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580 BCE
Pythagoras of Samos
G:\Europeana 1st\tangram1.jpg -
500 BCE
Pythagorean theorem
Is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
" The square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides" -
500 BCE
pythagorean theorem
This theorem may have more known proofs than any other (the law of quadratic reciprocity being another contender for that distinction); the book The Pythagorean Proposition contains 370 proofs. -
500 BCE
Pythagoras tangram
Pythagoras proof the own theorem using tangram -
500 BCE
Pythagorean theorem: history
There is debate whether the Pythagorean theorem was discovered once, or many times in many places, and the date of first discovery is uncertain, as is the date of the first proof. Historians of Mesopotamian mathematics have concluded that the Pythagorean rule was in widespread use during the Old Babylonian period. -
500 BCE
Pythagorean theorem: history
The history of the theorem can be divided into four parts: knowledge of Pythagorean triples, knowledge of the relationship among the sides of a right triangle, knowledge of the relationships among adjacent angles, and proofs of the theorem within some deductive system. -
500 BCE
Pythagorean theorem: history
Written between 2000 and 1786 BC, the Middle Kingdom Egyptian Berlin Papyrus 6619 includes a problem whose solution is the Pythagorean triple 6:8:10, but the problem does not mention a triangle. The Mesopotamian tablet Plimpton 322, written between 1790 and 1750 BC during the reign of Hammurabi the Great, contains many entries closely related to Pythagorean triples. -
300 BCE
Euclid's proof
Euclid's proof -
Einstein's proof by dissection without rearrangement
In Einstein's proof, the shape that includes the hypotenuse is the right triangle itself. The dissection consists of dropping a perpendicular from the vertex of the right angle of the triangle to the hypotenuse, thus splitting the whole triangle into two parts. Those two parts have the same shape as the original right triangle, and have the legs of the original triangle as their hypotenuses, and the sum of their areas is that of the original triangle. -
Proofs by dissection and rearrangement
Proof by rearrangement 1 -
Proofs by dissection and rearrangement
proof by rearrangement 2 -
Proofs by dissection and rearrangement
proof by rearrangement 3
