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why is the value of pi 3.14?

9 years ago

the pi value 3.14 because it is the ratio of the curcumeference and diameter of circle. (C/D) here The circumference of a circle is slightly more than three times as long as its diameter. The exact ratio is called π.    The ratio C/d is constant, regardless of the circle''s size. For example, if a circle has twice the diameter of another circle it will also have twice the circumference, preserving the ratio C/d. This definition of π is not universal, because it is only valid in flat (Euclidean) geometry and is not valid in curved (non-Euclidean) geometries. For this reason, some mathematicians prefer definitions of π based on calculus or trigonometry that do not rely on the circle. One such definition is: π is twice the smallest positive x for which cos(x) equals 0.

Archimedes computed upper and lower bounds of π by drawing a regular hexagon inside and outside a circle, and successively doubling the number of sides until he reached a 96-sided regular polygon. By calculating the perimeters of these polygons, he proved that 223/71 < π < 22/7 (3.1408 < π < 3.1429). Archimedes'' upper bound of 22/7 may have led to a widespread popular belief that π is equal to 22/7.

The Great Pyramid at Giza, constructed c. 2589–2566 BC, was built with a perimeter of about 1760 cubits and a height of about 280 cubits; the ratio 1760/280 ≈ 6.2857 is approximately equal to 2π ≈ 6.2832.

9 years ago
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
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9 years ago

Archimedes first calculated pi by using successive approximations with a compass. The most accurate
figure he could come up with was best expressed as
the fraction 22/7. However even he knew that he was limited by his crude tools. Pi is an irrational number.
This has been proven mathematically.
That means there is no fraction that can express it
exactly. As a decimal, it does not end or repeat.

pi=3.14159 26535 89793 23846.....