It was then notated that if triangle ABC is a right triangle, with a right angle at C, then c2 = a2 + b2. Earlier, the converse of this theorem appears to have been used. This became proposition number 47 from Book I of Euclid's Elements ("Pythagorean," 2007).
Although this theorem is traditionally associated with Pythagoras, it is actually much older.
More than a millennium before the birth of Pythagoras, four Babylonian tablets were created demonstrating some knowledge of this theorem, circa 1900-1600 B.C.. At the very least, these works represent the knowledge of at least special integers known as Pythagorean triples that satisfy it.
In addition, the Rhind papyrus, created around 1650 B.C., shows that Egyptians had knowledge of the theorem as well. However, the first proof of this theorem is still credited to Pythagoras, despite the fact that some scholars believe it was independently discovered in several different cultures ("Pythagorean," 2007).
In Euclid's Book I of the Elements, the work ends with the famous 'windmill' proof of the Pythagorean theorem. In Book VI of the Elements, Euclid later gives an even easier demonstration of the theorem, "using the proposition that the areas of similar triangles are proportionate to the squares of their corresponding sides. Apparently, Euclid invented the windmill proof so that he could place the Pythagorean theorem as the capstone to Book I" ("Pythagorean,"...
Pythagorean Triple is a term derived specifically from the theorem that a right triangle displays the equation. This theorem, named aptly the Pythagorean Theorem, states that "in any right-angled triangle, the square on the hypotenuse equals the sum of the squares on the other two sides" (Mack, 2010). How do the two relate? A Pythagorean Triple is simply the term derived for a, b, and c, provided that 1) a,
Pythagorean Theorem Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information, then they
Mathematical Happenings between Ancient Egypt and the 11th Century: Thales and Pythagoras Inspire the Grecian World In the 6th century, mathematics came to Greece and helped launch the next stage of mathematical evolution in the history of the West. Responsible for this movement were two people—first, Thales of Miletus; second, Pythagoras of Samos (Lewinter & Widulski, 2002). This paper will explain the important contributions that these two mathematicians made in this
He looks at three methods: history (melding information about the diverse geographical origins of algebra with the problems themselves), multiple representations (using notation, narrative, geometric, graphical, and other representations together to build understanding), and the object concept of function (teaching functions without generalizing about how traits of an individual relate to traits of a group). The article serves to offer some inventive solutions to a common problem in math
Chinese Mathematics In ancient China, the science of mathematics was subsumed under the larger practice of suan chu, or the "art of calculation." The Chinese are believed to be one of the first civilizations to develop and use the decimal numeral system. Their early mathematical studies have influenced science among neighboring Asian countries and beyond. This paper examines the history of mathematical knowledge in China. It looks at the early Chinese achievements
Euclid of Alexandria: 325 B.C. ~ 265 B.C. (?) The dates are not exact as little is known about Euclid's life. It is generally believed that he studied under the students of Plato and it is known that he established a school of mathematics and taught at the library in Alexandria. His most well-known work is The Elements, which is a wonderfully organized development of the plane and solid geometry, geometric
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