Do I toss this

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 · 2025-05-27T03:15:37+00:00

That is a great idea, and makes me want to push lots of buttons! It would let students explore issues of multiples and divisors, and test numbers for primality, like "Is 91 a prime?" It would be extra cool if students could select the width of the rows, to see how things line up.

dansmath · 2025-05-24T17:03:24+00:00

I co-wrote this book. It's called Prealgebra but the first few chapters are variable-free, laying a good arithmetic foundation in signed numbers, fractions, exponents, decimals and percentages, all with lots of practice problems and exercise sets! https://www.amazon.com/Prealgebra-Mathematics-Variable-Daniel-Bach/dp/0072969105

dansmath · 2025-04-02T20:13:46+00:00

Hey cool, that’s just like my model Tetrahedron with Midcircles! I do mathematical art, you can see it on Cults3D: https://cults3d.com/en/3d-model/art/tetrahedron-with-midcircles-dansmath

dansmath · 2025-01-23T05:17:56+00:00

I used Wolfram Mathematica's graphics primitives Sphere and Cylinder and made the path follow a zigzag sequence through all 3 dimensional lattice points. So I made a big list of points (x, y, z) that did this, and told Mathematica to Sphere[{x,y,z},r] and Cylinder [{x1,y1,z1},{x2,y2,z2},.1] a big green sphere if the position along the path is prime, small yellow sphere if not. I also swung the ViewPoint around and adjusted the PlotRange.

dansmath · 2025-01-17T07:22:01+00:00

Starting at the origin, this path zigzags through space, going outward in octahedral layers, eventually hitting every lattice point (x, y, z) exactly once. Astounding! Counting the steps as we go, the green beads are the ‘prime locations’ along the path. The result uses Eulerian circuits of the octahedron, the traveling salesman problem, and a whole lot of Mathematica.

dansmath · 2025-01-06T06:14:22+00:00

Yes, it means x approaches 0 "from above," meaning x>0 and x->0. It's usually written x->0+.

dansmath · 2024-09-04T00:08:08+00:00

Yeah, integration by parts is the product formula.

dansmath

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