Saturday, February 9, 2013

Snow Dance

Filed under: General,Geometry — m759 @ 2:09 PM

The Snow White dance from last Nov. 14
features an ad that was originally embedded
in an American Mathematical Society Notices
review describing three books of vulgarized
mathematics. These books all use "great
equations" as a framing device.

This literary strategy leads to a more abstract
snow dance. See the ballet blanc  in this journal
on Balanchine's birthday (old style) in 2003.
That dance involves equation (C) below.

Recall that in a unit ring ,
"0" denotes the additive identity,
"1" the multiplicative identity, and "-1" the
additive inverse of the multiplicative identity.

Three classic equations:

(A)  1 + 1 = 2    (Characteristic 0, ordinary arithmetic)

(B)  1 + 1 = 0   (Characteristic 2 arithmetic, in which 2 = 0)

(C)  1 + 1 = -1 (Characteristic 3 arithmetic, in which 2 = -1)

Cases (B) and (C), in which the characteristic is prime,
occur in Galois geometry.

For a more elaborate snow dance, see Master Class.

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