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 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 very strange pricing scheme:

A brilliant anagram from Colin Beveridge:

A gorgeous visualization of prime factors (from this Smithsonian blog post).

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:

Throwing an object at the same speed but different angles defines an ellipse via its maximum height https://t.co/vQ8NMssCMf

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〈 Berger | Dillon 〉 (@InertialObservr) July 22, 2019

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:

Putting sauce on a pizza. https://t.co/Oe9gsZaSjz

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Machine Pix (@MachinePix) August 28, 2016

**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:

(You’ve just got to click here, it’s amazing.)

For your trigonometric Halloween, the blood function:

Defining a radian with a wooden model:

Tragic Tweet Delete! -- I thought I would at least add it back : ) We are interested in sending these to folks, es… twitter.com/i/web/status/1…

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MathHappens (@MathHappensOrg) October 01, 2019

Simple harmonic motion:

Beautiful shapes created by simple harmonic motion 🧐 https://t.co/ifsFX4nfN9

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Fermat's Library (@fermatslibrary) January 02, 2020

**CALCULUS AND DYNAMICAL SYSTEMS**

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

Concepts without words: Integration and Riemann Sums
bit.ly/2E7iNU3
#math #science #iteachmath #mtbos… twitter.com/i/web/status/1…

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Tungsteno (@74WTungsteno) August 11, 2019

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:

In office hours, sophomore @JackSillin showed me this real world example of the butterfly effect. An unexpectedly… twitter.com/i/web/status/1…

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Steven Strogatz (@stevenstrogatz) September 10, 2019

The exquisite sensitivity of the double pendulum:

50 double pendulums, whose initial velocities differ only by 1 part in 1000 https://t.co/3b75BDkwF1

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〈 Berger | Dillon 〉 (@InertialObservr) September 30, 2019

### 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:

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

The normal distribution in action:

**MISCELLANEOUS**

Fascinating: Moore’s Law predictions vs actual growth in transistor count.
by @datagrapha
reddit.com/r/dataisbeauti… https://t.co/ZwN1dBGE1n

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Lionel Page (@page_eco) September 03, 2019

I had no idea you could do this to take a dead whiteboard marker and give it life again!
Source:… twitter.com/i/web/status/1…

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Robert Kaplinsky (@robertkaplinsky) July 06, 2019

Stumbled into reading about hermit crabs and wut: https://t.co/ERdEs8TwUK

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Derrick (@geekandahalf) November 29, 2019

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.)

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 ” >

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

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