Category Archives: infinity

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

Convergence

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