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Arithmetic Exercises
In the exercises below, assume that you are given pairs of points whose
distance apart represents a length.
- Addition and subtraction. Given segments of lengths
and
, construct a segment of length
or
.
- Multiplication. Given segments of lengths
,
, and
, construct a segment of length
.
- Division. Given segments of lengths
and
, construct a segment of length
. Using the result of the problem
above, show that if you also have a segment of length
, you can
construct a segment of length
.
- Square roots. Given segments of lengths
and
,
construct a segment whose length is
. Clearly, if one of
the segments has length
, you can construct a segment of length
using the same technique.
- Square a rectangle. Given a rectangle, construct a
square with exactly the same area.
- Construct a pentagon. Construct a regular pentagon.
For a hint, see the footnote2.
Zvezdelina Stankova-Frenkel
2000-11-13