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 of your chosen one, and multiply them. For example, suppose we pick . . The two Fibonacci numbers on either side of are and ; their product is .
Try this with a few different Fibonacci numbers. Better yet, make a table of your results for the first Fibonacci numbers. What do you notice? Can you express your observation algebraically? Can you prove it is true for every Fibonacci number? What does this have to do with the area paradox?