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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 footnote^{2}.

Zvezdelina Stankova-Frenkel
2000-11-13