Monthly Archives: May 2011

Post without words #1

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

Cassini’s identity

Posted on May 15, 2011 by Brent

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 Brent

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

Area paradox unmasked

Posted on May 8, 2011 by Brent

In my last post I presented a paradox, where a set of four pieces forming an 8×8 square could apparently be rearranged to form a 5×13 rectangle, summoning an extra unit of area out of thin air. Quite a few … Continue reading →

Posted in geometry, pictures, puzzles, solutions | Tagged , , , | 1 Comment

An area paradox

Posted on May 2, 2011 by Brent

Here’s a fun paradox which has been around for quite a while and was apparently a favorite of Lewis Carroll. As you can verify for yourself, the two figures above are composed of two different rearrangements of the same four … Continue reading →

Posted in challenges, geometry, paradox, pictures | Tagged , , | 18 Comments