Grant Sanderson

Happy Pi Day! In a certain sense, π is not a constant, but a variable. Using our usual Euclidean distance, it is 3.14159… but applying other L^p norms on ℝ², half the unit circle's perimeter will give other values. For instance, at p=1 (taxicab geometry), “π” = 2√2. At p ≈ 2.2, it's 3.20.

Happy Pi Day! In a certain sense, π is not a constant, but a variable. Using our usual Euclidean distance, it is 3.14159… but applying other L^p norms on ℝ², half the unit circle's perimeter will give other values. For instance, at p=1 (taxicab geometry), “π” = 2√2. At p ≈ 2.2, it's 3.20.

Much of Euclid’s Elements is easily misunderstood. Some proofs seem to have logical gaps. Some constructions seem pointless, others seem needlessly convoluted. Each of these provides a window into how the ancient Greeks thought about math and the philosophical role that geometry played.

New video on the details of diffusion models: youtu.be/iv-5mZ_9CPY Produced by Welch Labs, this is the first in a short series of 3b1b this summer. I enjoyed providing editorial feedback throughout the last several months, and couldn't be happier with the result.

New video! This covers the fundamentals of quantum computing and builds up to a step-by-step walk-through of an important algorithm in the field. youtu.be/RQWpF2Gb-gU

If you translate this setup into a quantum computer (explained in the video), Grover's algorithm offers a "faster" way to do this, in that it's O(√N).

New video! This covers the fundamentals of quantum computing and builds up to a step-by-step walk-through of an important algorithm in the field. youtu.be/RQWpF2Gb-gU

What do they do then? This video builds up to Grover’s algorithm, a general method in quantum computing for finding solutions to any NP problem, i.e., anything where you have a quick way to verify solutions, even if finding them in the first place may be hard.

New video! This covers the fundamentals of quantum computing and builds up to a step-by-step walk-through of an important algorithm in the field. youtu.be/RQWpF2Gb-gU

I have a pi-day challenge for all the physics students among you (or anyone willing to set up an experiment). If you share your results with me by March 10th, I may feature them in a video, depending on how good the results are and how many I get.

More generally, with a mass ratio of N-to-1, the number of collisions is around π / arctan(1 / sqrt(N)). So any big mass ratio gives you an approximation of pi by multiplying the number of collisions by arctan(1/sqrt(N))

I have a pi-day challenge for all the physics students among you (or anyone willing to set up an experiment). If you share your results with me by March 10th, I may feature them in a video, depending on how good the results are and how many I get.

Also, it's a wildly inefficient way to compute pi. To even get "3.14" you'd need this to work with a 10,000-to-1 mass ratio and have a way to count all 314 collisions. Matt Parker and I actually gave this a go, and the results were...okay, but could definitely have been improved :)

I have a pi-day challenge for all the physics students among you (or anyone willing to set up an experiment). If you share your results with me by March 10th, I may feature them in a video, depending on how good the results are and how many I get.

Many years ago I made this video about how two colliding blocks on a frictionless plane can compute pi. My challenge to you is simple: Implement this in practice.

New* video! If you’ve ever wondered what topology is, this problem is one of the best examples I know of to give an authentic sense of what it’s all about: youtu.be/IQqtsm-bBRU

Well, perhaps not “new” new. Books have a notion of a second edition, and while YouTube videos usually don’t, I wanted to make a new edition of one of the earliest videos on the channel, as this is one of my favorite pieces of math.