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Xuan tu or Hsuan thu (simplified Chinese: 弦图; traditional Chinese: 絃圖; pinyin: xuántú; Wade–Giles: hsüan 2 tʻu 2) is a diagram given in the ancient Chinese astronomical and mathematical text Zhoubi Suanjing indicating a proof of the Pythagorean theorem. [1] Zhoubi Suanjing is one of the oldest Chinese texts on mathematics. The ...
The Zhoubi is most famous for its presentation of Chinese cosmology and a form of the Pythagorean theorem. It claims to present 246 problems worked out by the Duke of Zhou as well as members of his court, placing its composition during the 11th century BC.
There is also the mathematical proof given in the treatise for the Pythagorean theorem. [4] The influence of The Nine Chapters greatly assisted the development of ancient mathematics in the regions of Korea and Japan. Its influence on mathematical thought in China persisted until the Qing dynasty era. Liu Hui wrote a detailed commentary in 263.
The Zhoubi Suanjing contains an in-depth proof of the Gougu Theorem, a special case of the Pythagorean theorem) but focuses more on astronomical calculations. However, the recent archaeological discovery of the Tsinghua Bamboo Slips , dated c. 305 BCE , has revealed some aspects of pre-Qin mathematics, such as the first known decimal ...
Liu provided a proof of a theorem identical to the Pythagorean theorem. [3] Liu called the figure of the drawn diagram for the theorem the "diagram giving the relations between the hypotenuse and the sum and difference of the other two sides whereby one can find the unknown from the known." [6]
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of 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.
Ne’Kiya Jackson and Calcea Johnson have published a paper on a new way to prove the 2000-year-old Pythagorean theorem. Their work began in a high school math contest.
It created mathematical proof for the Pythagorean theorem, [111] and a mathematical formula for Gaussian elimination. [112] The treatise also provides values of π , [ 106 ] which Chinese mathematicians originally approximated as 3 until Liu Xin (d. 23 AD) provided a figure of 3.1457 and subsequently Zhang Heng (78–139) approximated pi as 3. ...