Wild About Math! Making Math fun and accessible

30Jun/093

Now that the MMM #35 deadline has passed …

MMM #35 turned out to be harder than I thought judging by the small number of submissions I received.

I'll be giving away four prizes on Friday - two to the early submitters, one to .mau. for consistently submitting entries to the contest for a really long time, and one to a randomly selected person with a correct submission.

I'll discuss some of the solutions on Friday but, for now, check out these pictures I made. I came up with this problem by playing with the Fibonacci series and arranging rectangles.

Here is the problem description:

Let F(0)=1, F(1)=1, and F(n)=F(n-2)+F(n-1). This is the familiar Fibonacci series.

Simplify F(0)xF(1) + F(1)xF(2) + F(2)xF(3) + F(3)xF(4) + ... + F(n-1)xF(n) + F(n)xF(n+1)

Show your work.

Can you see how these pictures help one to see why the sum is what it is? Do you see why there are two different pictures?



Comments (3) Trackbacks (0)
  1. Nice!
    Do you have this before you know the answer to the problem or after?

  2. Hmmm – reminds me a lot of the golden rectangle.

  3. I can’t quite recall. I was going back and forth between the pictures and the formula.


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