Uploaded August 2026 | Updated September 2026, 1 week ago
A factorial is repeated multiplication and pi is a circle constant, so the two should have nothing to do with each other, but the moment you ask for the factorial of one half you get pi, and this video traces exactly where it enters: the Gamma function extends the factorial to every number, the factorial of one half turns out to be the area under a bell curve, and squaring that bell curve makes a perfectly round hill whose only clean integral is a full sweep around a circle.
CHAPTERS
0:00 Pi is sitting in a factorial
0:42 Factorials only live on the whole numbers
1:23 The Gamma function
3:13 Everything collapses to one number
3:46 It turns into a bell curve
4:31 Where the pi comes from
6:16 The sweep that is 2 pi
6:36 Why it had to be pi
7:11 The answer
7:50 What to watch next
This video was partially created using Manim.
Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.
#math #calculus #brithemathguy
A factorial is repeated multiplication and pi is a circle constant, so the two should have nothing to do with each other, but the moment you ask for the factorial of one half you get pi, and this video traces exactly where it enters: the Gamma function extends the factorial to every number, the factorial of one half turns out to be the area under a bell curve, and squaring that bell curve makes a perfectly round hill whose only clean integral is a full sweep around a circle.
CHAPTERS
0:00 Pi is sitting in a factorial
0:42 Factorials only live on the whole numbers
1:23 The Gamma function
3:13 Everything collapses to one number
3:46 It turns into a bell curve
4:31 Where the pi comes from
6:16 The sweep that is 2 pi
6:36 Why it had to be pi
7:11 The answer
7:50 What to watch next
This video was partially created using Manim.
Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.
#math #calculus #brithemathguy
