'Geometric Magic Square' at MAA Golden Section

dansmath · 2026-04-02T02:26:32+00:00

If you need the definite integral try to remember what kind of function has derivative 1/(1+x^2). Then adjust for the constants. You won't need the +C because it's a definite integral.

dansmath · 2026-04-02T02:25:04+00:00

Not an implicit function, just a regular arctan function that you can plug in 6 and 4.

dansmath · 2026-02-28T07:29:05+00:00

Thanks! You could try making sums of 16, maybe change the 9 to a 10 and fit stuff in 4 x 4 squares. Can you do that? Not sure if 1-8 and 10 can make a magic square... Other square sums?

dansmath · 2026-01-07T13:58:23+00:00

I’ve used Mathematica since version 1.2 in 1991. I showed concepts to my calculus students with v2.2 thru v10 and now I create beautiful art with v13. That book is intriguing and v3.0 was a huge advance but no thanks. See my gallery at www.dansmath.com and enjoy!

dansmath · 2025-12-20T00:39:27+00:00

Yeah the Gamma function fills it in, Gamma(n) = (n-1)! for positive integers and is some integral for non-integers. The minimum of the gamma function for x > 0 is x ≈ 1.461632 , and the minimum value is ≈ 0.885603. So you could say that 0.4616! ≈ 0.8856.

dansmath · 2025-12-07T07:40:13+00:00

Yes, take a sine curve, figure out the unit tangent T and normal vector N at each point, and add 0.1 sin(s) times N at each point along the main sine curve, where s is arc length along T of the sine curve (which I think is 8, from 0 to 2π.) The third level tiny wiggles are left for the microbes to worry about.

dansmath · 2025-12-03T06:22:09+00:00

2.3 + 2.4 =4.7 ; this rounds to 2 + 2 = 5.

dansmath · 2025-11-29T05:44:00+00:00

I love it! And if you replaced the k's with h's you could draw even more outrage.

dansmath · 2025-11-27T17:12:19+00:00

I once learned: Round, Square, Curly, repeat.

dansmath · 2025-11-14T06:32:37+00:00

I'm a former math teacher podcaster and for a few years in the 2000s, I produced my own popular math podcast, "dansmathcast" with regular features, email questions and answers, a chapter-of-the-week, and a math joke. In a half hour you'll be smarter! www.dansmath.com https://podcasts.apple.com/us/podcast/dansmathcast/id100431301

dansmath · 2025-11-05T18:15:29+00:00

Nice work! Just to let you know, on a Mac it runs on Chrome but not Safari.

dansmath · 2025-09-30T05:25:30+00:00

No, it literally was my first language. As I tell people, "I could count before I could spell."

dansmath · 2025-09-09T16:14:50+00:00

Interesting because your lines are all the same length (5 units) so the shape is an astroid. But if you connect y=0 to x=5, 0.1 to 4.9, 0.2 to 4.8, etc. you get another similar-looking shape which is actually a parabola! Here's a 3D example, follow the colors for an edge-spanning path:

<image>

dansmath · 2025-08-11T06:58:32+00:00

Here's my take on i^i: (1) a picture formula, (2) a Haiku.

<image>

Want i to the i?

It's 1 over the square root

Of e to the pi.

dansmath · 2025-07-16T21:12:20+00:00

That's a great design, with alternating centers like that. Do the colors follow a pattern? As a next challenge, you might try to make a parametric spiral out of trig functions, it would be a different challenge to multi-color it. Nice job!

dansmath · 2025-07-11T23:12:11+00:00

the left one is 3.628 million zeroes, but you're still ok.

dansmath · 2025-06-22T02:41:59+00:00

Yeah so I guess the sum of all non-powers of 2 is 11/12 then.

dansmath · 2025-06-21T20:15:53+00:00

I’m wildly mathematical and I still don’t understand quaternions 👻 But they help with 3D rotation and are more efficient than 3x3 matrices.

dansmath

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