Search Loci: Convergence:
A mathematician's reputation rests on the number of bad proofs he has given.
In J. E. Littlewood A Mathematician's Miscellany, Methuen & Co. Ltd., 1953.
Van Schooten's Ruler Constructions
Here is a trig table based on a circle of radius 200. Angles are given in degrees. You can tell that the circle is of radius 200 because the table gives sin 90 as 200.
1. How does sin 90 = 200 tell you that the circle is of radius 200?
2. How can you use this table to get our modern value of sin 45, which we know to be about 0.701?
3. How can you use this table to get cosines?
4. In this table, is it still true that tan x = sin x/cos x? How about sec x = 1/cos x? Why or why not?
5. Suppose ABC is a right triangle with right angle at C, and that sides a, b, c are opposite angles A, B, C, respectively. If b = 25 and if A = 40° , then use the table to find the length of side a. You should not convert to modern values of sine and cosine. In fact, it is better if you do not use any decimals, only fractions and whole numbers.
6. Suppose that ABC is a right triangle, with A = 20° and c = 40. Find a.