The objects of mathematics can have fascinating names. Mathematical words describe numbers, shapes, and logical concepts. Some are ordinary words adapted for a specific purpose, such as cardinal, cube, group, face, field, ring, and tree. Others are unusual, like cosecant, holomorphism, octodecillion, polyhedron, and pseudoprime. Some sound peculiar—deleted comb space, harmonicmap, supremum norm, twisted sphere bundle, to name a few. Mathematical words have appeared in poems (see [19]). Let us look at some mathematical words.

Lemniscate

Consider the lemniscate, a curve shaped like a figure-eight as shown in Figure 1.1. We learn in [46] that it gets its name from the Greek word lemniskos, a ribbon used for fastening a garland on one's head, derived from the island Lemnos where they were worn. By a coincidence, the end of the word lemniscate sounds like “skate,” and one can (with practice and skill) skate a figure-eight. Skating a lemniscate is portrayed in the animated Schoolhouse Rock segment “Figure Eight,” with the theme sung by jazz vocalist Blossom Dearie (1926–2009). She sings that a figure-eight is “double four,” which is probably the Indo-European origin of the word “eight.” In the animation, a girl daydreams of skating a figure-eight that turns into the infinity symbol ∞.