## Recipe for a Leibniz Quarter Pi

April 14, 2016 by richbeveridge

Ingredient:

Divide gently in a long division sauce pan:

Integrate briskly over a low flame:

Evaluate for and let stand at room temperature for 1000 terms for accuracy to three decimal places.

Add lemon zest to taste.

But this doesn’t look like a pi! or taste like a pi!

or a quarter pi!

Ah, but if we return to the original integral

and make the trigonometric substitution so that then:

and

which, if we return to the original substitution , we see that

So, , which means that:

and since , then

Enjoy your pi!

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on April 14, 2016 at 12:43 PM |george gheverghese josephThanks Rich Beveridge for thinking of me! Very entertaining. Can I use it in a book that I am writing and who should I acknowledge.George