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Recent Posts
 On the value of believing that you know the answer
 On the unreasonable efficiency of mathematical writing, part II
 On the unreasonable efficiency of mathematical writing
 On Teaching Loving Mathematics
 On the Value of Making up Your Own Question
 Squaring the Superhero
 On Trigonometric Nostalgia
 A Perfect Square Discovers Pi
Author Archives: danielmcquillan
On the value of believing that you know the answer
A beautiful inequality, the arithmetic meangeometricmean inequality (AMGM) seems reasonable but hard to prove. It states that the usual average of n positive real numbers is at least as big as the nth root of the product. We’ll experiment with … Continue reading
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On the unreasonable efficiency of mathematical writing, part II
The writing of mathematics is very efficient. Perhaps the teaching of mathematics can afford a little more redundancy. Here is a key example: Mathematical inductionthe champion of efficiency. The beautiful idea: Induction is often used (and usually taught) to prove … Continue reading
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On the unreasonable efficiency of mathematical writing
In literary writing, we are taught to provide an introduction, a body and a conclusion. We are encouraged to—inefficiently—relate parts of an essay to a central idea. In mathematics, our writing is at times too efficient. Perhaps the teacher can … Continue reading
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On Teaching Loving Mathematics
I love math—not because I think I’m good at it, but because it’s powerful, it’s supremely beautiful and it’s everywhere. Mathematicians and many others agree! However, it happens all too often that people claim not to agree. Teachers can change … Continue reading
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On the Value of Making up Your Own Question
First, we consider an example of how one might make up a question. Here is a nice fact: (1/2)+(1/3)+(1/6)=1 Let’s have some fun with this fact by making it the answer of a question. Think of it as a mystery … Continue reading
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Squaring the Superhero
I teach many different courses in mathematics. All of these courses contain wonderful material. I love math. Last year, my son asked me why some of the students at his elementary school did not seem to share my view regarding … Continue reading
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On Trigonometric Nostalgia
When my son asks me how something works, I often don’t have a satisfactory answer. After all, I can’t rip open my digital device and show him the parts in action. In sharp contrast, we can see exactly how a … Continue reading
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A Perfect Square Discovers Pi
Pi is defined as the ratio of the circumference of a circle, to its diameter. It follows (how?) that the same constant pi is also the number of r x r squares that have the same total area as a … Continue reading
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Welcome.
Dan McQuillan, Associate Professor of Mathematics Department of Mathematics Norwich University Northfield, VT 05663 802 4852323 dmcquill [at] norwich.edu There is a menu on the bottom of the above picture of Norwich University. Please explore various pages of this site … Continue reading
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