Pascal's Limacon

Given a circle with center A and a point C, here are three related ways of constructing Pascal’s Limacon: It is the isotomic (look it up) of the circle with pole C. It is the conchoid (look it up) of a circle centered at A whose circumference passes through C. It is an epitrochoid (look it up) formed by a circle of equal radius rolling around the original. This app constitutes a visual proof of the above, and depends on the fact that the composition of reflections in two parallel lines is equivalent to a translation of twice the distance between the lines.

Tags: Pascal, Limacon, Epitrochoid, Conchoid, Isotomic, Pedal, reflection

Pascal's Limacon

Explore this interesting curve by changing lengths, then see the animation which creates the limacon.

Tags: Limacon, Pascal, curve-animation

Circle isotomic

The circle isotomic is the locus of the reflections of a given point in the tangents to the circle. It is easy to convince yourself that it is also the envelope of the circles whose centers lie on the circle and which pass through the given point. The given point is C.  Try dragging it outside the circle.

Tags: isotomic, curve, envelope, limacon