# Browse Classroom Capsules and Notes

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Displaying 21 - 30 of 1209

This capsule  demonstrates the validity of a trigonometric identity by paper folding.

This project provides a very simple proof to the converse of Viviani's Theorem. It also points out certain properties can be used to generalize Viviani's Theorem to regular polygons...

Certain p-series are the focus of this capsule. This project comes with scenarios to help students "visualize" the convergence or divergence of the p-series.

Starting with a homework problem on combinations, the capsule applies the "checkerboard" logic to derive identities involving summing squares and cubes.

This capsule  started with two coffee cups that are complenetary, i.e., their profiles fit together. The author then explores the condition in which the two cups, obtained as solids of...

This capsule discusses a way to show each non-zero element of certain rings have a multiplicative inverse. The approach is to set up a system of linear equations and the solution is the...

In how many ways can a pet photographer pose $$C$$ cats, $$D$$ dogs, and $$E$$ emus? The problem, often called Smirnov`s problem,  has several practical applications and has been solved...

A visualization of the triple angle formulas for sines and cosines is presented.

The limit of the geometric mean of the first $$n$$ integers raised to the real positive power $$s$$, divided by their arithmetic mean is shown to be $$(s+1)/e^s$$. An elementary derivation of...

The authors consider three cointossing models in which “too much success” is defined by the occurrence of success runs of a certain length which causes play to stop. The objective...