Mathematician. Curley Chair in Liberal Arts at Dickinson College. Author of Tales of Impossibility and Euler's Gem. Now: divbyzero.bsky.social
Carlisle, PA
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I don't know my plan for Twitter/X. It is hard to give up after all the great people I've met and conversations I had in 13+ years, but the math community has moved to Bluesky. I will use divbyzero.bsky.social as my go-to site for posting math content now. Join us there!
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I don't know my plan for Twitter/X. It is hard to give up after all the great people I've met and conversations I had in 13+ years, but the math community has moved to Bluesky. I will use divbyzero.bsky.social as my go-to site for posting math content now. Join us there!
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In case you are moving to Bluebky, you can find me here: bsky.app/profile/divbyzero.b…
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New blog post! I used ChatGPT to help me create a Mandelbrot set in Excel! Here are the 30x30, 60x60, and 250x250 versions. I'm also including a few zoomed-in views. divisbyzero.com/2024/11/13/m…
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Some different bases for numbers and who used them.
Base 10: Egyptians
Base 60: Babylonians
Base 20: Mayans
Base 2: Computers
Base 16: Computers
Base 26: Microsoft Excel
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Here's a fun little "magic trick." Can you figure out how it works? Hint: even and odd numbers. I was thinking you could roll a die to determine how much to count each time. (I saw the trick was credited to Martin Gardner—true? Source?) piped.video/watch?v=DaWcL3oO…
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Here's another neat generative AI example.
It is well known, and not hard to show, that the main component of the Mandelbrot set is a cardioid. Looking around the Mandelbrot set, you'll see other cardioid-looking shapes. On the right, you can see the largest one. People who
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smaller heart-shape is the image of the unit circle under a messy complex map (see below). ams.org/journals/proc/1995-1… I wanted to see it with my own eyes, but I didn't want to have to figure out how to graph this beast. So, I asked ChatGPT for the code to graph it in Sage. I
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Another use of LLMs: I asked the following hard-to-google question.
What is it called when you take a famous phrase and swap out the words so the sentence still has the same form but is applied to something different? For instance, one could take the sentence "Happy families are
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all alike; every unhappy family is unhappy in its own way." from Anna Karenina and rephrase it as "X Y are all alike; every un-X Y is un-X in its own way."
Some examples include:
"Orange is the new black."
"To snack or not to snack. That is the question."
"AI is dead. Long live
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AI."
"Keep calm and wash your hands."
ChatGPT told me this is a "snowclone."
Indeed, there is a wikipedia page for the term en.wikipedia.org/wiki/Snowcl…
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Here are my attempt to get Dall-E to make a "Mandelbrot[wurst]" or "[Mandel]bratwurst."
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Dave Richeson retweeted
(Inspired by @divbyzero)
In an effort to get something other than politics into your feed, a fun fact about ‘49’
The sum of the digits of the square of 49 (2401) is the square root of 49
(More in the image below)
Src: Issue 49 of #SixSTEMTweets newsletter
Link in alt text
ALT This is from issue 49 of the #SixSTEMTweets newsletter Read and join at https://sixstemtweets.beehiiv.com
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In an effort to get something other than politics into your feed:
A Munchausen number is the sum of its digits raised to the power of that digit. 1=1¹ and 3435=3³+4⁴+3³+5⁵ are the only two examples if 0⁰ is defined as 1. If we take 0⁰=0, then 438579088 is another.
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I decided to make a little video using @geogebra illustrating the relative sizes of the planets, the orbits of the planets, and an assortment of stars (including WOH G64, the largest star of known radius—1540 times the radius of our sun!).
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