Monthly Archives: November 2011

Sigmas and sums of squares

Posted on November 29, 2011 by Brent

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!

Posted on November 21, 2011 by Brent

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

Posted on November 19, 2011 by Brent

When I moved this blog from my own custom WordPress installation to wordpress.com 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 | Comments Off on Old posts fixed

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

Posted on November 18, 2011 by Brent

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 , , , , , | Comments Off on Book review: Viewpoints: Mathematical Perspective and Fractal Geometry in Art

Fun with repunit divisors: more solutions

Posted on November 17, 2011 by Brent

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 | Comments Off on Fun with repunit divisors: more solutions

Fun with repunit divisors: proofs

Posted on November 16, 2011 by Brent

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

Posted on November 11, 2011 by Brent

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