[m4xr3sdEfault]*******,=,e \_ヾ(ᐖ◞ ) ID: 9d367b Nov. 28, 2018, 11:18 p.m. No.4069962   🗄️.is 🔗kun   >>0234

>>4069942

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. According to Joran Friberg, a historian of mathematics, evidence indicates that the Pythagorean theorem was well-known to the mathematicians of the First Babylonian Dynasty (20th to 16th centuries BC), which would have been over a thousand years before Pythagoras was born, thus an example of Stigler's law of eponymy.[

[m4xr3sdEfault]*******,=,e \_ヾ(ᐖ◞ ) ID: 9d367b Nov. 28, 2018, 11:46 p.m. No.4070093   🗄️.is 🔗kun   >>0105

In India, the Baudhayana Sulba Sutra, the dates of which are given variously as between the 8th and 5th century BC,[75] contains a list of Pythagorean triples discovered algebraically, a statement of the Pythagorean theorem, and a geometrical proof of the Pythagorean theorem for an isosceles right triangle. The Apastamba Sulba Sutra (c. 600 BC) contains a numerical proof of the general Pythagorean theorem, using an area computation. Van der Waerden believed that "it was certainly based on earlier traditions". Carl Boyer states that the Pythagorean theorem in Śulba-sũtram may have been influenced by ancient Mesopotamian math, but there is no conclusive evidence in favor or opposition of this possibility.[76]

[m4xr3sdEfault]*******,=,e \_ヾ(ᐖ◞ ) ID: 9d367b Nov. 28, 2018, 11:49 p.m. No.4070105   🗄️.is 🔗kun   >>0107 >>0111 >>0117 >>0127

>>4070093

With contents known much earlier, but in surviving texts dating from roughly the 1st century BC, the Chinese text Zhoubi Suanjing (周髀算经), (The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven) gives a reasoning for the Pythagorean theorem for the (3, 4, 5) triangle—in China it is called the "Gougu theorem" (勾股定理).[77][78] During the Han Dynasty (202 BC to 220 AD), Pythagorean triples appear in The Nine Chapters on the Mathematical Art,[79] together with a mention of right triangles.[80] Some believe the theorem arose first in China,[81] where it is alternatively known as the "Shang Gao theorem" (商高定理),[82] named after the Duke of Zhou's astronomer and mathematician, whose reasoning composed most of what was in the Zhoubi Suanjing.[83]

[m4xr3sdEfault]*******,=,e \_ヾ(ᐖ◞ ) ID: 9d367b Nov. 28, 2018, 11:50 p.m. No.4070107   🗄️.is 🔗kun   >>0111 >>0112 >>0117

>>4070105

Pythagoras, whose dates are commonly given as 569–475 BC, used algebraic methods to construct Pythagorean triples, according to Proclus's commentary on Euclid. Proclus, however, wrote between 410 and 485 AD. According to Thomas L. Heath (1861–1940), no specific attribution of the theorem to Pythagoras exists in the surviving Greek literature from the five centuries after Pythagoras lived.[84] However, when authors such as Plutarch and Cicero attributed the theorem to Pythagoras, they did so in a way which suggests that the attribution was widely known and undoubted.[5][85] "Whether this formula is rightly attributed to Pythagoras personally, […] one can safely assume that it belongs to the very oldest period of Pythagorean mathematics."[38]

[m4xr3sdEfault]*******,=,e \_ヾ(ᐖ◞ ) ID: 9d367b Nov. 28, 2018, 11:51 p.m. No.4070112   🗄️.is 🔗kun   >>0128

>>4070107

Around 400 BC, according to Proclus, Plato gave a method for finding Pythagorean triples that combined algebra and geometry. Around 300 BC, in Euclid's Elements, the oldest extant axiomatic proof of the theorem is presented.[86]