Category Archives: golden ratio

Nature by Numbers

Posted on June 6, 2012 by Brent

This has been making the rounds of the math blogosphere (blathosphere?), but in case you haven’t seen it yet, check out Cristóbal Vila’s awesome short video, Nature by Numbers. Especially appropriate given that I have been writing about Fibonacci numbers … Continue reading →

Posted in fibonacci, golden ratio, links, video | Tagged , , , , | 1 Comment

Explicit Fibonacci numbers

Posted on September 13, 2007 by Brent

Don’t worry, this post isn’t going to be X-rated! By explicit I mean not recursive. Remember that the Fibonacci numbers are defined recursively, that is, each Fibonacci number is given in terms of previous ones: . Doesn’t it make you … Continue reading →

Posted in famous numbers, fibonacci, golden ratio, proof | 4 Comments

Golden powers

Posted on September 10, 2007 by Brent

So, we know from a previous challenge that . That’s a pretty interesting property, which is shared only by its cousin, . I wonder whether other powers of have special properties too? Let’s see: Interesting! What about ? And ? … Continue reading →

Posted in famous numbers, fibonacci, golden ratio, induction, proof | 6 Comments

Challenge #10 Solution

Posted on September 8, 2007 by Brent

Have you tried solving Challenge #10 yet? Go try it first if you haven’t. It’s not too hard, I promise!

Posted in famous numbers, golden ratio, proof, solutions | 3 Comments

Golden ratio properties (Challenge #10)

Posted on September 6, 2007 by Brent

Remember the golden ratio, (phi)? It’s the positive solution to the equation , which can be found using the quadratic formula: Closely related is its cousin, (phi-hat) . As we’ll see, these famous constants actually relate to Fibonacci numbers in … Continue reading →

Posted in challenges, famous numbers, fibonacci, golden ratio, number theory, proof | 6 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

Challenge #5 Solution

Posted on September 7, 2006 by Brent

Okay, time for a solution to Challenge #5…

Posted in famous numbers, golden ratio, solutions | Comments Off on Challenge #5 Solution

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