Assignment VI Math for Poets 2007

Question 1. Consult the article 'The Trisection Problem' by Robert C. Yates in National Mathematics Magazine, Vol. 15, No. 3. (Dec., 1940), pp. 129-142. You may also try to find other sources yourself, as long as you give an argument for their reliability. Read what your source says about the problem of 'trisection of the angle'. It is not necessary to understand all algebra, since the conclusions are in geometrical language again, esepcially sections 3 and 5 are important.
Rephrase the problem in your own words. How old is the problem? The geometers who posed the problem could not solve it. What was eventually the solution, and when was it found?

Question 2. Formulate a geometrical construction problem that we have not yet discussed in class and describe the steps needed to construct the solution. If you cannot solve it (which may well happen, not because of lacking intelligence, but because of the internal structure of mathematics), write down at least one series of steps by which you tried to solve it. You may include a scan of your drawing in your document, but only a scan is not sufficient.

Question 3. A question from the book (2nd ed.: #18 on page 216).
The practical side of Pythagoras Suppose you are building a patio and you want to make certain that the sides of your patio meet at right angles. Give a practical and easy method, using your knowledge of the Pythagorean Theorem, to check that the angle between two adjacent sides is 90 degrees.