Monthly Archives: November 2011

Sigmas and sums of squares

Commenter Rachel recently asked, How would you find the sum of ? See here for an explanation of sigma notation—in this case it denotes the sum Of course, for any particular value of we can just plug in values and … Continue reading

Posted in algebra | Tagged , , , , | 6 Comments

Dimensions: go watch! now!

I finally got around to watching the Dimensions videos, which I mentioned once before. They are super cool and will be sure to blow your mind! They start by explaining some simple tools (stereographic projection) and intuition (with references to … Continue reading

Posted in fractals, geometry, links, video | Tagged , , , , | 2 Comments

Old posts fixed

When I moved this blog from my own custom WordPress installation to last March, the formatting, , and images on a number of old posts got screwed up. I have finally finished going back through all my old posts … Continue reading

Posted in meta

Book review: Viewpoints: Mathematical Perspective and Fractal Geometry in Art

This book is certainly quite different from the sort I usually read and review—but I am always interested in new and creative ways to teach mathematics! This is quite a fun book. It’s all about visual art and some of … Continue reading

Posted in books, fractals, geometry, pattern, pictures, review | Tagged , , , , ,

Fun with repunit divisors: more solutions

In Fun with repunit divisors I posed the following challenge: Prove that every prime other than 2 or 5 is a divisor of some repunit. In other words, if you make a list of the prime factorizations of repunits, every … Continue reading

Posted in arithmetic, iteration, modular arithmetic, number theory, primes, programming, proof, solutions | Tagged

Fun with repunit divisors: proofs

As promised, here are some solutions to the repunit puzzle posed in my previous post. (Stop reading now if you don’t want to see solutions yet!) Prove that every prime other than 2 or 5 is a divisor of some … Continue reading

Posted in iteration, modular arithmetic, number theory, pattern, primes, proof | Tagged , , , , | 1 Comment

Fun with repunit divisors

In honor of today’s date (11/11/11), here’s a fun little problem (and some follow-up problems) I’ve seen posed in a few places (for example, here is a very similar problem). If I recall correctly, it was also a problem on … Continue reading

Posted in arithmetic, challenges, modular arithmetic, number theory, primes | Tagged , , | 16 Comments