332 Answers- TWO SQUARES IN ONE
Place the two squares together, so
that AB and CD are straight lines.
Then find the center of the larger
square, and draw through it the line
EF parallel to AD. If you now make
GH (also through the center) perpen-
dicular to EF, you can cut out the
four pieces and form the lower square,
as shown.
[This dissection was discovered
about 1830 by Henry Perigal, a British
stockbroker and amateur mathemati-
cian, and first published by him in- It is one of the best of many
ways to demonstrate the Pythagorean
theorem by cutting. See the chapter
on "Paper Cutting" in my New Mathe-
matical Diversions from Scientific
~~-------+---,BAmerican (Simon & Schuster, 1966).
-M.G.]357. CUTTING THE VENEER
The illustration will show clearly how the veneer may be cut. Squares A
and B are cut out entire, as in Figure I, and the four pieces C, D, E, F will fit
together, as in Figure 2, to form a third square.
1
~-!---1 C: .... A! : ......... - :E. ....^2
_E.... : .... : ........ -
....... : ......... ; :B: .... : ......... ~ C F...
.... : ....
F
D