# Browse Classroom Capsules and Notes

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Displaying 131 - 140 of 1209

A derivation of the formulas $$\max(r,s)=\frac{1}{2}(r+s+|r-s|)$$ and $$\min(r,s)=\frac{1}{2}2(r+s-|r-s|)$$

In the decimal expansion of an irrational square root, not all digits are equally likely to appear.

A discussion of compass and straightedge methods for approximate trisection of an angle

A proof that $$\lim_{n \rightarrow \infty} \frac{\sqrt[n]{n!}}{n} = \frac {1}{e}$$.

The Factorial Triangle is a relative of Pascal's Triangle with many applications

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...