Log24

Tuesday, July 6, 2010

Window, continued

Filed under: General,Geometry — Tags: , — m759 @ 10:31 AM

"Simplicity, simplicity, simplicity!  I say, let your affairs
be as two or three,
and not a hundred or a thousand;
instead of a million count half a dozen,
and keep your accounts on your thumb-nail."
— Henry David Thoreau, Walden

This quotation is the epigraph to Section 1.1 of
Alexandre V. Borovik's
Mathematics Under the Microscope:

Notes on Cognitive Aspects of Mathematical Practice
(American Mathematical Society, Jan. 15, 2010, 317 pages).

From Peter J. Cameron's review notes for
his new course in group theory

http://www.log24.com/log/pix10A/100705-CameronExample.jpg

From Log24 on June 24

Geometry Simplified

Image-- The Four-Point Plane: A Finite Affine Space
(an affine  space with subsquares as points
and sets  of subsquares as hyperplanes)

Image-- The Three-Point Line: A Finite Projective Space
(a projective  space with, as points, sets
  of line segments that separate subsquares)

Exercise

Show that the above geometry is a model
for the algebra discussed by Cameron.

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