104 Geometrical Problems- DRAWING A STRAIGHT LINE
If we want to describe a circle we use an instrument that we call a pair of
compasses, but if we need a straight line we use no such instrument-we em-
ploy a ruler or other straight edge. In other words, we first seek a straight line
to produce our required straight line, which is equivalent to using a coin,
saucer, or other circular object to draw a circle. Now, imagine yourself to be
in such a position that you cannot obtain a straight edge-not even a piece
of thread. Could you devise a simple instrument that would draw your
straight line, just as the compasses describe a circle?
It is an interesting abstract question, but, of course, of no practical value.
We shall continue to use the straightedge.
- DRAWING AN ELLIPSE
I suppose a large proportion of my readers are familiar with this trick for
drawing an ellipse. It is very useful if you have to cut a mount for a portrait
or to make an oval flower bed. You drive in two pins or nails (or, in the case
of the flower bed, two stakes) and enclose them with an endless band
of thread or string, as shown in our diagram, where the pins are at A and B,
and the pencil point, at C, stretches the loop of thread. If you keep the thread
taut and pass the pencil all round until you come back to the starting point
you will describe the perfect oval shown.
But I have sometimes heard the complaint that the method is too haphazard:
that it was only by a lot of trials that you can draw an ellipse of the exact di-
mensions required. This is a delusion, and it will make an interesting little
puzzle to show at what distance apart
the pins should be placed, and what
length the string should be, to draw
an ellipse, say, twelve inches in length
by eight inches in breadth.
Can you discover the simple rule
for doing this?305. THE BRICKLAYER'S TASK
When a man walked in his estate, one of the walls was partly level and
partly over a small rise or hill, precisely as shown in the drawing herewith,