You're probably familiar with ellipses, parabolas and hyperbolas formed from intersections of planes and cones. Ellipsoids, paraboloids and hyperboloids seem...
I don't know about the Spirograph trademark, but a few years ago, I set out to buy a Spirograph for myself. I had a couple when I was a teenager in the 1960s...
I first became interested in the curve traced out by the intersection of a cylinder and a sphere in 1985, when I took multivariable calculus and first learned...
oops... missed a dir. http://xahlee.org/surface/whitney_umbrella/whitney_umbrella.html Xah xah@... http://xahlee.org/PageTwo_dir/more.html ... On Jan...
often, the parametric formula given for the Whitney umbrella x^2-y^2*z == 0 is x := u * v y := u z := v^2 but this creates a squashed version. I wonder if...
It is nice... Is Gauss curvature zero everywhere? How is the variation of principal curvatures? I am sure it is a simple expression. It was mentioned in...
It is a self intersecting surface. I too wish know how the strange singularity at middle point of z-axis has been described. ( u=v= x=y=z = 0). ... ===== ...
i'm reading _Elementary geometry of differentiable curves_ by C G Gibson. in chapter 7, it introduces Contact Function. I find it quite unnatural and hard to...
Mike Williams send me some wonderful parametric formulas for modeling seashells. ... spindle shell R=1; // radius of tube N=5.6; // number of turns H=4.5;...
the following are some wonderful seashell formulas, of Mike's original message. Xah xah@... http://xahlee.org/PageTwo_dir/more.html ... Begin forwarded...
Impressive, it was called Cornucopia.. There was one on Version 2 front end images of Mathematica also. I also played with such parametrizations before. Shall ...
recently i started a mailing lists on Python and Java programing. I started it about a month ago, in which i give daily tips or commentary about them as i...
... I want to learn some orbital mechanics and electrodynamics. So I'm interested in vector fields. Don't have a text handy but IIRC there are level surfaces;...
hi Hop, you might find this wikipedia article useful: http://en.wikipedia.org/wiki/Vector_calculus Xah xah@... http://xahlee.org/PageTwo_dir/more.html ...
here are 3 curves illustrating 3 cusps (at t=0) that has different curvatures. {t^2, t^3} {t^2, t^5} {t^2 + t^3, t^4} first case has curvature Infinity. Second...
new page on cusps, with illustrations: http://xahlee.org/SpecialPlaneCurves_dir/Cusp_dir/cusp.html Xah xah@... http://xahlee.org/PageTwo_dir/more.html...
Just created a page on curvature and tangent circle. See http://xahlee.org/SpecialPlaneCurves_dir/Curvature_dir/curvature.html the interesting idea is the...
i just learned that the locus of cusps of parallel curves is the evolute of the given curve. this is interesting, because it is a alternative definition of ...
Yes,Xah, I also found it intriguing... the base circle is evolute of all parallel involutes, in perhaps the simplest 2D plane example. In fact,this is how...
I added a photo page on Curlicue. See http://xahlee.org/SpecialPlaneCurves_dir/Curlicue_dir/curlicue.html has anyone seen interesting examples? i know that...
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