# Browse Classroom Capsules and Notes

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Displaying 1061 - 1070 of 1214

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.

The author states a "Master Theorem" from which, exploiting concavity, he deduces several classical inequalities.

The creation of 'extriangles' based on a given triangle is iterated, giving rise to four quadrilaterals each with area five times the area of the original triangle.

This note places a primality test developed by Dennis P. Walsh ("A curious test for primes," this Magazine 80(4), October 2007, 302-303) in context by providing increasingly simpler test...
The author shows that two ostensibly different generalizations of the Fundamental Theorem of Algebra are equivalent.

This paper offers a visual illustration of the fact that every octagonal number is the difference of two squares.