Sines and cosines (part 2)

In my previous post I asked the following question. What -values satisfy the equation ? More generally, let  and . Let be the composition of with itself times. Similarly, let be the composition of with itself times. What are the solutions to ? First, let us look at some properties of the iterates of and . is periodic with…

Sines and cosines (part 1)

A friend asked me the following question. What -values satisfy the equation ? It occurred to me to ask a more general question. Let  and . Let be the composition of with itself times. Similarly, let be the composition of with itself times. What are the solutions to ? Is it possible answer this question? Always? Sometimes? Never? I’ll post my…

New graduation requirement

One of my colleagues sent me the link to the most recent comic at xkcd.com. He wrote: “College graduates should be required to say why this is funny as a condition of graduation, a part of numerosity.”

Top 8 most popular polygons

Web surfers love lists—best Twitter apps, best albums, greatest films, world’s richest, best colleges (no, wait, we’re not supposed to like this list). So, I thought I’d serve up a list for my audience. The top 8 most popular polygons. My inspiration The idea for this list came to me while my kids were watching…

Happy square root day!

Happy square root day! Today is the third of nine square root days this century. The first was January 1, 2001 (1/1/01), then February 2, 2004 (2/2/04). Today is March 3, 2009 (3/3/09). The last square root day of this century will be September 9, 2081 (9/9/81). Please act responsibly on this nerdy holiday and…