Browse Classroom Capsules and Notes

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Displaying 1051 - 1060 of 1209

Analytic proofs for the generation of conic sections

Descriptions of the behavior of a family of functions

The author presents a simple proof of a special case of Dirichlets celebrated theorem on primes in arithmetic progressions.

An arctangent identity is presented visually.

Bernoullis inequality is presented visually.
For what positive number $$x$$ is the $$x$$-th root of $$x$$ the greatest?
A visual proof of the ordering of the means in the title is presented.
Two trigonometric sums are viewed pictorially.
An example is given where Newton's method converges but the limit does not satisfy the equation.
The author investigates the graph of a quartic polynomial with inflection points and finds many regularities, some involving the Golden Ratio.