HPS 0628 | Paradox | |
Back to doc list
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.