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The curve which is the envelope of reflected (catacaustic) or refracted (diacaustic) rays of a given curve for a light source at a given point (known as the radiant point).

A plane curve discovered by Maclaurin but first studied in detail by Cayley. The name Cayley's sextic is due to R. C. Archibald, who attempted to classify curves in a paper ...

The involute of the circle was first studied by Huygens when he was considering clocks without pendula for use on ships at sea. He used the circle involute in his first ...

The envelope of a one-parameter family of curves given implicitly by U(x,y,c)=0, (1) or in parametric form by (f(t,c),g(t,c)), is a curve that touches every member of the ...

The pedal curve of an epicycloid x = (a+b)cost-b[((a+b)t)/b] (1) y = (a+b)sint-bsin[((a+b)t)/b] (2) with pedal point at the origin is x_p = 1/2(a+2b){cost-cos[((a+b)t)/b]} ...

The locus of a point P (or the envelope of a line) fixed in relation to a curve C which slides between fixed curves. For example, if C is a line segment and P a point on the ...

A hypotrochoid is a roulette traced by a point P attached to a circle of radius b rolling around the inside of a fixed circle of radius a, where P is a distance h from the ...

Meißner (1911) showed how to modify the Reuleaux tetrahedron (which is not a solid of constant width) to form a surface of constant width by replacing three of its edge arcs ...

A convex figure constructed by iteratively halving the base of an equilateral triangle and then sliding adjacent triangles so that they slightly overlap. Combining several ...

A rotor is a convex figure that can be rotated inside a polygon (or polyhedron) while always touching every side (or face). The least area rotor in a square is the Reuleaux ...