# Browse Classroom Capsules and Notes

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Displaying 1 - 10 of 133

The author considers two infinite decimals, where the $n$th digit is the last non-zero digit of $n!$, creating the number $F$, and using $n^n$, creating the number $P$. The author shows...

The geometry of Archimedes` proof of a formula for a sum of squares is depicted visually.

This capsule uses the determinants of matrices to study Fibonacci numbers. Specifically, the sum property of the determinant is used to derive identities between Fibonacci numbers.

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...

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

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...

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.

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

Every integer can be expressed in base $2$ using the set $\{-1, 0, 1\}$ as coefficients. Does one need to use this set, or might another set of numbers do as well? The author investigates...