*This capsule applied the concept of cross ratio in complex analysis to derive the Pythagorean Theorem. It appears to be the first in the literature to use this approach to prove the famous...*

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*A technique is introduced for the purpose of finding the relative maximum values of the probability density function. The crux is to find the critical numbers of the exponential of the...*

*Based on the notion of "arithmetic triangles," arithmetic quadrilaterals are defined. It was proved by using an elliptic curve argument that no such quadrilateral can be inscribed on...*

*This capsule discusses an alternative way of examining the Fibonacci sequence. As a result, a class of generalized Fibonacci sequences of numbers can be defined.*

*An example in business calculus is used to show a short-cut to compute the discrepancy between the difference of values and the differential for certain class of functions.*

*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...*