Why We Love Math!

In honor of The Hobbit, I have a riddle for you.

My first is twice in apple but not once in tart. My second is in liver but not in heart. My third is in giant and also in ghost. Whole I'm best when I am roast. What am I?

(And your answer is...?)


Ever since my commitment to become a math teacher, I have taken it on as my duty to show the world why we love math. From circle packing holiday cookies to figuring out the probability of how much I need a puppy (which is 1, by the way), math has been a prominent feature in the lives of Daniel and me. So, in true Caitlin-fashion, I have an experiement for you:

Step 1: Scrounge together 2 quarters, a regular sized piece of paper and a pencil.
Step 2: Place both quarters flat on the piece of paper so that one quarter is placed above the other and are only touching at one point on their ridges. (I would suggest making both Washington's facing up).
Step 3: Mark the top coin at the point where it touches the other coin.
Step 4: Rotate the top coin (the one with the mark) around the other coin in a smooth fashion. With your pencil, draw the path of the mark on the coin on your paper. This should also be a smooth curve. (Note: it does NOT matter which way you rotate the coin, either to the left or right will work.)
Step 5: Once the rotated quarter returns to its starting position, you are done. Remove both quarters from the piece of paper and look at the curve you've drawn.

A hint to what your picture should look like can be found in the answer to the following riddle:

What can warm without heat? What can make a man both strong and weak? What can you feel that you can not touch? What can move you that can not be budged?



(If you wouldn't mind, take a picture of your design so I can put it in here for all to see.)