Mathematics

Mathematics has always been of great interest to me. I received an BS in mathematics in 2015, and I worked for several years as a specialized instructor for a private tutoring company. While I'm nowhere near an expert, I still find many topics in math to be fascinating.

Here I write documents about various facets of math that catch my attention. Not only do I hope to share some of my passions, but I also want to get practice and experience in using digital tools to study and present mathematical topics. Updates will be irregular and perhaps infrequent.

All documents are also available to download in PostScript.

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[2024-01-19] Doubling by Reversing

Does there exist a number that doubles in value when its digits are reversed?

[2023-07-14] A Proof that 0.999...=1

Simple properties of real numbers aid in a rigorous proof of this unintuitive result.

[2023-01-23] The Limit of Compound Interest

A calculus proof of a frequently-cited pre-calculus concept.

[2022-09-06] My Tangent Construction

A homemade compass-and-straightedge method that demonstrates the inefficiencies of certain forms of mathematics.

[2022-03-02] Generating Crossed Ladders

Finding the width of a hallway with two criss-crossing ladders is tricky, but finding integer-length ladders that yield an integer-width hallway might not be so hard.

[2022-01-02] Inverting an Angle Trisection

In a reversal of the classic Greek problem, given a certain geometric construction, try to find the angle it trisects.

[2021-12-22] A Proof that 0/0=2

Where is the flaw in this analysis-based proof of a well-known facetious result?

[2021-12-10] Another Fractional Problem

Using explicit boundary conditions in searching for potential solutions rather than validating candidate solutions.

[2021-11-18] Integrating the Standard Normal Distribution

An elementary method of determining the area under the famous probability curve is unit.

[2021-10-01] Furstenberg as an Introduction to Topology

A topological proof that there are infinitely many primes serves a surprisingly-elegant first step into the subject.

[2021-09-22] The Geometry of the Trigonometric Maclaurin Series

Recreating a little-known geometric argument that underpins the terms of the famous Maclaurin series for sine and cosine.

[2021-09-09] A Fractional Problem

A straightforward problem with some definitions that lead to important constraints on its solutions.

[2021-06-01] "Slide and Divide" Explained

A factorization method that hides it mathematically-correct processes behind some ugly and unjustifiable manipulations.

[2021-04-21] Analyzing a Trigonometric Cubic Formula

The machinery behind an elegant cosine-based method of finding roots of cubic equations.

[2021-04-05] Intuiting the Quadratic Formula

My understanding of how each term in a quadratic equation affects its roots, and where the terms of the quadratic formula come from.

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[Last updated: 2024-01-19]