Dave Richeson
@divbyzero.bsky.social
Mathematician. John J. & Ann Curley Chair in Liberal Arts at Dickinson College. Author of Tales of Impossibility and Euler's Gem. Coffee drinker. [Everything in the timeline before October 2024 was imported from my Twitter/X feed 2008-24.]
I'm playing around with Caleb Madrigal's "Fuzzy Graph" graphing "nonbinary" calculator. Rather than plotting where y equals f(x) (a binary condition), it shades the plot according to how close y is to f(x). fuzzygraph.com
November 14, 2025 at 6:12 PM
I'm playing around with Caleb Madrigal's "Fuzzy Graph" graphing "nonbinary" calculator. Rather than plotting where y equals f(x) (a binary condition), it shades the plot according to how close y is to f(x). fuzzygraph.com
Theorem. There exist irrational numbers x and y such that x^y is rational.
November 13, 2025 at 10:03 PM
Theorem. There exist irrational numbers x and y such that x^y is rational.
The more holes, the better. With a 36-spoke wheel, it would look like this. (Also, my method works best when there are a prime number of holes.)
November 11, 2025 at 8:17 PM
The more holes, the better. With a 36-spoke wheel, it would look like this. (Also, my method works best when there are a prime number of holes.)
I brought my cardioid to campus.
November 11, 2025 at 7:57 PM
I brought my cardioid to campus.
TIL about the color "olo," which only five humans have seen. Olo is short for (0,1,0), which means that the scientists figured out how to excite only the middle-wavelength M-cone in the eye. This hue below is most similar to olo. en.wikipedia.org/wiki/Olo_(co...
November 11, 2025 at 5:28 PM
TIL about the color "olo," which only five humans have seen. Olo is short for (0,1,0), which means that the scientists figured out how to excite only the middle-wavelength M-cone in the eye. This hue below is most similar to olo. en.wikipedia.org/wiki/Olo_(co...
Giant cardioid: version 2.5. Version 1.0 was made using Pex tubing and grommet tape. Version 2.0 was made from laser-cut pieces. The wood was too fragile, and it broke during construction. In version 2.5, I made the pieces wider and I used thicker wood. Success, I'd say! The diameter is about 5 ft.
November 9, 2025 at 4:34 PM
Giant cardioid: version 2.5. Version 1.0 was made using Pex tubing and grommet tape. Version 2.0 was made from laser-cut pieces. The wood was too fragile, and it broke during construction. In version 2.5, I made the pieces wider and I used thicker wood. Success, I'd say! The diameter is about 5 ft.
I had a really nice couple of days at Oberlin College hanging out with @baabbbaash.bsky.social, his colleagues, and students! While walking around campus, I saw this unusual window. Assuming it is the unit circle, what's the equation of the ellipse?
November 8, 2025 at 12:10 AM
I had a really nice couple of days at Oberlin College hanging out with @baabbbaash.bsky.social, his colleagues, and students! While walking around campus, I saw this unusual window. Assuming it is the unit circle, what's the equation of the ellipse?
I just taught induction in my intro-to-proofs class. I told them the base case is usually easy and the inductive step is more challenging. Here's a blog post I wrote giving an example of the opposite. TL;DR: the product rule for n functions. divisbyzero.com/2018/11/07/p...
October 30, 2025 at 5:48 PM
I just taught induction in my intro-to-proofs class. I told them the base case is usually easy and the inductive step is more challenging. Here's a blog post I wrote giving an example of the opposite. TL;DR: the product rule for n functions. divisbyzero.com/2018/11/07/p...
I met with my knot theory independent study students today. The topic: braids. I broke out these "BraidTiles" that I made several years ago. You can download a printable pdf here (recommendation: print them on cardstock): divisbyzero.com/2019/05/01/b...
October 29, 2025 at 7:09 PM
I met with my knot theory independent study students today. The topic: braids. I broke out these "BraidTiles" that I made several years ago. You can download a printable pdf here (recommendation: print them on cardstock): divisbyzero.com/2019/05/01/b...
In my intro-to-proofs class, I like to assign induction problems that aren't only sum/product formulas. For this problem, I made and laser cut this puzzle: Begin with a 2ⁿx2ⁿ grid of squares. Black out a single square. Prove that it is possible to tile the rest of the grid with trominos.
October 29, 2025 at 1:56 PM
In my intro-to-proofs class, I like to assign induction problems that aren't only sum/product formulas. For this problem, I made and laser cut this puzzle: Begin with a 2ⁿx2ⁿ grid of squares. Black out a single square. Prove that it is possible to tile the rest of the grid with trominos.
If you're looking for a Halloween activity to do with your kids or students, you can make a "Flex-a-ghoul"—this is a Halloween-themed hexaflexagon that I made. There's a printable PDF on my blog: divisbyzero.com/2022/11/01/h...
October 27, 2025 at 3:02 PM
If you're looking for a Halloween activity to do with your kids or students, you can make a "Flex-a-ghoul"—this is a Halloween-themed hexaflexagon that I made. There's a printable PDF on my blog: divisbyzero.com/2022/11/01/h...
I am doing some laser cutting outside. It is producing a lot of smoke! I am hoping the neighbors don’t call the fire department.
October 27, 2025 at 1:42 PM
I am doing some laser cutting outside. It is producing a lot of smoke! I am hoping the neighbors don’t call the fire department.
I met with my independent study knot theory students today. We discussed Seifert surfaces (orientable surfaces whose boundaries are knots and links), and I showed them @mathforge.org's Seifert surface pieces. They had fun playing with them. github.com/loopspace/Se...
