Category Archives: infinity

Recounting the Rationals, part I

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

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

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

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


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

And here are the solutions to Challenge #2…

Posted in infinity, solutions | 4 Comments

Challenge #2

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

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

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