maths humour

At Least One

"At least one" is a mathematical term meaning one or more. It is commonly used in situations where existence can be established but it is not known how to determine the total number of solutions.

One of the three jokes known to Christopher, the protagonist in the novel The Curious Incident of the Dog in the Night-Time, concerns the preciseness with which mathematicians apply the term "at least one." As told by Christopher (Haddon 2003, p. 142), the joke runs as follows. "There are three men on a train. One of them is an economist and one of them is a logician and one of them is a mathematician. And they have just crossed the border into Scotland (I don't know why they are going to Scotland) and they see a brown cow standing in a field from the window of the train (and the cow is standing parallel to the train). And the economist says, 'Look, the cows in Scotland are brown.' And the logician says, 'No. There are cows in Scotland of which at least one is brown.' And the mathematician says, 'No. There is at least one cow in Scotland, of which one side appears to be brown.' And this is funny because economists are not real scientists and because logicians think more clearly, but mathematicians are best."

GEOMETRY

Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects like the point, line, circle, triangle, and polygon), solid geometry (dealing with objects like the line, sphere, and polyhedron), and spherical geometry (dealing with objects like the spherical triangle and spherical polygon). Geometry was part of the quadrivium taught in medieval universities.

A mathematical pun notes that without geometry, life is pointless. An old children's joke asks, "What does an acorn say when it grows up?" and answers, "Geometry" ("gee, I'm a tree").

Historically, the study of geometry proceeds from a small number of accepted truths (axioms or postulates), then builds up true statements using a systematic and rigorous step-by-step proof. However, there is much more to geometry than this relatively dry textbook approach, as evidenced by some of the beautiful and unexpected results of projective geometry (not to mention Schubert's powerful but questionable enumerative geometry).

The late mathematician E. T. Bell has described geometry as follows (Coxeter and Greitzer 1967, p. 1): "With a literature much vaster than those of algebra and arithmetic combined, and at least as extensive as that of analysis, geometry is a richer treasure house of more interesting and half-forgotten things, which a hurried generation has no leisure to enjoy, than any other division of mathematics." While the literature of algebra, arithmetic, and analysis has grown extensively since Bell's day, the remainder of his commentary holds even more so today.

Formally, a geometry is defined as a complete locally homogeneous Riemannian manifold. In , the possible geometries are Euclidean planar, hyperbolic planar, and elliptic planar. In , the possible geometries include Euclidean, hyperbolic, and elliptic, but also include five other types.

i

The" imaginary number (also called the imaginary unit) is defined as the square root of , i.e., . Although there are two possible square roots of any number, the square roots of a negative number cannot be distinguished until one of the two is defined as the imaginary unit, at which point and can then be distinguished. Since either choice is possible, there is no ambiguity in defining as "the" square root of .

In Mathematica, the imaginary number is implemented as I. For some reason, engineers and physicists prefer the symbol j to , probably because the symbol (or ) is commonly used to denote current.

In the novel The Da Vinci Code, the character Robert Langdon jokes that character Sophie Neveu "believes in the imaginary number because it helps her break code" (Brown 2003, p. 351). In the movie Proof (2005), the character Hal Dobbs (played by Jake Gyllenhaal) is a mathematics graduate student whose rock-and-roll band "plays" a song called "." The joke is that when the band "plays" the song, they remain silent and motionless for several minutes since the song is "imaginary." In Isaac Asimov's short story "The Imaginary" (1942), eccentric psychologist Tan Porus explains the behavior of a mysterious species of squid by using imaginary numbers in the equations which describe its psychology. The anthology Imaginary Numbers: An Anthology of Marvelous Mathematical Stories, Diversions, Poems, and Musings (Frucht 2000) includes many other works involving imaginary numbers.

The following mathematical joke exhibits the strange way in which mathematicians think. "Rrrrrring. Operator: I'm sorry, the number you have dialed is imaginary. Please multiply by and dial again." A variant of this joke, actually left on one mathematician's phone by his son states, "I'm sorry, the number you have dialed is an imaginary number. Please rotate by 90 degrees and try again." Taking this joke one step further gives the "identity"

8 x i =∞