# Browse Classroom Capsules and Notes

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Displaying 1011 - 1020 of 1212

A short proof of the well-known fact that the unit interval $[0,1]$ is uncountable is presented by means of a simple infinite game. The author also used this game to show that a (non-empty)...

Various examples of convergent Newton sequences which do not converge to a zero of the underlying function are given.

The author discusses an intuitive direct proof of the fact that functions with zero derivative must be constant, which turns into a rigorous proof by simply invoking the completeness of the...

Infinite series representing several functions, and several series representing $\pi$ are derived using tabular integration by parts.

The author uses elementary geometric methods to calculate the fraction of the area of a soccer ball covered by pentagons.

Three lemmas of interest in themselves from which Euler's Triangle Inequality follows are proved wordlessly.

A triangle labeled two different ways verifies the double angle formula for sines.

The authors discuss ways to induce students to recognize the use of symmetry to evaluate challenging integrals, and to prevent student sidesteps.

The author gives a synthetic geometric proof answering the question in the title of the paper.

The author uses the golden matrix ring $Z(A)$ generated by $A= \left[ \begin{array}{cccc} 0 & 1 \\ 1 & 1 \end{array} \right]$ to prove certain identities involving Fibonacci...