# Browse Classroom Capsules and Notes

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The author proves visually that if $$a$$ and $$b$$ are the legs and h the altitude to the hypotenuse $$c$$ of a right triangle, then $$(1/a)^2 + (1/b)^2 = (1/h)^2$$.
Arguments for certain sums of sines and cosines are given.
This article gives an explanation why the solution to a number partitioning problem would be $$3$$. The answer is that $$3$$ is close to $$e$$.
The article attempts to explain why exponential functions were chosen to define hyperbolic functions.
An elementary proof for the generalized Schwarz inequality.

Cramer's Rule gives an explicit formulation for the unique solution to a system of $$n$$ equations in $$n$$ unknowns when the coefficient matrix of the system is invertible.  The...

A simple and clever way to compute the entry in the pascal triangle using numbers in any row above the row to which the desired entry belongs.

The authors discuss the evaluation of certain improper integrals by first transforming them.

The Golden Mean is found in electric circuit theory.

The author provides a short proof of Cramer’s rule that avoids using the adjoint of a matrix.