Geometrical Problems
- MAKING A PENTAGON
"I am about to start on making a
silk patchwork quilt," said a lady, "all
composed of pieces in the form of a
pentagon. How am I to cut out a true
pentagon in cardboard, the sides of
which must measure exactly an inch?
Of course, I can draw a circle and
then by trial with the compass find
five points equidistant on the circum-
ference" (see the illustration), "but
unless I know the correct size of my
circle the pentagon is just as it hap-
pens, and the sides are always a little
more, or -a little less, than an exact
inch."Could you show her a simple and
direct way of doing it without any
trial?- WITH COMPASSES ONLY
Can you show how to mark off the four comers of a square, using the
compasses only? You simply use a sheet of paper and the compasses, and
there is no trick, such as folding the paper.- LINES AND SQUARES
Here is a simple question. With how few straight lines can you make
exactly one hundred squares?
Thus, in the first diagram it will be found that with nine straight lines I
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