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

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*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...*