Darts in Higher Dimensions (with 3blue1brown) - Numberphile
Why Hacker News recommends it
Used as a friendly example of high-dimensional geometry showing up in a simple problem, and of ball volume shrinking inside a hypercube.
What it is
Numberphile talks with Grant Sanderson of 3Blue1Brown about a darts puzzle with a shrinking bullseye. Solving it takes the volumes of high-dimensional spheres, and the answer turns up Euler's number.
Recommended by 1 HN commenters across 1 different months, 2021 to 2023.
What Hacker News said
Recommends jstx1 · 2023-05 · on “Counterintuitive Properties of High Dimensional Space”
You can and as the dimensions go up the volume of the inscribed ball as a percentage of the volume of the hypercube shrinks down a lot. There's a nice video about this from Numberphile and 3blue1brown - [this video]
Cites jstx1 · 2021-09 · on “A mathematician's guided tour through higher dimensions”
I think it's easier to approach higher dimensions without talking about spatial dimensions at all. For example - Darts in Higher Dimensions, 3blue1brown and Numberphile - [this video] Or even more trivially, you can think of a table where every row is some entity and every column is some attribute associated to it. For example, make a spreadsheet where each row is a person and the columns are age, height, weight, salary, and years to retirement - then you can think of each person as a point in 5-d space. And some properties are intuitively obvious - for example as you keep adding more columns it becomes more difficult to find people who are similar to each other. It's a pretty accessible way to i
Cites jhncls · 2021-11 · on “Euler’s number pops up in situations that involve optimality”
In a unique Numberphile video featuring Grant Sanderson (3blue1brown), this weird number pops up in a game of darts. [0] [this video]
Cites gorloth · 2022-01 · on “A high-dimensional sphere spilling out of a high-dimensional cube”
Higher dimensional geometry can show up in lower dimensional problems. This numberphile video ( [this video] ) involves a puzzle about throwing darts at a dart board which is solved by using the volumes of 4+ dimensional spheres.