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3.14159 26535 89793 23846 26433... Uses; Area of a circle; Circumference; Use in other formulae; ... is the principal value of the complex logarithm) [note 4] ...
In ancient China, values for π included 3.1547 (around 1 AD), (100 AD, approximately 3.1623), and 142 / 45 (3rd century, approximately 3.1556). [55] Around 265 AD, the Wei Kingdom mathematician Liu Hui created a polygon-based iterative algorithm and used it with a 3,072-sided polygon to obtain a value of π of 3.1416.
In this animation N takes various increasing values from 1 to 100. The computation of (1 + iπ / N ) N is displayed as the combined effect of N repeated multiplications in the complex plane, with the final point being the actual value of (1 + iπ / N ) N. It can be seen that as N gets larger (1 + iπ / N ) N approaches a ...
3.14159 26535 89793 23846 [Mw 1] [OEIS 1] Ratio of a circle's circumference to its diameter. 1900 to 1600 BCE [2] Tau: 6.28318 53071 79586 47692 [3] [OEIS 2] Ratio of a circle's circumference to its radius. Equivalent to : 1900 to 1600 BCE [2] Square root of 2, Pythagoras constant. [4]
3.125: 1 Between 1 BC and AD 5: Liu Xin [7] [11] [12] Unknown method giving a figure for a jialiang which implies a value for π ≈ 162 ⁄ (√ 50 +0.095) 2. 3.1547... 1 AD 130: Zhang Heng (Book of the Later Han) [2] √ 10 = 3.162277... 736 ⁄ 232: 3.1622... 1 150: Ptolemy [2] 377 ⁄ 120: 3.141666... 3: 250: Wang Fan [2] 142 ⁄ 45: 3 ...
An 1897 political cartoon mocking the Indiana pi bill. In 1894, Indiana physician Edward J. Goodwin (c. 1825 – 1902 [2]), also called "Edwin Goodwin" by some sources, [3] believed that he had discovered a way of squaring the circle. [4]
The Chinese mathematician Liu Hui in 263 CE computed π to between 3.141 024 and 3.142 708 by inscribing a 96-gon and 192-gon; the average of these two values is 3.141 866 (accuracy 9·10 −5). He also suggested that 3.14 was a good enough approximation for practical purposes.
The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.