Words for Number Concepts

 Odd Even Square Cube Product Numerator Denominator Quotient Ratio Factor Prime Number Limit Exponent Imaginary Number Transcendental Boundary Condition Algebra Arithmetic Logical Equation Inequality Maximum Constraint Probability

Rational and Unit Fraction are other phrases that have different meanings in today's mathematical context than in the past. Probability is the basis of gambling and many games. Some terms above are historic. They remain valid but awkward and sometimes obstacles. The years 1991 and 2002 have special numbers. No other 20th century year reads the same left to right and right to left. Like years 1997 and 1939, 1991 is odd. But year 2002 is divisible by two, hence even. It possesses the reversible quality, and so has palindrome nature. 1991 and 2002 are joined additively by the (odd) palindrome 11. Are there other such years possessing this property with no palindrome between them?.

I know what a unit is but thought it very odd that this statement went over my head a few years ago. You know of course that the Egyptians used only unit fractions. - numbers via hieroglyphics has more on this topic. But notice that the word fraction was seen as ordinary or usually understood, and not placed in the above table! So we need another set, terms for K-12.

Although square, cube and exponent are well known concepts you may find combining the following two facts with practical answers sought below them oddly troubling and a poor fit with other number topics.
• Every squared positive integer can be represented as the sum of adjacent odd numbers.
• Every cubed positive integer can be represented as the sum of adjacent odd numbers.
• 92 = 81 = ?? (what sum of adjacent odd numbers)
• 73 = 343 = ?? (what sum of adjacent odd numbers)
The word factor could help someone trying to discuss in ordinary words the elements of equations shown at solution. An easy-to-read description of   factorial   joining it with factor could help some people. Reasons for the enormous quantities from multiplying many factors ... and how exclamation points () convey a special notion could help.

Finally, isn't it odd that a batter who hits once in three at bats in a baseball game, and the next time has a single success in two tries doesn't bat five-sixths? It depends on which arithmetic you use for fraction addition. Two "unconventional" possibilities are baseball and electrical. But isn't it odd that we think them unconventional?

Oddly enough we consider limits to be known only for a few hundred years although the Greeks knew a great deal about their
use to determine circle areas. They used nested circles and both described and evaluated a hard-to-compute nonzero limit1.

1Kasner and Newman, Mathematics and the Imagination, NY: Simon and Schuster, 1940; ISBN 1-55615-104-7 Redmond: WA, Tempus Books of Microsoft Press, 1989, Fig. 125, p. 311.
 4/4/06 Version http://www.cs.ucla.edu/~klinger/gnames.html ©2006 Allen Klinger