Pi
lastmod 2026-02-04created 2014-09-114 edits
Da Vinci's calculation of the area of a circle Pi is a mathematical constant representing the ratio of a circle's circumference to its diameter. It is used throughout many areas of mathematics and physics. It is written with the Greek letter π and read as "pi".
Definition and main text
The formula for a circle's circumference follows from the definition of pi, so it is treated as self-evident.
Since the time of Archimedes, various techniques for finding the area of a circle have been known. One widely used method is the quadrature using a regular hexagon devised by Leonardo da Vinci. As in the figure on the left, Leonardo da Vinci used a regular hexagon to rearrange a divided circle into a rectangle and calculated the area of the circle.
As in the figure, imagine dividing the circle into infinitely many triangles. If the number of triangles is n, then 삼각형 1개의 밑변 = 원의둘레 / n. The following formulas then hold.
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1개 삼각형의 넓이 = 2πr / n × r / 2 = πr² / n -
원의 넓이 = 1개 삼각형의 넓이 × n = πr² / n × n = πr²
Therefore the following formula holds.
One way to compute pi is to use the fact that arctan(1) = π / 4 and expand the arctan function as a Taylor series.
See also
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References
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Wikipedia-pi_ko.pdf ↩