High School Math

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Friday, January 28, 2005

Pi = 3.14159


That the ratio of the circumference to the diameter of a circle is constant (namely, pi) has been recognized for as long as we have written records.

A ratio of 3:1 appears in the following biblical verse: And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about. (I Kings 7, 23; II Chronicles 4, 2.)

The ancient Babylonians generally calculated the area of a circle by taking 3 times the square of its radius (=3), but one Old Babylonian tablet (from ca. 1900-1680 BCE) indicates a value of 3.125 for pi.

The first theoretical calculation of a value of pi was that of Archimedes of Syracuse (287-212 BCE), one of the most brilliant mathematicians of the ancient world. Archimedes worked out that 223/71 < pi < 22/7. Archimedes's results rested upon approximating the area of a circle based on the area of a regular polygon inscribed within the circle and the area of a regular polygon within which the circle was circumscribed. Beginning with a hexagon, he worked all the way up to a ploygon with 96 sides!

European mathematicians in the early modern period developed new arithmetical formulae to approximate the value of pi, such as that of James Gregory (1638-1675), which was taken up by Leibniz as :
pi/4 = 1 - 1/3 + 1/5 - 1/7 . . . .

The symbol for pi was introduced by the English mathematician William Jones in 1706. This symbol was adopted by Euler in 1737 and became the standard symbol for pi.

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