by Betty Fei, directed by Nick Hilditch. Thank you so much to our patrons for your support! Without you this video would not be possible. Steph, Jack Ta, Jose Fernandez-Calvo, PnDAA , Marcel Trompeter-Petrovic, Radoslava Vasileva, Sandra Tersluisen, Fabian Amels, Sammie Goh, Mattia Veltri, Quentin Le Menez, Sarabeth Knobel, Yuh Saito, Joris Debonnet, Martin Lõhmus, Patrick leaming, Heather Slater, Muhamad Saiful Hakimi bin Daud, Dr Luca Carpinelli, Janie Jackson, Jeff Hanevich, Christophe Dessalles, Arturo De Leon, Delene McCoy, Eduardo Briceño, Bill Feaver, Ricardo Paredes, Joshua Downing, Jonathan Reshef, David Douglass, Grant Albert, Paul Coupe.

https://wn.com/How_Many_Ways_Are_There_To_Prove_The_Pythagorean_Theorem_Betty_Fei

Check out our Patreon page: https://www.patreon.com/teded View full lesson: https://ed.ted.com/lessons/how-many-ways-are-there-to-prove-the-pythagorean-theorem-betty-fei What do Euclid, 12-year-old Einstein, and American President James Garfield have in common? They all came up with elegant proofs for the famous Pythagorean theorem, one of the most fundamental rules of geometry and the basis for practical applications like constructing stable buildings and triangulating GPS coordinates. Betty Fei details these three famous proofs. Lesson by Betty Fei, directed by Nick Hilditch. Thank you so much to our patrons for your support! Without you this video would not be possible. Steph, Jack Ta, Jose Fernandez-Calvo, PnDAA , Marcel Trompeter-Petrovic, Radoslava Vasileva, Sandra Tersluisen, Fabian Amels, Sammie Goh, Mattia Veltri, Quentin Le Menez, Sarabeth Knobel, Yuh Saito, Joris Debonnet, Martin Lõhmus, Patrick leaming, Heather Slater, Muhamad Saiful Hakimi bin Daud, Dr Luca Carpinelli, Janie Jackson, Jeff Hanevich, Christophe Dessalles, Arturo De Leon, Delene McCoy, Eduardo Briceño, Bill Feaver, Ricardo Paredes, Joshua Downing, Jonathan Reshef, David Douglass, Grant Albert, Paul Coupe.

• published: 11 Sep 2017
• views: 3701839

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1:57

Pythagorean Theorem | MathHelp.com

Need a custom math course? Visit https://www.MathHelp.com. This lesson covers the Pythago...

published: 18 Jan 2016

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Pythagorean Theorem | MathHelp.com

Pythagorean Theorem | MathHelp.com

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• published: 18 Jan 2016
• views: 1587194

Need a custom math course? Visit https://www.MathHelp.com. This lesson covers the Pythagorean Theorem, which states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse, or a^2 + b^2 = c^2. Students are then asked to find missing side lengths of right triangles using the Pythagorean Theorem.

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11:04

Pythagorean Theorem

This geometry video tutorial provides a basic introduction into the pythagorean theorem. ...

published: 29 Dec 2017

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Pythagorean Theorem

Pythagorean Theorem

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• published: 29 Dec 2017
• views: 592599

This geometry video tutorial provides a basic introduction into the pythagorean theorem. It explains how to use it to find missing sides and solve for x. In addition, it provides examples of solving word problems using pythagorean theorem for shapes such as right triangles, squares, rhombuses, and trapezoids. This video explains how to calculate the perimeter of a rhombus and the area of a trapezoid using the pythagorean theorem as well as the side length of a square given the length of the diagonal. This geometry video contains plenty of examples and practice problems. Polygons: https://www.youtube.com/watch?v=E_-3ulbtcLk Quadrilaterals: https://www.youtube.com/watch?v=ogcH3eM5beM Points, Lines, Planes, & Segments: https://www.youtube.com/watch?v=dDWjhRfBsKM Similar Triangles: https://www.youtube.com/watch?v=YiFwvAFk-xs Pythagorean Theorem: https://www.youtube.com/watch?v=d8EA5TxGzcY _________________________________ The Distance Formula: https://www.youtube.com/watch?v=YDvUy5VYm9E Distance Between 2 Points - 3D: https://www.youtube.com/watch?v=0c6cP2zLC2c Special Right Triangles - 30 60 90: https://www.youtube.com/watch?v=p70UBGCHZrQ Special Right Triangles - 45 45 90: https://www.youtube.com/watch?v=xzMirNSv1d0 Trigonometric Ratios: https://www.youtube.com/watch?v=9-eHMMpQC2k _________________________________ Angle of Elevation Word Problems: https://www.youtube.com/watch?v=uyKvSe6Ltgs Finding The Missing Side of a triangle: https://www.youtube.com/watch?v=tielQ3ejh70 Finding The Missing Angle of a Triangle: https://www.youtube.com/watch?v=4Dv5IFqATrc Two Triangle Trigonometry Problems: https://www.youtube.com/watch?v=OTP885mApV8 How To Find The Area of a Rectangle: https://www.youtube.com/watch?v=M8JdRHeQBW8 ________________________________ Final Exams and Video Playlists: https://www.video-tutor.net/ Full-Length Videos and Worksheets: https://www.patreon.com/MathScienceTutor/collections

