Unique Pi Value
If x = (pi + 3)/2
Then 2x = pi + 3
2x(pi - 3) = (pi + 3)(pi - 3)
2(pi)x - 6x = pi^2 - 9
9 - 6x = pi^2 - 2(pi)x
9 - 6x + x^2 = pi^2 - 2(pi)x + x^2
(3 - x)^2 = (pi - x)^2
3 - x = pi - x
3 = pi
But pi does not equal 3 !
What is wrong here?
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, but one Old Babylonian tablet (1900-1680 BCE) has a pi value of 3.125.
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 polygon 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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