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Browse Classroom Capsules and Notes

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Displaying 141 - 150 of 1211

Elementary methods for bounding definite integrals

What right triangles with legs of integer length have the property that their area equals their perimeter?

Generalizations of the problem: A goat is tethered to the edge of a disc shaped field of radius \(r\). The goat's rope is of length \(kr\). If the field is \(n\)-dimensional, what fraction...

Generalization of the fact that \(n^2-n+2\) is the maximum number of disjoint regions in the plane that can be formed by \(n\) circles using the basic set operations

This article characterizes the points \((x, y)\) in the plane for which the determinant of a matrix of a particular form involving \((x, y)\) is \(0\).  The matrices of interest have the...

Elementary derivation for probability of relative primality

Classroom demonstrations of physical properties

Counting techniques for sequences of zeros and ones

Uses geometry and integration to relate hyperbolic and exponential functions

Elementary properties of tournaments are used to sum geometric series.