The Pythagorean Theorem, also known as Pythagoras' Theorem, or the hypotenuse theorem, is largely credited to the Greek mathematician, Pythagoras of Samos (570-495 B.C.). Though many knew of this relationship of right triangles and hypotenuses long before Pythagoras, it is named after him because he wrote the first known proof which spread throughout the world. Other versions of this notion were developed by mathematicians in Egypt, Babylon, India, and China centuries before Pythagoras (Overduin). It is difficult to pinpoint the exact origin of the theorem, but many individuals have proved it and contributed to the understanding of it throughout the years. This page consists of some highlights in history of the Pythagorean Theorem. The following individuals and groups of people are only a few of those who have contributed to this essential theorem.
It is said that Pythagoras discovered "his theorem" in a palace hall. He studied the stone square tiles when he was bored and pictured right triangles within the tiling. He recognized that the area of the squares on the side lengths were equal to the square on the hypotenuse. From this observation he believed that the same would be true for right triangles of unequal side lengths. Sometime after this experience, he arrived at the proof of his theorem by the deductive method (Agarwal). The following picture is an example of what the Pythagorean Theorem looks like within square tiles. Although it may not be exactly what Pythagoras saw, this visual depiction gives an idea of how the Pythagorean Theorem can be represented within square tiling.
One of the earliest recorded uses of the Pythagorean Theorem (or the idea of it) was in Egyptian hieroglyphics. Some Egyptian workers constructed a tool which formed right triangles by measuring the distance of each side of the triangle. This was done primarily by the 3-4-5 rule, the converse of the theorem for a special case. The device consisted of a rope with 12 equally spaced knots and made a triangle of side lengths 3, 4, and 5. Their goal was to form a right triangle with the knotted rope and machine. From the known side lengths and the special case of the Pythagorean theorem, they guaranteed a triangle with a 90 degree angle. Although it was not a proof of the theorem, the Egyptians recorded the earliest known application of it by displaying a hieroglyphic image of their work. (Sparks) Although they used an application of Pythagoras' Theorem to create right triangles, it is unclear whether or not the Egyptians knew anything about the theorem when developing their workman's rope (Agarwal).
Euclid is well known for his contributions to geometry, including his propositions, postulates, and common notions. He wrote and organized these propositions in 300 B.C. They are referred to as Eudlid's Elements which is one of the most significant mathematics texts of all time. Among his propositions is a proof of the Pythagorean Theorem. While many proofs of the theorem are formed algebraically, Euclid used a more geometric style proof. He began with geometric squares depicting the "squared" sides of the right triangle. The proof he developed was included in Book I of his proposition, it was later simplified and the simplified version is found in Euclid's Book VI. Others mathematicians have used his proof to create versions of their own based on the propositions he related in his text. (Euclid's Proof of the Pythagorean Theorem – Writing Anthology, n.d.)
A former U.S. President is among the many listed contributors to proofs of the Pythagorean Theorem. Before he chose the route of politics and became the President of the United States, James A. Garfield had plans to become a math teacher. In 1876 he published a proof of the theorem based upon the area of a trapezoid. His approach to the problem gave yet another proof of the Pythagorean Theorem and a new way of looking at and understanding the idea of right triangles. (Kelley)