# Browse Classroom Capsules and Notes

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Displaying 11 - 20 of 1212

This capsule applied the concepts from linear algebra to prove the relations of sample corelation coefficients.

This capsule discusses the mathematics of a real-life experience with dogs playing fetch into the water. The leap-off point chosen by the dog turned out to ones that will either minimize the...

This capsule provides a simple  proof to Archimede's problem related to areas enclosed by a parabolic segment. The idea of the proof comes from elementary physics instead of geometry...

This capsule follows the technique of random tilings used in the proof of the closed form for Fibonacci Numbers. By relaxing the condition of probability, the authors are able to obtain...

A variation of the birthday problem is being considered: what is the probabibility of $2$ out of $n$ people to have their birthday on a particular day? Furthermore, this capsule...

This capsule introduces a straightfoward way of calculating partial fraction decomposition for functions of specific forms by long division. The obtained partial fractions can be easily...

Based on a closed form and recurrence relation of Catalan numbers, the authors proves their parity and primality.

This article generalizes a problem of dogs fetching a ball in the water and presents it as a problem of calculus of variation.

This capsule investigates the sequences that converge to Euler's constant. By utilizing the geometric description of the terms, the author can obtain a rate of convergence comparable to...

This capsule introduces a way of producing the Möbius function in Number Theory through the algebra of formal series. The author hopes that this exposition can lobby more mathematicians...