Let ABCD be a rectangle, and P any point in the interior. Prove that AP

^{2}+ PC

^{2}= BP

^{2}+ PD

^{2}.

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E16. A Property of rectangles

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Someone showed me the following problem at the meeting of ATMIM (Association of Teachers of Mathematics in Massachusetts.) It's proof is a great non-routine use of the Pythagorean theorem. I think the proof is too easy to post, but if anyone can't figure it out, post a comment and I will make the solution available.

Let ABCD be a rectangle, and P any point in the interior. Prove that AP^{2} + PC^{2} = BP^{2} + PD^{2}.

Let ABCD be a rectangle, and P any point in the interior. Prove that AP

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From time to time I will post an elementary mathematics problem which I hope readers may enjoy. "Elementary" to me means that the problem does not require any specialized mathematical knowledge beyond high-school mathematics to solve. Some of these elementary problems will be very simple, others will require a great deal of cleverness. Elementary math problems will be denoted by the letter E followed by the problem number.

I will sometimes post a link to a solution. If I haven't yet posted a link, you may send me your answer and if it is correct I will credit you on the blog. To send answers, please mailto: peterash3@gmail.com.

Thanks,

Peter

I will sometimes post a link to a solution. If I haven't yet posted a link, you may send me your answer and if it is correct I will credit you on the blog. To send answers, please mailto: peterash3@gmail.com.

Thanks,

Peter

From time to time post problems that are somewhat more advanced than those in the Elementary Math Problems. These problems will require a knowledge of some college-level mathematics, either for their statement or for the solution that I know. Advanced math problems will be denoted by the letter A followed by the problem number.

I will sometimes post a link to a solution. If I haven't yet posted a link, you may send me your answer and if it is correct I will credit you on the blog. To send answers, please mailto: peterash3@gmail.com.

I will sometimes post a link to a solution. If I haven't yet posted a link, you may send me your answer and if it is correct I will credit you on the blog. To send answers, please mailto: peterash3@gmail.com.

Here are some recent reviews on mathematics, learning theory, education, and related technology:

The Number Sense: How the Mind Creates Mathematics by Stanislaus Dehaene, Oxford University Press 1997

Three Books on the Riemann Hypothesis

The King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry by Siobhan Roberts, Walker and Company, 2006

The Poincare Conjecture: In Search of the Shape of the Universe, Donal O'Shea, Walker & Company, 2007

Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being, George Lakoff and Rafael E. Nunez, Basic Books, 2000.

The Number Sense: How the Mind Creates Mathematics by Stanislaus Dehaene, Oxford University Press 1997

Three Books on the Riemann Hypothesis

The King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry by Siobhan Roberts, Walker and Company, 2006

The Poincare Conjecture: In Search of the Shape of the Universe, Donal O'Shea, Walker & Company, 2007

Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being, George Lakoff and Rafael E. Nunez, Basic Books, 2000.

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