Projective Reduction
Recall the
“fish-tail” diagram:
* *
|\ /|
| \ / |
x | * |
y z
= x<+>y
| /|\ |
|/ |z\|
*--*--*
If you flip
this diagram left for right, then the lengths x, y and z remain the same; so x<+>y = y<+>x. Commutativity is
illustrated by reflection.
If you stretch it vertically then x, y and
z become kx, ky and kz; so k(x<+>y) = kx <+> ky.
So distribution is illustrated by stretching.
So
commutativity and distribution for reduction relate to the symmetries of the
fish-tail diagram. The associative law is more complicated. It is illustrated
by this diagram:![](data:image/png;base64,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)
AC, DE, FG, HI
and JK are parallel;
ABC, CIJ, BGJ,
BEH, AEGIK and ADFHJ are collinear.
If AC = x, JK
= y and AB = z, then
IH = x<+>y ; GF =
y<+>z ; DE =
(x<+>y) <+>z
But (x<+>y)<+>z = x<+>(y<+>z);
So the AC and FG fishtail meets at E;
Therefore C, E and F are collinear.
If AC,
DE, FG, IH and JK are parallel;
and ABC,
CIJ, BGJ, BEH, AEGIK and ADFHJ are collinear;
then CEF
are collinear.
That theorem
in affine geometry is equivalent to the associative law for reduction. I
therefore call this the Affine Reductive Associative Theorem. Here is a
projective version of the diagram, with D omitted, and including L as a point
at infinity:
Given these
collinearities:
ABCL, FGL,
HIL, JKL, CIJ, BGJ, BEH, AEGIK, AFHJ
Then CEF are
collinear.
This theorem
is a consequence of Pappus’s Hexagon Theorem:
for BCL are collinear points and FHJ are collinear points; therefore the
opposite sides of the hexagon BHLFCJ meet in three collinear points: EGI. This
proof from Pappus does not assume that the three lines BCL, FHJ and EGI meet at
a point, as they do here.
So the associativity of
reduction is a consequence of a special case of Pappus’s Hexagon Theorem!
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