Changes

Some ancients expressed '''<big><math>\pi</math></big>''' by using fractional approximations. The Rhind, or Ahmes Papyrus (''c.'' 1650 B.C.)<ref>http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egyptpapyrus.html</ref><ref>https://www.math.tamu.edu/~don.allen/history/egypt/node3.html</ref> has shown that the [[ancient Egypt]]ians had determined the value for '''<big><math>\pi</math></big>''' to be 3.1605. The [[Babylonia]]n value from the same era was 3 1/8 = 3.125.<ref>Boyer, ''A History of Mathematics'', 2nd edition</ref>, coming to within 1 percent accuracy for both<ref>https://www.maa.org/press/periodicals/convergence/mathematical-treasure-old-babylonian-area-calculation</ref>.

Some ancients expressed '''<big><math>\pi</math></big>''' by using fractional approximations. The Rhind, or Ahmes Papyrus (''c.'' 1650 B.C.)<ref>http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egyptpapyrus.html</ref><ref>https://www.math.tamu.edu/~don.allen/history/egypt/node3.html</ref> has shown that the [[ancient Egypt]]ians had determined the value for '''<big><math>\pi</math></big>''' to be 3.1605. The [[Babylonia]]n value from the same era was 3 1/8 = 3.125.<ref>Boyer, ''A History of Mathematics'', 2nd edition</ref>, coming to within 1 percent accuracy for both<ref>https://www.maa.org/press/periodicals/convergence/mathematical-treasure-old-babylonian-area-calculation</ref>.

[[Archimedes]] of Syracuse (287-212 BC) carried out "the first theoretical calculation" of '''<big><math>\pi</math></big>'''.<ref>[http://veling.nl/anne/templars/Pi_through_the_ages.html Pi through the ages]</ref>, using regular polygons with a total of 96 sides, within and circumscribing a circle, and in about 225 B.C. he came up with a formula between the folowing numbers:  

[[Archimedes]] of Syracuse (287-212 BC) carried out "the first theoretical calculation" of '''<big><math>\pi</math></big>''',<ref>[http://veling.nl/anne/templars/Pi_through_the_ages.html Pi through the ages]</ref> using regular polygons with a total of 96 sides, within and circumscribing a circle, and in about 225 B.C. he came up with a formula between the folowing numbers:  

<center><math>3 \dfrac {1} {7} < \pi < 3 \dfrac {10} {71}</math></center>

<center><math>3 \dfrac {1} {7} < \pi < 3 \dfrac {10} {71}</math></center>