factorial values for fractions. It was a breakthrough
young Euler, working on (1/2)!, because it introduces
pi to number theory:
https://www.apmep.fr/IMG/pdf/Article_probleme_Bale.pdf 🙀
* * *
Euler was trying to find a general method that works
for both integers and fractions. Having done so, and
looking at the numbers for (1/2)!, he remembered that
the English mathematician John Wallis had used this to
express the area of a semi-circle of diameter 1, pi/4.
The formula is slow; 100 000 iterations to see where we are.
In 1729 - aged 22 - he published the gamma function.,
Later, he would solve the Basel problem, for which an approximation
was known, but no one had seen the connection with pi.
Euler caught it. And eventually, the gamma function would use
notions from calculus.
* * *
Euler was trying to find a general method that works
for both integers and fractions. Having done so, and
looking at the numbers for (1/2)!, he remembered that
the English mathematician John Wallis had used this to
express the area of a semi-circle of diameter 1, pi/4.
The formula is slow; 100 000 iterations to see where we are.
In 1729 - aged 22 - he published the gamma function.,
Later, he would solve the Basel problem, for which an approximation
was known, but no one had seen the connection with pi.
Euler caught it. And eventually, the gamma function would use
notions from calculus.
And because no math party is ever complete without Gauss:
source: Wikipedia
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