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THE VIDEO SHELF · high-dimensional geometry

Strange Spheres in Higher Dimensions - Numberphile

Matt Parker on Numberphile explains the strange properties of spheres in higher dimensions, such as how they poke out of their bounding boxes. It uses Pythagoras to build intuition for 4D and beyond.

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Why HN readers recommended it

Recommended whenever the counterintuitive geometry of high-dimensional spheres comes up, including in vector embedding discussions.

This is a summary from the source dataset, not an endorsement by Hacker News or the video creator.

Video & recommendation details

Creator / channel
Numberphile
Topic
high-dimensional geometry
Format
explainer
Level
general
HN recommenders in dataset
2
HN mentions in dataset
4
Recommendation years in dataset
2020–2025

These counts and years describe the included Hacker News records; they are not YouTube views or the video’s publication date.

From the original HN conversations

Excerpts from the recorded comments. Follow each source for the full comment and surrounding discussion.

  • Generalizations to higher dimensions[1] also have some fun properties. For one, the volume of a n-dimensional sphere (ball) goes to zero as n goes to infinity. But not in a trivial way: given a radius r, you can find the number of dimensions n that …

    magicalhippo on Hacker News · 2020-02
    In Volume of a Sphere

  • There is a good numberphile video about that [VIDEO] It contains also a hilarious reference to the "parker circle:.

    ithkuil on Hacker News · 2025-05
    In A visual exploration of vector embeddings

Summaries, classifications and recommendation records are from the HackerTube source dataset. Read about this library and its limitations.

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