October 22, 2025 at 7:12 PM
I met with my independent study knot theory students today. We discussed Seifert surfaces (orientable surfaces whose boundaries are knots and links), and I showed them @mathforge.org's Seifert surface pieces. They had fun playing with them. github.com/loopspace/Se...
It is fall break here. I asked for volunteers who happened to be on campus to test my idea for making a giant string-art cardioid. It worked pretty well, and I have some concrete ideas for improvement in version 2.0. (This circle has about a 20 ft. circumference and 239 holes.)
October 21, 2025 at 8:43 PM
It is fall break here. I asked for volunteers who happened to be on campus to test my idea for making a giant string-art cardioid. It worked pretty well, and I have some concrete ideas for improvement in version 2.0. (This circle has about a 20 ft. circumference and 239 holes.)
Here's a neat puzzle from Martin Gardner's January 1958 column. It is surprising (but true) that you can turn a punctured torus ("inner tube") inside out. Suppose we drew a circle on the outside and the inside of the tube; they are linked. Turn the torus inside out. Now they are not linked. Explain!
October 21, 2025 at 4:59 PM
Here's a neat puzzle from Martin Gardner's January 1958 column. It is surprising (but true) that you can turn a punctured torus ("inner tube") inside out. Suppose we drew a circle on the outside and the inside of the tube; they are linked. Turn the torus inside out. Now they are not linked. Explain!
I need some 50 foot lengths of string for a project I'm working on. On a whim, I asked ChatGPT how to visualize 50 feet. The more I look at the response, the funnier it gets.
• A mature oak tree can be much taller than 50'
• Why use 6' as the default adult height?
• When I think of "cars in a row,"
• A mature oak tree can be much taller than 50'
• Why use 6' as the default adult height?
• When I think of "cars in a row,"
October 19, 2025 at 2:44 PM
I need some 50 foot lengths of string for a project I'm working on. On a whim, I asked ChatGPT how to visualize 50 feet. The more I look at the response, the funnier it gets.
• A mature oak tree can be much taller than 50'
• Why use 6' as the default adult height?
• When I think of "cars in a row,"
• A mature oak tree can be much taller than 50'
• Why use 6' as the default adult height?
• When I think of "cars in a row,"
In my mailbox today!
This is one of my favorite results partly because my plan was just to use technology to sum the lengths. But when I started working on it, this nice closed form just popped out!
This is one of my favorite results partly because my plan was just to use technology to sum the lengths. But when I started working on it, this nice closed form just popped out!
October 15, 2025 at 1:46 PM
In my mailbox today!
This is one of my favorite results partly because my plan was just to use technology to sum the lengths. But when I started working on it, this nice closed form just popped out!
This is one of my favorite results partly because my plan was just to use technology to sum the lengths. But when I started working on it, this nice closed form just popped out!
I got this email. I'm not expecting a package. But, also, in the sans serif font, it is unclear if AI is A-i, like "[A]rtificial [I]ntelligence," or A-L, like "[Al]bert."
[I copied and pasted it into Word and changed the font. It is the former. (???)]
[I copied and pasted it into Word and changed the font. It is the former. (???)]
October 15, 2025 at 1:20 PM
I got this email. I'm not expecting a package. But, also, in the sans serif font, it is unclear if AI is A-i, like "[A]rtificial [I]ntelligence," or A-L, like "[Al]bert."
[I copied and pasted it into Word and changed the font. It is the former. (???)]
[I copied and pasted it into Word and changed the font. It is the former. (???)]
The response took 27 seconds. (Source: www.infinitelymore.xyz/p/monkey-mad...)
October 11, 2025 at 12:28 AM
The response took 27 seconds. (Source: www.infinitelymore.xyz/p/monkey-mad...)
I was curious if ChatGPT 5 could solve this entertaining logic problem (created by @joeldavidhamkins.bsky.social). I shared the screenshot below and gave it the prompt "Solve the following logic problem." It requires figuring out the logic and matching it to a "scene." Its response in the next post.
October 11, 2025 at 12:28 AM
I was curious if ChatGPT 5 could solve this entertaining logic problem (created by @joeldavidhamkins.bsky.social). I shared the screenshot below and gave it the prompt "Solve the following logic problem." It requires figuring out the logic and matching it to a "scene." Its response in the next post.
Very nice! If you follow the link to Want and Zhang's preprint, here's the figures they gave.
October 9, 2025 at 3:54 PM
Very nice! If you follow the link to Want and Zhang's preprint, here's the figures they gave.
New blog post! Through a sequence of images, I verify that the unknotting number of the connected sum of a (2,7) torus knot and its mirror is less than 6: I show that this first image is the connected sum, and after changing those crossings, it produces the unknot! divisbyzero.com/2025/10/08/t...
October 9, 2025 at 3:00 AM
New blog post! Through a sequence of images, I verify that the unknotting number of the connected sum of a (2,7) torus knot and its mirror is less than 6: I show that this first image is the connected sum, and after changing those crossings, it produces the unknot! divisbyzero.com/2025/10/08/t...
We got a bag of goodies this summer at the MoMath MOVES conference. It contained these three dice with colored pips. Does anyone know if they come from a game of some sort? They were just in there by themselves.
September 20, 2025 at 6:02 PM
We got a bag of goodies this summer at the MoMath MOVES conference. It contained these three dice with colored pips. Does anyone know if they come from a game of some sort? They were just in there by themselves.
My colleague sent this to me.
A ∩ Aᶜ ≠ ø ?
🤣🤣🤣
A ∩ Aᶜ ≠ ø ?
🤣🤣🤣
September 20, 2025 at 4:25 PM
My colleague sent this to me.
A ∩ Aᶜ ≠ ø ?
🤣🤣🤣
A ∩ Aᶜ ≠ ø ?
🤣🤣🤣