A (cata)caustic is the envelope of lines reflected in a curve. The caustic formed by parallels lines reflected in a semicircle is a cardioid, such as can be seen in the bottom of this MSE coffee mug.

Other envelopes include evolutes. An evolute is the envelope of the normal lines to a given curve; the given curve is the involute of the evolute.

A famous involute is the cycloid, which the involute of itself (and therefore the evolute of itself, too). Because the cycloid is a tautochrone, Huygens used it to design a clock (left, Fig. II), which Coster made (right):

The involute of a circle (the smaller ones) can be used to design gear teeth that roll off each other without slipping (thus minimizing heating due to friction):

A (cata)caustic is the envelope of lines reflected in a curve. The caustic formed by parallels lines reflected in a semicircle is a cardioid, such as can be seen in the bottom of this MSE coffee mug.

Other envelopes include evolutes. An evolute is the envelope of the normal lines to a given curve; the given curve is the involute of the evolute.

A famous involute is the cycloid, which the involute of itself (and therefore the evolute of itself, too). Because the cycloid is a tautochrone, Huygens used it to design a clock (left, Fig. II), which Coster made (right):

The involute of a circle (the smaller ones) can be used to design gear teeth that roll off each other without slipping (thus minimizing heating due to friction):