the equation for the Cassinian oval http://xahlee.org/SpecialPlaneCurves_dir/CassinianOval_dir/ cassinianOval.html in Bipolar coordinate is: r1 r2 == b^2. my...
... Xah, Glad you started this nice group for curve and surface fans... Ok.. in curves like the Conics, Cassinian ovals, Apollonius Circles, Lines of force and...
Hi Narasimham, I have hardly seen bi-polar coordinate mentioned in math literatures i've came across, except in just the name in some books on curves. Do you...
... literatures ... Do ... to ... any math involved? Could you give an example? ... see. This is covered in several textbooks on functions of complex ...
i just discovered a truly excellent program for plane geometry http://mathsrv.ku-eichstaett.de/MGF/homes/grothmann/java/zirkel/doc_en/ index.html written in...
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 ...
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