vlorbik’s 7-color theorem. take n+1.

June 15, 2020 in Finite Geometry, Graphics, Lectures Without Words, MathEdZine

the seven black triangles are

the blends
Mud Yellow Purple
Mud Red Green
Mud Blue Orange

the blurs
Yellow Blue Green
Yellow Red Orange
Blue Red Purple
and

the ideal
Purple Orange Green.

the “theorem” in question is then that
when the “colors” MRBGPYO are arranged
symmetrically (in this order) around a circle
(the “vertices”of a “heptagon”, if you wanna
go all technical), these Color Triples will
each form a 1-2-4 triangle.

but wait a minute, there, vlorb. what the devil
is a 1-2-4 triangle. well, as shown on the “ideal”
triple (center bottom), the angles formed by these
triangles have the ratios 1:2:4. stay after class
if you wanna hear about the law of sines.

note here that a 1-4-2 triangle is another beast altogether.
handedness counts. (but only to ten… sorry about that.)

anyhow, then you can do group theory. fano plane.
th’ simple group of order 168. stuff like that.
all well known before i came and tried to take
the credit for the coloring-book approach.

with, so far anyway, no priority disputes.
okay then.

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