# Monthly Archives: September 2011

## Playing with the Form of an Answer – The Shad-Fack Transom problem

A recent article in The College Mathematics Journal entitled The Shad-Fack Transom by Annalisa Crannell explores several methods of finding the radius of the small circle tucked up in the corner of a square circumscribed about another larger circle. In … Continue reading

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## Completing the Square – Fast and Formal

Here is a strictly formal way to complete the square. We want to express in the form .  We may want to do this for many reasons, for example, to graph a quadratic function (parabola), to solve a quadratic equation, … Continue reading

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## Exaggerate to Teach

My wife was watching a Clinton Anderson video on training horses.  I was fascinated.  The man was training a horse at the same time he was teaching us how to train a horse and the horse was not necessarily his … Continue reading

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## Real Numbers in Calculus

In my last post I alluded to the hand-waving we do discussing limits in calculus because students have a imprecise conception of real numbers.  The clever article in the current The College Mathematics Journal, The Intermediate Value Theorem is NOT … Continue reading

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## Calculus Counterexamples

Counterexamples are important tools in mathematical argumentation.  As a math instructor I naturally gravitate to refutation by counterexample when an erroneous statement arises.  My students however are less familiar with this type of argument, so first I give this example.  … Continue reading

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## “Stupid Mistakes”

So-called “stupid mistakes” are really failures of character.  This dawned on me over 30 years ago when I was tutoring a bright teenager.  I was using Birkoff and MacLane to teach beginning group theory to the boy.  In exchange his … Continue reading

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