Category Archives: infinity

Recounting the Rationals, part I

Posted on December 27, 2007 by Brent

This is the first in a series of posts I’m planning to write on the paper “Recounting the Rationals“, by Neil Calkin and Herbert Wilf, mathematicians at Clemson University and the University of Pennsylvania, respectively. I’m really excited about it, … Continue reading →

Posted in counting, infinity, number theory, pattern, sequences | 19 Comments

Open problems: Twin prime conjecture

Posted on April 10, 2007 by Brent

Oops, so much for posting once a week! My excuse is that I’ve been hard at work on my book. Well, nothing to do but get right back at it. I promise* I will be better** about posting regularly*** from … Continue reading →

Posted in challenges, famous numbers, infinity, primes | 3 Comments

New bookshelf entry: The Book of Numbers

Posted on September 20, 2006 by Brent

After seeing John H. Conway and Richard Guy‘s The Book of Numbers cited in yet another interesting article/book/whatever, I finally decided that I clearly had to read it. (It seems to get cited a lot in certain circles.) I wasn’t … Continue reading →

Posted in books, famous numbers, geometry, golden ratio, infinity, links, primes | 3 Comments

The Mandelbrot Set

Posted on May 8, 2006 by Brent

For those of you already familiar with the Mandelbrot Set, I suppose this will be like visiting with an old friend. For those of you who aren’t — you’re in for a treat! Okay, you say, that looks pretty cool … Continue reading →

Posted in convergence, fractals, infinity, iteration | 1 Comment

Convergence

Posted on March 20, 2006 by Brent

Let’s dig a little deeper behind the solutions to Challenges #1 and #2. What on earth does it mean for an infinite expression to have a “value”? Well, as noted in the solution to Challenge #1, what we’re really talking … Continue reading →

Posted in convergence, infinity | 3 Comments

Challenge #2 Solution

Posted on March 19, 2006 by Brent

And here are the solutions to Challenge #2…

Posted in infinity, solutions | 4 Comments

Challenge #2

Posted on March 10, 2006 by Brent

Can you apply the techniques learned from the solution to Challenge #1 in order to find a value for these expressions? 1. 2. 3.

Posted in challenges, infinity | 9 Comments

Challenge #1 Solution

Posted on March 10, 2006 by Brent

Read on for the solution to Challenge #1… but give it a try first if you haven’t already!

Posted in famous numbers, golden ratio, infinity, solutions | 7 Comments

Challenge #1

Posted on March 8, 2006 by Brent

What better way to start things off than a challenge? Challenging problems are the golden road to discovering mathematical beauty: they spark interest, invite exploration, require thought and creativity, and usually beg to be tweaked, generalized, and otherwise turned into … Continue reading →

Posted in challenges, infinity | 8 Comments