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## Arithmetic Exercises

In the exercises below, assume that you are given pairs of points whose distance apart represents a length.

1. Addition and subtraction. Given segments of lengths and , construct a segment of length or .
2. Multiplication. Given segments of lengths , , and , construct a segment of length .
3. 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 .
4. 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.
5. Square a rectangle. Given a rectangle, construct a square with exactly the same area.
6. Construct a pentagon. Construct a regular pentagon. For a hint, see the footnote2.

Zvezdelina Stankova-Frenkel 2000-11-13