Category Archives: mathematics

adaptive sampling

Posted on Wednesday, 2016 May 25 by Anton

I got an interesting idea today. As you may already know, I’ve been making models of Klein bottles an’ stuff; heretofore they’ve all been in the form of bent rods, but where possible I’d prefer a continuous surface. (A hollow … Continue reading →

Posted in mathematics | 2 Comments

Scribbles: The Ensmoothening, Part II

Posted on Sunday, 2015 December 20 by Anton

One thing I noticed in that last series of charts is that more than one degree of discontinuity doesn’t help: the best-looking curves are mostly on the diagonal, where only the last nonzero derivative is discontinuous. Here, therefore, are those … Continue reading →

Posted in curve-fitting | 2 Comments

ensmoothening scribbles

Posted on Sunday, 2015 December 06 by Anton

Presented for your consideration: the somewhat disappointing results of an experiment in using piecewise polynomial spirals, of varying degrees of continuity, to fit the Takana — disappointing in that few if any of the curves are as pretty as I … Continue reading →

Posted in curve-fitting | 4 Comments

logarithmic birthday

Posted on Sunday, 2015 June 07 by Anton

I’m exp(4) years old!

Posted in mathematics, me!me!me! | Leave a comment

alternate poker

Posted on Saturday, 2015 May 09 by Anton

Suppose your deck has more than four suits, or some number other than thirteen cards per suit. What happens to the ranks of poker hands? 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 … Continue reading →

Posted in games, mathematics | 3 Comments

elusive avoidance

Posted on Monday, 2015 January 26 by Anton

I’ve been designing printable models of the Lawson-Klein surface w = cos(u) cos(2v) x = cos(u) sin(2v) y = sin(u) cos(v) z = sin(u) sin(v) As you can plainly see, this figure lives in S3 (positively curved 3-space), so stereographic … Continue reading →

Posted in mathematics, merch | 2 Comments

unapologetically one-sided

Posted on Saturday, 2014 June 07 by Anton

My newest design on Shapeways is a model of the Lawson-Klein surface : a stereographic projection of ( cos(u)cos(2v), cos(u)sin(2v), sin(u)cos(v), sin(u)sin(v) )