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 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

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