Hello everyone!

For those of you who missed it, I posted a proof of the Pythagorean Theorem every day last week.  For easy reference, here are the links:

Square Rearrangement - Trapezoid Area - Sliding Parallelograms

Euclid - Power of a Point - Similar Triangles - Scaled Copies

All these proofs, and many more (103, as I write this) can be found here.  There are all sorts of spiffy ideas in there, including dissections, tessellations, and even a proof based on Newtonian mechanics.  The language is a bit dense, so I'm happy to clarify any of those proofs in the comments.

 

So why have I done this?  Really, what I want you to take away from this week is that you can look at the same problem in a lot of different ways.  We've taken techniques from seven different branches of geometry and used them to prove the same theorem.  There's always more than one way to find the right answer.  And the more tools you have at you disposal, the easier it becomes to get there.

This applies in the real world too.  As Abraham Maslow (the psychologist with the pyramid) once said, "If all you have is a hammer, every problem starts to look like a nail."  If you only know one way to solve problems, you'll use it even when it doesn't work.  The more different approaches you can try, the easier it is to overcome your problems.  So please, go out and learn about as many different ideas as you can find.  Math, science, humanities, art, any ideas you come across may help you along the way.

 

Sorry for all the philosophical ramblings.  I'll be back next week with more math.

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