Title Mathematical Coloring Book Mathematical Analysis Physics & Mathematics Euclidean Geometry Convex Geometry Polytopes 1.8 MB 38
##### Document Text Contents
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A Mathematical Coloring Book

by Marshall Hampton

Dedicated to Violet Hampton

Version 0.94

Send comments and suggestions to [email protected]

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Figure 1: Schlegel projection of an icosahedron

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Figure 18: Archimedean and Exponential Spirals

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Figure 19: Cobweb diagram of the logistic map # 1.

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be 3264 real conics to five circles. I still don’t know the answer, but this picture of
some of the real tangent conics to five circles on a regular pentagon might help give
some intuition...

13. Geodesics in the unit disk model of hyperbolic space. This is an approximation to a
tiling by pentagons in which four pentagons meet at each vertex.

14. Part of the hyperbolic plane tiled with stars. In hyperbolic space, each of these stars
is the same size and the edges are ”straight” - i.e. geodesics.

15. The Gröbner fan of the ideal < x5 − y4, y5 − z4, z5 − x4 >.

16. Gröbner fan of the ideal < x3 − y2, y3 − z2, z3 − x2 >

17. Gröbner fan of the vortex problem ideal defined by

−6xyz + xy + xz + 6yz − y2 − z2,

−6xyz + xy + 6xz + yz − x2 − z2,

−6xyz + 6xy + xz + yz − x2 − y2

The variables are the squares of the distances between the three vortices. This equa-
tions determine the stationary configurations of three equal-strength vortices.

18. An Archimedean spiral (r = t) and an exponential spiral (r = e15.73t; chosen arbitrarily
to make things look nicer).

19. Cobweb diagram for the logistic map f(x) = 3.9x(1− x). The graphs of the function
f(x) and its first two iterates f(f(x)) and f(f(f(x))) are plotted.

20. Cobweb diagram for the logistic map f(x) = 3.9605x(1−x). The graphs of the function
f(x), f(f(x)) and f(f(f(f(x)))) are plotted. This parameter for the logistic map is
sitting in a small period-4 window.

21. Equipotential lines for the equal-mass three-body problem. The levels are not equally
spaced in value.

22. Orbits in the planar circular restricted three-body problem with µ = .5 (equal mass
primaries).

23. Sierpinski triangle. One of the first fractal structures considered, it and similar fractals
are important in the topological classification of continua. It has Hausdorff dimension
log(3)/ log(2) ≈ 1.585.

24. Nested circles and Koch snowflakes (finite iterates). The Koch snowflake is one of the
first fractals ever constructed (1906).

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25. Inverse images of two circles, radii 1 and 1/4, under a quadratic map. Image is rotated
90 degrees for a better aspect ratio on the page (so the imaginary axis is horizontal).
The map is z → z2 − .99 + 0.1I.

26. Inverse images of three circles, radii 1, 1/2, and 1/4, under a quadratic map. Image
is rotated 90 degrees for a better aspect ratio on the page (so the imaginary axis is
horizontal). The map is z → z2 − 0.8 + .156I.

27. Hypotrochoid - ? (x(t), y(t)) = (8cos(t) + 8cos(17t/2), 8sin(t)− 8sin(17t/2)).

28. Rotationally symmetric arrangement of parallelogram tiles. The most acute angles in
the three types of tiles in this and the next three figures have angles π/7, 3π/14, and
2π/7.

29. Another rotationally symmetric arrangement of parallelogram tiles.

30. Another rotationally symmetric arrangement of parallelogram tiles.

31. Symmetric Venn diagram for 5 sets represented by ellipses. Discovered by Branko
Grunbaum in 1975.

32. “Adelaide”. A beautiful 7-set symmetric Venn diagram discovered independently by
Branko Grunbaum and Anthony Edwards.

33. Limacons r = 1 + q cos(t) with q ∈ [0, 5].

34. Lissajous curve x = cos(12t), y = sin(13t).