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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
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