It would be great if I wrote a post actually combining probability and spirographs, but that’s not what this is. This is two completely different topics, joined together by the fact that they both elicited conversation during or after dinner last night.
The Probability Problem:
Suppose your school collects Box Tops, and to encourage you to turn them in, for each 10 you turn in each month you’re entered into a drawing for a Webkinz (so if you turn in 20, you’re entered twice). The least well formed question is: if you were able to generate at least one group of 10 per month, is it better to enter them once a month, or to save them all until the end in the hopes of maximizing the opportunity for that single month? Feel free to put answers in the comments!
I have an idea as to the answer to this in simplest terms, and also an idea as to the answer in practical terms. In reality, we work on the system of turning them in whenever we remember, which is something between the two extremes.
The Spirograph Site:
I was surfing the web, and found a site called Spirograph Math (which is actually part of a larger site, but this is the game that occupied me). You have one circle going around the other, and you can trace the design like a spirograph. You can also pause, change the color, etc. It draws pretty pictures like this:
I think you could use math as an excuse for playing with it. For example, can you predict how many times the second circle will go around the first before repeating, or how many lines of symmetry the final figure will have? (One thing to note: the Pen Position is set relative to the center of Radius B: if the Pen Position matches Radius B, it means the Pen is on the edge of the second circle, larger and it’s on the outside of that circle, and smaller and it’s on the inside.)