Today on my morning ride my mind began to wander, and I started thinking about my shoes. I've had this pair for about three years, and they've taken me over 10,000 miles. Thinking about those numbers, I began to to think about how far the shoes travel to take me a mile. The pattern in space the shoe follows is a cycloid or a curtate cycloid, according to one contestant over on 50+. Given those facts, how does one calculate the distance a shoe travels when the bike goes one mile?

I think I have the answer, and I'd like to ask for your's. Here are what I think are the relevant facts: Average speed: 17.3 miles per hour. Average cadence 78 rpm. Crankarm length 175 mm. If you think additional facts are relevant, please so state. Answer must be in feet, and show your work.