Let S be a semicircle of radius R contained in the first quadrant and with center at (R,0). We define a function f from the positive reals to itself by the following procedure. (See picture below.)

For a positive real number r, first draw a circle, C(r), of radius r centered at the origin. Next draw a straight line, L(r), through the two points (0,r) and the point of intersection of S and C(r). Then f(r) is defined as the x-coordinate of the point of intersection of L(r) and the x-axis.

What is the limit of f(r) as r goes to zero?

(Before diving in to the problem, what does your geometric intuition say the answer should be?)

---

Puzzler: The English language is probably the only language in which you could hold a spelling bee. There are so many words with silent letters! The question for this week is: Just how bad is the spelling of the English language?

For each of the 26 letters of the English alphabet, try to find a word, 26 words in all, containing that letter as a silent letter. Note that some letters can be more silent than others; for example, it could be argued that the word "spelling" has one of its l's silent. But there are other words in which it is "more silent."

---

Go to the Bradley University Home Page

You are visitor number 4441 to this page. Page last updated 30 March 1997.