# Browse Classroom Capsules and Notes

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Displaying 1011 - 1020 of 1209

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...

The Fermat point of a triangle is used to present simple geometric proofs of the inequalities in the title of the paper.
The area under the segment of a parabola is found via the volume of a pyramid.
A few simple models in the fields of neuroscience and high voltage engineering are presented and discussed.