# Monthly Archives: January 2009

## Carnival of Math #48, and Monday Math Madness #25

The 48th Carnival of Mathematics is posted at Concrete Nonsense. My favorite posts include Foxmath’s post about a strange iterated sequence involving pi and this amazing picture of a fractal cabbage. Also near and dear to my heart is Mark … Continue reading

Posted in challenges, counting, famous numbers, fractals, links | Tagged , , , , | 1 Comment

## More on repetend lengths

In a previous post, I noted that the length of the repetend (repeating portion of the decimal expansion) of a fraction with prime denominator p is at most p-1, and in fact divides p-1. I also said: In fact, there’s … Continue reading

Posted in group theory, number theory, pattern, primes | Tagged , , , , | 6 Comments

## New bookshelf entry: The Annotated Turing

For my birthday I got, among other things, a copy of The Annotated Turing: A Guided Tour Through Alan Turing’s Historic Paper on Computability and the Turing Machine, by Charles Petzold. I haven’t finished reading it yet, but so far, … Continue reading

Posted in books, computation, people | Tagged , , | 6 Comments

## More on decimal expansions

Today, I’d like to answer some of the questions I raised in the Decimal Expansion Zoo: Which decimal expansions terminate, and which are repeating—and how does it relate to the denominator? As we know, the decimal expansion of every rational … Continue reading

Posted in number theory, pattern | Tagged , | 15 Comments

## Carnival of Mathematics and other links

The 47th Carnival of Mathematics has been put together by jd2718; go give it a read! Some of my favorite posts include factoring by puzzles, teaching binary numbers, the 2009 game, cliques of dichotomies, but there is lots of other … Continue reading

Posted in links | | 1 Comment

## Predicting pi: pretty graphs and convergents

Recall the challenge I posed in a previous post: given the sequence of integers , what can you learn about (assuming you didn’t know anything about it before)? The answer, as explained in another post, is that you can learn … Continue reading

Posted in convergence, famous numbers, pattern, sequences | Tagged , , , | 5 Comments

## Post #100 102!

After just over two and a half years of writing The Math Less Traveled, I’ve reached 100 posts! (Well, 102 actually, I seem to have missed 100…) It’s a little hard to believe I’ve actually written that much, and kept … Continue reading

Posted in meta | 6 Comments