Category Archives: golden ratio

Nature by Numbers

This has been making the rounds of the math blogosphere (blathosphere?), but in case you haven’t seen it yet, check out Crist√≥bal 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

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

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

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)

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

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

Okay, time for a solution to Challenge #5…

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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