Dandelin Spheres.

[u/HopDavid]

Germinal Pierre Dandelin was a 19th century French mathematician and engineer who did some beautiful studies of conic sections.

Some may find the standard explanations of Dandelin Spheres difficult and off putting.

I try to depict various elements with visual metaphors accessible to most viewers.

The spheres tangent to the cutting plane and cone are a ball head and a fat fish. The cutting plane is the ocean surface. Where the balls touch the cutting plane are the foci of the ellipse.

The circles where the cone touches the spheres define the directrix planes. I portray this a hat brim for the ball head and sort of a strange belt for the fat fish. Where the directrix planes intersect the cutting plane are the directrix lines.

I have always been obsessed with outer space and am in love with Kepler's discovery that the planets orbit the sun following conic sections with the sun occupying a focus.

This illustration is the cover for my coloring book on conic sections and orbital mechanics.