Chapter 43

Lewis Carroll’s unused

geometry pillow problem

According to [Rowe], one of the pillow problems Lewis Carroll had at-
tempted but did not include in his collection of pillow problems was the
following.

Given a triangleABC, to find, by paper folding, a linewhich

intersectsACandABatY andZrespectively) such that if

A′is the reflection ofAin, then the reflections ofBinA′Z

and ofCinA′Ycoincide.

W



C

A

B

A′

Z

Y

The pointW is both the reflection ofBinA′Y, and that ofC in
A′Z. It follows thatA′B=A′W=A′C, andA′is on the perpendicular
bisector ofBC.