HPS 0628 Paradox

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Assignment 12. Geometric Constructions 2

For submission

1. Show that (i) squaring a circle is equivalent to (ii) constructing an interval of length π. That is, show that
a. (i) deductively entails (ii); and
b. (ii) deductively entails (iii).

2.
a. Which of the following are within the field of constructible numbers:
√2, √3, √8, 3√2, 3√3, 3√8, 4√2, 4√3, 4√8 ?

b. Show that those you find to be in the field are in the field.

3. A four-dimensional cube of side L has volume L4. If we have a unit four-dimensional cube, determine whether it is possible to double the cube, that is, to construct a four-dimensional cube of twice the volume.