The World of Mathematics
In Figure 1 you see the ἁρβηλος,
the figure used by Archimedes
to prove a number of inter-
esting theorems about
tangent circles. The
proofs are in his
Book of Lemmas.
See the paper
from my talk
on the arbelos.
Here is a remarkable fact that I just read in the latest American Mathematical Monthly, August-September 2006, in a note on geometric series. Can you prove it?
Welcome to Tom Rike’s Mathematics Page
Heptadecagon
The figure at the right is a star formed with parts of the longest diagonals of a regular 17-gon. It is inlaid at the base of a statue of Gauss in his home town of Brunswick. Gauss at the age of 19 proved that a compass and straightedge construction of a 17-gon is possible.
My talk on the heptadecagon at the Berkeley Math Circle. HeptadecagonBMC.pdf
The figure above gives a visual proof of a packing problem that is suggested by a French confection,
the calisson, which is formed by two equilateral triangles that share an edge.
Theorem: In any packing of a hexagonal box , the number of calissons with a given orientation is one-third of the total number of calissons in the box.
Of course, the theorem is obvious. as soon as one steps out of the plane and views the three visible, equal faces of a cube
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