I really suck at math, especially when continuous functions are involved (ie non-CS-y math). Usually when mathy articles are posted on HN, I quickly give up, but I just ate this article up. I'm really impressed with the clear explanation, it's quite something! Thanks for writing this!
whyandgrowth · 20m ago
This is very interesting, but I have 3 questions:
1. Why exactly n = 2 minimizes π. The article shows this graphically, but there is no formal proof (although the Adler & Tanton paper is mentioned). It would be interesting to understand why this is the case mathematically.
2. How to calculate π for n-metrics numerically. The general idea of "divide the circle into segments and calculate the length by the metric" is explained, but the exact algorithm or formulas are not shown.
3. What happens when n → 0. It mentions that "the concept of distance breaks down," but it does not explain exactly how and why this is so.
mistercow · 2m ago
> How to calculate π for n-metrics numerically. The general idea of "divide the circle into segments and calculate the length by the metric" is explained, but the exact algorithm or formulas are not shown.
I feel like that would have been a bit in the weeds for the general pacing of this post, but you just convert each angle to a slope, then solve for y/x = that slope, and the metric from (0,0) to (x,y) equal to 1, right? Now you have a bunch of points and you just add up the distances.
NooneAtAll3 · 7m ago
and hackernews' font has the worst pi :/
isoprophlex · 33m ago
I love these little mathematical snippets, where I (as a math noob) can't tell if the result is trivial or deeply profound
1. Why exactly n = 2 minimizes π. The article shows this graphically, but there is no formal proof (although the Adler & Tanton paper is mentioned). It would be interesting to understand why this is the case mathematically.
2. How to calculate π for n-metrics numerically. The general idea of "divide the circle into segments and calculate the length by the metric" is explained, but the exact algorithm or formulas are not shown.
3. What happens when n → 0. It mentions that "the concept of distance breaks down," but it does not explain exactly how and why this is so.
I feel like that would have been a bit in the weeds for the general pacing of this post, but you just convert each angle to a slope, then solve for y/x = that slope, and the metric from (0,0) to (x,y) equal to 1, right? Now you have a bunch of points and you just add up the distances.
At least to me it's provocative