gallery

dan and the giant sphere

dan and the giant sphere

at a small hideaway in sonoma, california lives a metal sphere apparently about 7 feet in diameter, and hence about 22 feet around.

that's an interesting pattern on the surface. any guess as to how many little shapes cover the sphere? my hand fits through one of them. is it a polyhedron?

dansmath logo (3D star - top view)

dansmath logo (3D star - top view)

starting with the outer red curve (a slightly wiggly circle), the curves change color as they march inward toward the center of curvature at each point. the slight wobble is magnified, especially vertically, as the curves go from orange to blue-green. this object has become my go-to lo-go.

sidetracked loop

sidetracked loop

The loop is flanked by two parallel companion curves at equal distance along the normal direction; one towards the center of curvature, one away from it. 

Complex of loops

Complex of loops

The red curve has spawned seven more curves, changing in color and form based on the outer loop.

saddle traces

saddle traces

The base grid is moved up to the saddle by z = y^2 – x^2 + 5. Trace curves are shown for x = 1.0 (blue) and y = 0.5 (red).

loopy dingles

loopy dingles

a 3D loopy curve is adorned with parallel curves and lots of struts with a colored ball on the end of each one.

pin cushion

pin cushion

a central curve (not shown) wiggles just enough so that the normal and binormal vectors oscillate wildly and form a torus.

twisty bundle

twisty bundle

the curves have three twists in them due to something going on with the tangent vectors or curvature, or maybe they just needed a change.

purple surfaced curve

purple surfaced curve

i used this as a demo file in my presentation "visions of math" at the ibooks author conference in october 2016. a central red curve with parallel curves and struts in the normal direction.

music saddle

music saddle

the x, y, and z coordinates vary as the blue ball goes along the saddle curve. we can keep track of each coordinate using three musical scales. one of the notes is wrong.

saddle bundle

saddle bundle

more parallel curves spin off of the red saddle, in towards the center of curvature at each point. then the dreaded self-intersection occurs.

spheres in a wire basket

spheres in a wire basket

i dreamed up a twisty central curve and made mathematica draw the curves around it, the spheres just touching the wires.