---
title: "The most beautiful formula not enough people understand"
url: https://daily.dev/posts/the-most-beautiful-formula-not-enough-people-understand-pllp1eazr
source_url: https://www.youtube.com/watch?v=fsLh-NYhOoU
type: video:youtube
source: "3Blue1Brown"
published: 2026-02-27T16:46:58.217Z
updated: 2026-02-27T16:47:17.772Z
tags: ["machine-learning", "math", "statistics"]
reading_time: 60
upvotes: 1
comments: 0
language: en
---

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# The most beautiful formula not enough people understand

**[3Blue1Brown](https://daily.dev/sources/3blue1brown)** · 60 min read · 1 upvotes · 0 comments

## Summary

A lecture-style exploration of the formula for the volume of an n-dimensional ball. Starting from intuitive probability puzzles (what's the chance that x²+y² ≤ 1 for random x,y?), it builds up to the general formula V_n = π^(n/2) / (n/2)! · r^n. Key ideas include: the relationship between a ball's volume and its surface area via derivatives/integrals, an Archimedean projection argument generalized to higher dimensions via a 'knight's move' recurrence, the gamma function extending factorials to half-integers, and the surprising fact that unit ball volumes peak around 5 dimensions and then shrink toward zero in higher dimensions — a counterintuitive result relevant to machine learning, cryptography, and quantum mechanics.

## Full article

daily.dev links to this article rather than hosting it. Read it at the original source: <https://www.youtube.com/watch?v=fsLh-NYhOoU>

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---

Tags: [#machine-learning](https://daily.dev/tags/machine-learning), [#math](https://daily.dev/tags/math), [#statistics](https://daily.dev/tags/statistics)

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