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Darts in Higher Dimensions (with 3blue1brown) - Numberphile

Numberphile

4.7M subscribers • 28 videos on Hallway

YouTube
  • Recommended by 1 person: 1 on Hacker News.
  • Presented by Grant Sanderson, creator of 3Blue1Brown

Intermediate. Assumes working knowledge.

2.1M views6 years ago1 recommendation

Computer scienceMath for programmersComputation and complexity

Grant Sanderson explains a high-dimensional darts puzzle where the volume of hyperspheres reveals Euler's number.

Grant Sanderson from 3Blue1Brown joins us to discuss an intriguing puzzle with a shrinking bullseye. More links & stuff in full description below ↓↓↓ 3Blue1Brown: youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw Grant Sanderson on the Numberphile podcast: youtu.be/A0RH93XvSyU Greg Egan's tweet which started it all: twitter.com/gregegansf/status/1160461092973211648 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. simonsfoundation.org/outreach/science-sandbox/ And support from Math For America - mathforamerica.org/ NUMBERPHILE Website: numberphile.com/ Numberphile on Facebook: facebook.com/numberphile Numberphile tweets: twitter.com/numberphile Subscribe: bit.ly/Numberphile_Sub Videos by Brady Haran Grant did the animations for this one! Patreon: patreon.com/numberphile Numberphile T-Shirts: teespring.com/stores/numberphile Brady's videos subreddit: reddit.com/r/BradyHaran/ Brady's latest videos across all channels: bradyharanblog.com/ Sign up for (occasional) emails: eepurl.com/YdjL9 Special thanks to our friend Jeff for the accommodation and filming space.

Why it's here

1 person recommends this

What people say. Recommended as an intuitive introduction to high-dimensional geometry and how counterintuitive properties of hyperspheres arise.

jstx1on Hacker News • Recommends

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 - link to this video
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jstx1on Hacker News • Mentions

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 - link to 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…
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jhnclson Hacker News • Mentions

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 link to this video
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gorlothon Hacker News • Mentions

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 ( link to this video ) involves a puzzle about throwing darts at a dart board which is solved by using the volumes of 4+ dimensional spheres.
View on Hacker News