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12:55

Math Antics - The Pythagorean Theorem

Learn more at mathantics.com Visit http://www.mathantics.com for more Free math videos and...

published: 03 May 2017

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Math Antics - The Pythagorean Theorem

Math Antics - The Pythagorean Theorem

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• published: 03 May 2017
• views: 2786378

Learn more at mathantics.com Visit http://www.mathantics.com for more Free math videos and additional subscription based content!

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0:40

Pythagoras’ theorem, an animated explanation!

(a^2)+(b^2) does indeed equal (c^2) !!! A visual proof! Technical info: Computer Generate...

published: 21 Jan 2015

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Pythagoras’ theorem, an animated explanation!

Pythagoras’ theorem, an animated explanation!

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• published: 21 Jan 2015
• views: 148301

(a^2)+(b^2) does indeed equal (c^2) !!! A visual proof! Technical info: Computer Generated motion graphics, created in Adobe After effects. Credit: Sound effects sourced from: pacdv.com freewavesamples.com soundbible.com

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0:19

Pythagoras' Theorem edit 🐐🔥 | #shorts #maths

published: 18 Feb 2023

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Pythagoras' Theorem edit 🐐🔥 | #shorts #maths

Pythagoras' Theorem edit 🐐🔥 | #shorts #maths

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• published: 18 Feb 2023
• views: 11688053

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6:31

GCSE Maths - Pythagoras' Theorem And How To Use It #120

This video covers how to use Pythagoras' Theorem, which helps us to find the length of a m...

published: 19 Sep 2021

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GCSE Maths - Pythagoras' Theorem And How To Use It #120

GCSE Maths - Pythagoras' Theorem And How To Use It #120

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• published: 19 Sep 2021
• views: 297370

This video covers how to use Pythagoras' Theorem, which helps us to find the length of a missing side in a right-angle triangle. This video is suitable for maths courses around the world. KS3 - All on your course GCSE Foundation - All on your course GCSE Higher - All on your course A-level - All on your course Maths Playlist: https://www.youtube.com/playlist?list=PLidqqIGKox7XPh1QacLRiKto_UlnRIEVh GCSE Chemistry playlist: https://www.youtube.com/watch?v=fN8kH9Vvqo0&list=PLidqqIGKox7WeOKVGHxcd69kKqtwrKl8W GCSE Biology Playlist: https://www.youtube.com/watch?v=--dIBinUdeU&list=PLidqqIGKox7X5UFT-expKIuR-i-BN3Q1g GCSE Physics Playlist: https://www.youtube.com/watch?v=aHVJfRxeAxo&list=PLidqqIGKox7UVC-8WC9djoeBzwxPeXph7

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0:44

Pythagorean theorem water demo

Wheel with liquid demonstrates the Pythagorean theorem at Brentwood.

published: 14 Apr 2009

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Pythagorean theorem water demo

Pythagorean theorem water demo

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• published: 14 Apr 2009
• views: 2932831

Wheel with liquid demonstrates the Pythagorean theorem at Brentwood.

