The Most Imaginary Number… is Real!

On the eve of “π Day,” a hush has fallen on the mathematical internet. Everyone is gearing up, getting ready to celebrate the beauty of the transcendental number π. Indeed, π is an amazing number. I have a book coming out in October about the geometric problems of antiquity (Tales of Impossibility: The 2000-Year Quest…

Tangent lines to the sine function with rational slope

Today I was wondering the following thing (I won’t bore you with how I ended up with this question): Are there any rational values of for which the line is tangent to the graph of Clearly the answer is yes: But my gut feeling was that this was the only such After some head scratching,…