Category Archives: fibonacci

Fibonacci multiples

Posted on May 15, 2012 by

I haven’t written anything here in a while, but hope to write more regularly now that the semester is over—I have a series on combinatorial proofs to finish up, some books to review, and a few other things planned. But … Continue reading →

Posted in arithmetic, challenges, fibonacci, number theory, pattern | Tagged , | 9 Comments

Post without words #1

Posted on May 24, 2011 by
Posted in fibonacci, pattern, pictures, posts without words | Tagged , | 13 Comments

Cassini’s identity

Posted on May 15, 2011 by

My previous post asked you to take any Fibonacci number, square it, and also multiply the two adjacent Fibonacci numbers, and see if a pattern emerged. Here’s a table I made for the first 6 Fibonacci numbers: (Hmm, the numbers … Continue reading →

Posted in algebra, fibonacci, induction, pattern, proof, solutions | Tagged , , | 8 Comments

A Fibonacci pattern

Posted on May 13, 2011 by

Recall the Fibonacci numbers, , the sequence of numbers beginning with where each subsequent number is the sum of the previous two: Try this: pick any Fibonacci number. Square it. Now, look at the two Fibonacci numbers on either side … Continue reading →

Posted in algebra, arithmetic, challenges, fibonacci, pattern, sequences | Tagged , , | 4 Comments

Math Teachers at Play #21

Posted on December 19, 2009 by

Math Teachers at Play #21 is up at Math Mama Writes…, and it includes this cute puzzle, which Sue apparently made up herself: The Numberland News runs personal ads. 21 was looking for a new friend and put an ad … Continue reading →

Posted in fibonacci, links, number theory, puzzles | Tagged , , , , , , | 13 Comments

m-bracelets

Posted on November 22, 2009 by

It is easy to generalize number bracelets to moduli other than 10—at each step, add the two previous numbers and take the remainder of the result when divided by m. Here are some pretty pictures I made of the resulting … Continue reading →

Posted in arithmetic, fibonacci, iteration, pattern, pictures, sequences | 6 Comments

Explicit Fibonacci numbers

Posted on September 13, 2007 by

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

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

Golden ratio properties (Challenge #10)

Posted on September 6, 2007 by

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

A few related problems…

Posted on August 8, 2007 by

Here is a collection of interesting math problems. Despite appearances, they all have something in common. Can you figure out what it is? A single pair of baby rabbits is placed on an island. They take one month to grow … Continue reading →

Posted in famous numbers, fibonacci, pattern, sequences | 3 Comments