# 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)

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

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

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

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

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

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

# 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

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.