Changes

Unlike Van Ceulen, Newton did not consider his calculations to be an achievement. "I am ashamed to tell you to how many figures I carried these computations, having no other business at the time," he wrote.<ref>Beckmann, Petr (2015-01-06). ''A History of Pi'' (Kindle Locations 2249-2250). St. Martin's Press. Kindle Edition.</ref>

Unlike Van Ceulen, Newton did not consider his calculations to be an achievement. "I am ashamed to tell you to how many figures I carried these computations, having no other business at the time," he wrote.<ref>Beckmann, Petr (2015-01-06). ''A History of Pi'' (Kindle Locations 2249-2250). St. Martin's Press. Kindle Edition.</ref>

[[Gottfried Leibniz|Gottfried Wilhelm von Leibniz]] (1646-1716) published a series for '''<big><math>\pi</math></big>''' in 1673, coming up with the formulas:

[[Gottfried Leibniz|Gottfried Wilhelm von Leibniz]] (1646-1716) published a series for '''<big><math>\pi</math></big>''' in 1673, coming up with the formulas:

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In 1706, John Machin, secretary of [[England]]'s Royal Society, developed a quickly converging formula for '''<big><math>\pi</math></big>''' and used it to calculated the first 100 digits. In 1844, the idiot savant Johann Dase of [[Hamburg]] used Machin's formula to calculate 200 digits in less than two months.<ref>Beckmann</ref> In contrast, William Shanks spent twenty years calculating '''<big><math>\pi</math></big>''' to 707 places, a task he completed in 1873. In 1945, it was discovered that only the first 527 of Shanks's digits were correct.

In 1706, John Machin, secretary of [[England]]'s Royal Society, developed a quickly converging formula for '''<big><math>\pi</math></big>''' and used it to calculate the first 100 digits. In 1844, the idiot savant Johann Dase of [[Hamburg]] used Machin's formula to calculate 200 digits in less than two months.<ref>Beckmann</ref> In contrast, William Shanks spent twenty years calculating '''<big><math>\pi</math></big>''' to 707 places, a task he completed in 1873. In 1945, it was discovered that only the first 527 of Shanks' digits were correct.

ENIAC, the first electronic [[computer]], took seventy hours to calculate 2,037 digits in 1949. In 2008, the first million digits of '''<big><math>\pi</math></big>''' were published on [[Project Gutenberg]].<ref>Hemphill, Scott, ''[https://www.gutenberg.org/ebooks/50 Pi to 1,000,000 places]''.</ref> In 2014, the anonymous programmer Houkouonchi calculated the first 13.3 trillion digits of '''<big><math>\pi</math></big>''' in 208 days.<ref>Yee, Alexander, "[http://www.numberworld.org/y-cruncher/ y-cruncher - A Multi-Threaded Pi-Program]"</ref> This result has not been published.

ENIAC, the first electronic [[computer]], took seventy hours to calculate 2,037 digits in 1949. In 2008, the first million digits of '''<big><math>\pi</math></big>''' were published on [[Project Gutenberg]].<ref>Hemphill, Scott, ''[https://www.gutenberg.org/ebooks/50 Pi to 1,000,000 places]''.</ref> In 2014, the anonymous programmer Houkouonchi calculated the first 13.3 trillion digits of '''<big><math>\pi</math></big>''' in 208 days.<ref>Yee, Alexander, "[http://www.numberworld.org/y-cruncher/ y-cruncher - A Multi-Threaded Pi-Program]"</ref> This result has not been published.