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12:55

An Introduction to the Pythagorean Theorem | Math with Mr. J

Welcome to An Introduction to the Pythagorean Theorem with Mr. J! Need help with the Pytha...

published: 21 Apr 2023

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An Introduction to the Pythagorean Theorem | Math with Mr. J

An Introduction to the Pythagorean Theorem | Math with Mr. J

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• published: 21 Apr 2023
• views: 583544

Welcome to An Introduction to the Pythagorean Theorem with Mr. J! Need help with the Pythagorean Theorem? You're in the right place! Whether you're just starting out, or need a quick refresher, this is the video for you if you're looking for help with the Pythagorean Theorem. Mr. J will go through examples of right triangles and explain the Pythagorean Theorem. About Math with Mr. J: This channel offers instructional videos that are directly aligned with math standards. Teachers, parents/guardians, and students from around the world have used this channel to help with math content in many different ways. All material is absolutely free. #MathWithMrJ Click Here to Subscribe to the Greatest Math Channel On Earth: https://goo.gl/XHTrfY Follow Mr. J on Twitter: @MrJMath5 Email: [email protected] Music: https://www.bensound.com/royalty-free-music Hopefully this video is what you're looking for when it comes to the Pythagorean Theorem. Have a great rest of your day and thanks again for watching! ✌️✌️✌️ ✅ Thanks to Aloud, this video has been dubbed into Spanish and Portuguese. #DubbedWithAloud English This video has been dubbed into Spanish (United States) and Portuguese (Brazil) using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu. Spanish Este video ha sido doblado al español con voz artificial con https://aloud.area120.google.com para aumentar la accesibilidad. Puede cambiar el idioma de la pista de audio en el menú Configuración. Portuguese Este vídeo foi dublado para o português usando uma voz artificial via https://aloud.area120.google.com para melhorar sua acessibilidade. Você pode alterar o idioma do áudio no menu Configurações.

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3:56

Field Dimensions and the Pythagorean Theorem - A word Problem

published: 07 Dec 2024

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Field Dimensions and the Pythagorean Theorem - A word Problem

Field Dimensions and the Pythagorean Theorem - A word Problem

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5:17

How many ways are there to prove the Pythagorean theorem? - Betty Fei

Check out our Patreon page: https://www.patreon.com/teded View full lesson: https://ed.te...

published: 11 Sep 2017

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How many ways are there to prove the Pythagorean theorem? - Betty Fei

How many ways are there to prove the Pythagorean theorem? - Betty Fei

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• published: 11 Sep 2017
• views: 3701839

Check out our Patreon page: https://www.patreon.com/teded View full lesson: https://ed.ted.com/lessons/how-many-ways-are-there-to-prove-the-pythagorean-theorem-betty-fei What do Euclid, 12-year-old Einstein, and American President James Garfield have in common? They all came up with elegant proofs for the famous Pythagorean theorem, one of the most fundamental rules of geometry and the basis for practical applications like constructing stable buildings and triangulating GPS coordinates. Betty Fei details these three famous proofs. Lesson by Betty Fei, directed by Nick Hilditch. Thank you so much to our patrons for your support! Without you this video would not be possible. Steph, Jack Ta, Jose Fernandez-Calvo, PnDAA , Marcel Trompeter-Petrovic, Radoslava Vasileva, Sandra Tersluisen, Fabian Amels, Sammie Goh, Mattia Veltri, Quentin Le Menez, Sarabeth Knobel, Yuh Saito, Joris Debonnet, Martin Lõhmus, Patrick leaming, Heather Slater, Muhamad Saiful Hakimi bin Daud, Dr Luca Carpinelli, Janie Jackson, Jeff Hanevich, Christophe Dessalles, Arturo De Leon, Delene McCoy, Eduardo Briceño, Bill Feaver, Ricardo Paredes, Joshua Downing, Jonathan Reshef, David Douglass, Grant Albert, Paul Coupe.

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Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation":

where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides.

Although it is often argued that knowledge of the theorem predates him, the theorem is named after the ancient Greek mathematician Pythagoras (c. 570 – c. 495 BC) as it is he who, by tradition, is credited with its first recorded proof.There is some evidence that Babylonian mathematicians understood the formula, although little of it indicates an application within a mathematical framework.Mesopotamian, Indian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases.

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This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Pythagorean_theorem

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Ancient Greek letter and math symbol pi. Credit. Shisma/Wikimedia Commons/ CC BY 4.0 ... The number’s first three digits are 3.14 ... The famous mathematician used the Pythagorean Theorem to find that the number was between 3 1/7 and 3 10/71 ... 3.14159265358979.

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