What is One?

This weeks guest blogger is Gary from GaryJones


As it's the 1^st of the 1^st I thought I'd share some facts about the number 1. The following have been pulled from three different resources.

• 1 is the the first natural number, the first square number, the first cube number, the different between two consecutive numbers and the multiplicative identity (when you multiply a number by 1 the number does not change).


• 1 is not a prime number; prime numbers have exactly two distinct factors.


• An ace is number one in playing cards. French playing cards are marked '1' instead of 'A'.


• A cyclops is a creature with one eye and a dromedary is a camel with only one hump.


• There is only one of lots of things. There is only one planet Earth, there is only one Atlantic Ocean and there is only one you. All of these are unique.


• Words beginning with uni- often mean there is one of something. For example, unicycles have one wheel and unicorns have one horn. Unisex means the two sexes appearing as one because they are indistinguishable by hair or clothing.


• The letters A, B, C, D, E, M, T, U, V, W and Y all have one line of symmetry.


• The international dialling code for the USA and Canada is 01.


• Mathematicians define a 'sphere' as the surface of a sphere, not a solid ball, so a sphere has 2 sides: the outside and the inside. However, there are also 1-sided surfaces!


• A Möbius strip has one edge and one surface. It is easy to make by taking a long strip of paper, giving it one twist and joining together the ends. Ask one of your friends to colour one side of the strip red and the other side green. This turns out to be impossible because the strip has only one side.


• Mono- can also mean that there is one of something. A monocle is an eyeglass with only one lens, and a monorail is a railway where the track consists of a single rail. Monochrome means using only one colour, like a black-and-white photograph. Chemical names often include mono-; for example carbon monoxide is a poisonous gas whose molecules have only one atom of oxygen.


• Hydrogen has the atomic number 1.


• Why 1=0! (pronounced "zero factorial")? Because 4! = 4x3x2x1 and 3! = 3x2x1. Therefore 4! = 4x3! In the same way 3! = 3x2! and 2! = 2x1! So it follows that 1! = 1x0! Therefore 0! must be equal to 1 or 1! would be 0... And so 2! would be zero and then 3! and so on.


• January has always been month 1 in Gregorian and Julian Calendars. Before around 713 BC however, March was the first month in the Roman calendar.


• Benford's law states that in a huge assortment of number sequences - in listings, tables of statistics, random samples from a day's stock quotations, a tournament's tennis scores, the populations of towns, electricity bills in the Solomon Islands, and much more, the digit 1 tends to occur with probability ~30%, much greater than the expected 11.1% (i.e., one digit out of 9). Dr. Nigrini gained recognition by applying a system he devised based on Benford's Law to some fraud cases in Brooklyn. The idea underlying his system is that if the numbers in a set of data like a tax return more or less match the frequencies and ratios predicted by Benford's Law, the data are probably honest. But if a graph of such numbers is markedly different from the one predicted by Benford's Law, he said, "I think I'd call someone in for a detailed audit".


• During any police lineup the suspects wear nos. 2 through 9 because it is considered too suggestive to make anyone display the no. 1!


• 1 symbolizes the essence of all phenomena, which is a single unity, before being divided. It represents also the contrast between essence and existence; the enduring and the ephemeral; the unity in diversity (one/many). According to Hopper, the first advance towards counting is with the use of words for one and for many, the differentiation from the self from the group. We still say 'numero uno' to speak of ourselves.


• "Taiji" (also termed as "Dayi" or "Taiyi"), in the Mystical Numbers of Taoism, represents the ONE, the Ultimate, the Order. The martial art known as "Taijiquan" based its movement's philosophies upon the notion of Taiji.


• In the English language, there is a word with just ONE vowel which occurs 6 times: indivisibility.


• The roots of the word one (un-, sim-) are hidden in the following words: inch, onion, ounce, primal, primrose, prince, simple, single, simulate, unanimous, unicorn, uniform, unify, union, unique, unit, universe; alone, any, lonely, only, none. In French: ensemble, oignon, premier, printemps, sanglier, semblable, sincère.

What interesting facts, mathematical or otherwise do you know that involve the number 1?