Insights & Essays
From casual daily questions to deep technical dives.
A collection of essays recording unfiltered thoughts and discoveries, spanning across various fields.
The Computational Cost of Mixed Numbers
Is the standard school method always optimal? An engineering perspective on efficiency and the value of questioning the "obvious."
The Mathematics and Implementation of Make 10
Why is "Proof by Exhaustion" the most elegant solution? A firmware engineer's algorithmic approach to the classic puzzle using 4 distinct digits.
Fraction Division: Why "Flip and Multiply"?
Moving beyond rote memorization. An algebraic proof using complex fractions to explain the logical reasoning behind multiplying by the reciprocal.
What is Pi ($\pi$)?
The infinite world beyond 3.14. Why is it irrational? From Archimedes' polygons to Monte Carlo simulations, exploring the history of calculation.
The Singularity of Math: Why You Must Not Divide by Zero
What is the difference between "Undefined" and "Indeterminate"? Explaining why division by zero is forbidden, from calculator errors to SPICE Singular Matrices.
The Formula Containing Every Image
Tupper's Self-Referential Formula Generator. A mathematical library of Babel where your name, history, and future already exist at a specific height $k$.
Why Doesn't SPICE Converge?
The mathematical meaning hidden in "Timestep too small". Analyzing Newton's method divergence and Predictor failures.
Is 0.999... Really 1?
Is an infinite decimal "infinitely close" or "exactly the same"? Proofs via algebraic and intuitive approaches.
How to Find a Lost Bluetooth Earphone??
Even without signal strength, you can find "where the connection breaks." A geometric search algorithm using boundary points of the "connection limit circle."
Why is Minus x Minus = Plus?
Physical intuition using "velocity and time" vs. rigorous algebraic proof based on the distributive property. The importance of revisiting definitions.