And the envelope please...

What is the phantom curve you see when you look at a set of lines, perpendicular to a set of chords through a common point in a circle?

Tags: envelope, circle, ellipse, hyperbola

Rotating Ellipses with Arcs

Now that you know how two ellipses can rotate such that they are tangent to each other and a third larger ellipse (see this app); the next challenge is to figure out how an arc placed on each ellipse can be constrained (with proportional points along the ellipses) such that each arc always covers half of the ellipse and one endpoint is on the tangent point of the two smaller ellipses.

Tags: Ellipses, conics, puzzler, arcs

Inverted Trammel 2

Archimedes trammel draws an ellipse if used properly. Turning the trammel upside down gives a curve which is certainly not an ellipse.

Tags: Trammel-2

Rotating Ellipses

Two ellipses rotate within a third such that the two smaller ellipses are always tangent to each other and the larger ellipse. Adjusting the variable X demonstrates this rotation. All three ellipses are constrained only by their implicit equations, and the moving ellipses' equations include functions of X that allow them to rotate. Can you figure out what the equations are (the other constants in the equations are a, b, h, and k)?

Tags: Ellipses, conics, puzzler