Date modified: Thu 2023-05-11 . 11:51 AM
Date created: Sat 2023-10-07 . 09:02 PM
# Rolling a coin around other coins. Take two coins of the same size and place them touching each other on the table. Now fixing one of them, roll the other coin without slipping around the fixed coin. As you make the rolling coin roll around the fixed coin once, how many times has the rolling coin turn around? Is it, (1) One time, (2) two times, (3) three times, (4) other? ![[Excalidraw/Rolling a coin around other coins 2023-05-07 18.41.10.excalidraw.svg]]And what if the fixed coin is **twice** as large as the rolling coin? Or if the rolling coin rolls over **several** fixed coins? ![[Excalidraw/Rolling a coin around other coins 2023-05-07 19.00.33.excalidraw.svg]] In general, let us say the radius of the rolling coin is $1$, and the fixed coins have radius $r$, and denote the **turning number** $T(r,n)$ to be the number of times the the rolling coin would turn after rolling around $n$ coins in a row without slipping, each with radius $r$. What is this function $T(r,n)$? --- #puzzle #geometry