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 JUSTJO1111 rated 29 months ago - 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...
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3 Reviews
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- shoerob rated 19 months ago
- My eyes were immediately drawn towards the dog. Look at it's tail wag at a billion miles per hour!
- JUSTJO1111 rated 29 months ago
- 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 (pi=3), but one Old Babylonian tablet (from ca. 1900-1680 BCE) indicates a value of 3.125 for pi.
Ancient Egyptians calculated the area of a circle by the following formula (where d is the diameter of the circle):
formula: [(8d)/9] squared
This yields an approximate value of 3.1605 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!
Circle with inscribed and circumscribed hexagons.
Archimedes's method for approximating the value of pi.
(Source: http://www.math.psu.edu/dna/graphics.html#archimedes)
The approximate area of the circle lies between the areas of the circumscribed and the inscribed hexagons.
- Heggs rated 29 months ago
- More than I needed to know about pi but incredibly cool.
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