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 as my go-to site for posting math content now. Join us there!.

By the way, I just downloaded all my tweets so I'd have them for the future. It is a huge file, but the interface is pretty convenient. I was worried that X might have discontinued that option. Although all the branding is Twitter, everything downloaded without problems.

In case you are moving to Bluebky, you can find me here:

These are all screenshots of my Excel spreadsheet! You can download the spreadsheet from my blog.

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.

I guess, now that I've posted this, I realize this isn't *quite* right. If A is 0, then after Z would be BA. If A was 1, then after Z would be A[0].

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

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?)

typed in my request and pasted a screenshot of the equation from the article. Within five minutes, it was plotted! I then took a true cardioid, scaled and translated it so it was atop the other heart-shaped curve. As you can see, they are nearly indistinguishable!.4/4

smaller heart-shape is the image of the unit circle under a messy complex map (see below). 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 .3/4

know about complex dynamics told me that although these smaller shapes look like cardioids, they aren't cardioids. They are slightly deformed. Not that I doubted them, but I wanted to see this written down somewhere. I found this article from 1995, which says that this .2/4.

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 .1/4

AI."."Keep calm and wash your hands.". ChatGPT told me this is a "snowclone.". Indeed, there is a wikipedia page for the term

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.

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.

Here are my attempt to get Dall-E to make a "Mandelbrot[wurst]" or "[Mandel]bratwurst."

RT @hschhaya: (Inspired by @divbyzero). In an effort to get something other than politics into your feed, a fun fact about ‘49’. The sum of….

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.

Here's the @geogebra applet.

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!).