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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
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 Dimensions, fibration, polytope, projection, video
2 Comments
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
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 repunit
Comments Off on Fun with repunit divisors: more solutions
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 divisibility, Fermat, prime, proof, repunit
1 Comment
Fun with repunit divisors
In honor of today’s date (11/11/11), here’s a fun little problem (and some followup 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 divisors, primes, repunit
16 Comments