Puzzle: However fast a train is travelling, part of it is moving backwards. Which part?
For the answer, see the end of this post.
Timelapse image of bike with lights on the wheel-rims. [Photo from Website of Alexandre Wagemakers, with thanks]
Imagine a small light fixed to the rim of a bicycle wheel. As the bike moves, the light rises and falls in a series of arches. A long-exposure nocturnal photograph would show a cycloid, the curve traced out by a point on a circle as it rolls along a straight line. A light at the wheel-hub traces out a straight line. If the light is at the mid-point of a spoke, the curve it follows is a curtate cycloid. A point outside the rim traces out a prolate cycloid, with a backward loop. [TM076; or search for “thatsmaths” at irishtimes.com ]
![RIght: John Venn (1834–1923) with signature. Left: Stained glass window at Gonville & Caius College showing Venn diagram [images Wikimedia Commons].](https://thatsmaths.files.wordpress.com/2014/08/venn-with-window.jpg)
ThatsMaths 