A Compendium of Cool Internet Math Things

Here’s an experience I’ve had roughly six million times.

1. A mathematical topic arises.
3. In order to find it, I am forced to read all of the tweets, ever.
4. I am reminded that “all of the tweets ever” is rather too many tweets.

So about a year ago I started a compendium. Tweets, yes, but also videos, apps, memes… anything stimulating or arresting that I can use to embroider my lessons. For a while, this document lived where all important documents live: as a gmail draft. But now I share it as a blog post, and I intend to continue updating it as new ones cross my ken.

NOTE: I will, where convenient, use screenshots and links, because WordPress’s embedded tweets sometimes take ages to load.

NUMBER AND SCALE

A brilliant anagram from Colin Beveridge:

The timeless classic Powers of Ten, arguably the best film of 1977 (suck it, Annie Hall):

The mesmerizing interactive “Scale of the Universe” app (which requires you to enable Flash, but just do it).

Also, this black hole:

ALGEBRA

An ellipse as the maximum heights of a family of projectiles:

And again, this time for figuring out the scoring system in Australian Rules Football:

Four place mats, arranged to make a quadratic identity at the dinner table:

Polar coordinates on pizza:

GEOMETRY AND TRIGONOMETRY

Volumes of a cylinder, a sphere, and a cone:

Volumes of earth, earth’s air, and earth’s water:

Animated visual proof that any polygon can be rearranged into any other polygon of equal area:

For your trigonometric Halloween, the blood function:

Defining a radian with a wooden model:

Simple harmonic motion:

CALCULUS AND DYNAMICAL SYSTEMS

Riemann sums (comparing upper and lower sums as the grid is refined):

A professor solves an optimization problem (“smallest surface area for a given volume”), writes a company that makes cat food to ask why they don’t use this solution, and receives an incredibly thoughtful and interesting reply:

A real-life butterfly effect:

The exquisite sensitivity of the double pendulum:

PROBABILITY AND STATISTICS

Independence is a delicate and rare phenomenon:

What do probabilistic words really mean?

I see you Anscombe’s Quartet, and I raise you the Datasaurus:

A delightful game aptly called Guess the Correlation:

The dangers of using r^2 as an effect size estimate:

The normal distribution in action:

MISCELLANEOUS

Moore’s Law, and the glorious improbability of that exponential growth:
Quick sort, in an image:
Centrifugal force to restore a whiteboard marker:
Voronoi diagrams (i.e., which national park is closest to you?):
Set theory (specifically, the power set), where each rectangle is one of the possible sets of these 4 elements (ranging from the empty set in the middle, to the set of all four):
Mathematics in nature:

6 thoughts on “A Compendium of Cool Internet Math Things”

1. What does it mean for the probablistic words to represent percentages lower than 0% or higher than 100%? Perhaps just that the person making the plot doesn’t understand boundaries? Or that they used the wrong kernel when doing kernel density estimation? (A beta distribution would make a good kernel here, but a Gaussian does not.)

2. Benjamin Doerr says:

That blood function was not too hard to figure out. Took me ten seconds. 🙂 https://www.desmos.com/calculator/jbwyuvhlud

On Wed, 4 Mar 2020 at 10:01, Math with Bad Drawings wrote:

> Ben Orlin posted: “Here’s an experience I’ve had roughly six million > times. A mathematical topic arises. “You know,” I say, “someone has a great > tweet about this… somewhere…” In order to find it, I am forced to read > all of the tweets, ever. I am reminded that “all ” >

3. Rachel K says:

Love this collection! Here’s a suggestion for an addition: The Mathematical Functions Grimoire! http://fungrim.org

4. With an spirit somewhere in the middle between “Scale of the Universe” and “Powers of Ten”, you may find helpful Universcale by Nikon; https://www.nikon.com/about/sp/universcale/
I usually show it to pupils when introducing scientific notation/negative exponents