# Browse Classroom Capsules and Notes

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Displaying 121 - 130 of 1209

Using a generalized Fibonacci sequence to determine the expected number of tosses of a fair coin to first obtain $$n$$ consecutive heads

Examples of an elementary transcendental function having three different kinds of asymptotes $$x-a-0, y-b=0, y=mx+c$$ and defined by one single equation in its domain of definition

A simple, natural way to geometrically read off the complex roots of a real quadratic equation

Using the Arithmetic-Geometric Means Inequality and the Mean Value Theorem to show that the maximum value of $$x^{1/x}$$ occurs at $$x = e$$

Using induction to investigate the symmetric difference of $$n$$ sets

An elementary proof of Heron's Formula

Using a convexity argument to show that you can never lose money by income averaging (on your income tax) as opposed to computing the standard tax

Constructing Pythagorean systems with any number of terms

Generalizations of the Archimedean result that ratio of the volume of a sphere to that of its circumscribing cylinder is the same as the ratio of their respective surface areas

A simple derivation of the formula for the distance from a point to a line