Pythagorean Theorem
Pythagorean theorem
The Pythagorean theorem is one of the most famous theorems of geometry. It is often attributed to Pythagoras of Samos (Greece), who lived in the sixth century b.c. The theorem states that in any right triangle, the square of the hypotenuse of the triangle (the side opposite the right angle) is equal to the sum of the squares of the other two sides, or c^{2} = a^{2} + b^{2}.
This theorem was probably known long before the time of Pythagoras; it is thought to have been used by the ancient Egyptians and Babylonians. Nevertheless, Pythagoras (or some member of his school) is credited with the first proof of the theorem.
The converse of the Pythagorean theorem is also true. That is, if a triangle with sides a, b, and c has c^{2} = a^{2} + b^{2}, we know that the triangle is a right triangle.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"Pythagorean Theorem." UXL Encyclopedia of Science. . Encyclopedia.com. 17 Jun. 2019 <https://www.encyclopedia.com>.
"Pythagorean Theorem." UXL Encyclopedia of Science. . Encyclopedia.com. (June 17, 2019). https://www.encyclopedia.com/science/encyclopediasalmanacstranscriptsandmaps/pythagoreantheorem
"Pythagorean Theorem." UXL Encyclopedia of Science. . Retrieved June 17, 2019 from Encyclopedia.com: https://www.encyclopedia.com/science/encyclopediasalmanacstranscriptsandmaps/pythagoreantheorem
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.
Pythagorean theorem
Py·thag·o·re·an the·o·rem / pəˌ[unvoicedth]agəˈrēən; pī/ a theorem attributed to Pythagoras that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"Pythagorean theorem." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. 17 Jun. 2019 <https://www.encyclopedia.com>.
"Pythagorean theorem." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. (June 17, 2019). https://www.encyclopedia.com/humanities/dictionariesthesaurusespicturesandpressreleases/pythagoreantheorem
"Pythagorean theorem." The Oxford Pocket Dictionary of Current English. . Retrieved June 17, 2019 from Encyclopedia.com: https://www.encyclopedia.com/humanities/dictionariesthesaurusespicturesandpressreleases/pythagoreantheorem
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.
Pythagorean Theorem
Pythagorean Theorem
One of the most famous theorems in all mathematics, often attributed to Pythagoras of Samos (Greece) in the sixth century BC, states the sides a, b, and c of a right triangle satisfy the relation c^{2} = a^{2} + b^{2}, where c is the length of the hypotenuse of the triangle and a and b are the lengths of the other two sides.
This theorem was known earlier to the Babylonians, Chinese, and Egyptians. Pythagoras is said to have traveled to Babylon as a young man, where he could have learned the famous theorem. Nevertheless, Pythagoras (or some member of his school) is credited with the first proof of the theorem.
The converse of the Pythagorean theorem is also true. That is if a triangle with sides a, b, and c has a^{2} = b^{2} + c^{2}, we know that the triangle is a right triangle.
A special form of the theorem was used by the Egyptians for making square corners when they resurveyed land adjacent to the Nile river after the annual flood. They used a rope loop with 12 knots tied at equal intervals along the rope. Three of the knots were used as the vertices of a triangle. Since 3^{2} + 4^{2} = 5^{2} we know, by the converse of the Pythagorean theorem, that we have a right triangle.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"Pythagorean Theorem." The Gale Encyclopedia of Science. . Encyclopedia.com. 17 Jun. 2019 <https://www.encyclopedia.com>.
"Pythagorean Theorem." The Gale Encyclopedia of Science. . Encyclopedia.com. (June 17, 2019). https://www.encyclopedia.com/science/encyclopediasalmanacstranscriptsandmaps/pythagoreantheorem1
"Pythagorean Theorem." The Gale Encyclopedia of Science. . Retrieved June 17, 2019 from Encyclopedia.com: https://www.encyclopedia.com/science/encyclopediasalmanacstranscriptsandmaps/pythagoreantheorem1
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.
Pythagorean Theorem
Pythagorean theorem
One of the most famous theorems of geometry , often attributed to Pythagoras of Samos (Greece) in the sixth century b.c., states the sides a, b, and c of a right triangle satisfy the relation c2 = a2 + b2 where c is the length of the hypotenuse of the triangle and a and b are the lengths of the other two sides.
This theorem was likely to have been known earlier to be the Babylonians, Pythagoras is said to have traveled to Babylon as a young man, where he could have learned the famous theorem. Nevertheless, Pythagoras (or some member of his school) is credited with the first proof of the theorem.
The converse of the Pythagorean theorem is also true. That is if a triangle with sides a, b, and c has a2 = b2 + c2, we know that the triangle is a right triangle.
A special form of the theorem was used by the Egyptians for making square corners when they resurveyed the land adjacent to the Nile river after the annual flood. They used a rope loop with 12 knots tied at equal intervals along the rope. Three of the knots were used as the vertices of a triangle. Since 32 + 42 = 52 we know, by the converse of the Pythagorean theorem, that we have a right triangle.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"Pythagorean Theorem." The Gale Encyclopedia of Science. . Encyclopedia.com. 17 Jun. 2019 <https://www.encyclopedia.com>.
"Pythagorean Theorem." The Gale Encyclopedia of Science. . Encyclopedia.com. (June 17, 2019). https://www.encyclopedia.com/science/encyclopediasalmanacstranscriptsandmaps/pythagoreantheorem0
"Pythagorean Theorem." The Gale Encyclopedia of Science. . Retrieved June 17, 2019 from Encyclopedia.com: https://www.encyclopedia.com/science/encyclopediasalmanacstranscriptsandmaps/pythagoreantheorem0
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.