S3E37. Sine as an infinite product and its three applications
In this episode we will see why "most people" cannot handle mathematics by going over a rigorous-enough proof of the famous decomposition of the trigonometric function of sine into an infinite product, along with three popular applications of that decomposition. It takes us about 55 minutes, give or take, to develop the basic workable product and when you think that we are done that is when the real mathematics kicks in, we roll up the sleeves and go to work. The three popular applications of the result derived in this episode are 1) the Wallis formula for pi (1:36:55), 2) the decomposition of the sibling function of cosine into an infinite product (1:40:26) and 3) the reflection formula for the Gamma function (1:47:42).

▶︎
Instant Karma, Embarrassing Drift, and Road Rage on the Autobahn! | #GERMAN #DASHCAM | #384

▶︎
The Theology of the Holy Spirit Explained and Defended

▶︎
S3E40. How CS and Group Theory found a diamond

▶︎
Math News: The Additivity Conjecture in Knot Theory is FALSE!

▶︎
2026 Fields Medal: Jacob Tsimerman

▶︎
Pt. 4 – Lagrangian surfaces in 4-manifolds | Joshua Greene, Boston College | IAS/PCMI

▶︎
2026 Fields Medal: Hong Wang

▶︎
S3E38. What mathematicians do all day or Euler-Poisson integral evaluation via the Squeeze Theorem

▶︎
How Bees CRACKED a 2,000-Year-Old Math PROBLEM!

▶︎
Nobody Explained the Schrödinger Equation Like THIS!

▶︎
The Scariest Chart in Electrical Engineering

▶︎
S3E30. A Loxodrome, a deduction of an equation

▶︎
2026 Fields Medal: Yu Deng

▶︎
S3E39. A bead sliding off of a massless rod that rotates with a decreasing angular velocity

▶︎
S3E34. Hyperbolic functions defined by a direct analogy with circular functions

▶︎
CHOSEN ONE!! YOUR IDENTITY REVEAL JUST SHOOK THE INTERNET... AND THEIR MINDS

▶︎
S3E28. In Like A Lion, Out Like A Lamb

▶︎
S3E25. A divisibility-by-7 test design via Reduce-And-Conquer

▶︎
We're 99.9% sure this pattern is true, but no one can prove it

▶︎
