Tuesday, July 6, 2010

Window, continued

“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


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)


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

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