Insights & Essays
From casual daily questions to deep technical dives.
A collection of essays recording unfiltered thoughts and discoveries, spanning across various fields.
Mathematical Questions & Foundations
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.
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.
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 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.
Is 0.999... Really 1?
Is an infinite decimal "infinitely close" or "exactly the same"? Proofs via algebraic and intuitive approaches.
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.
Everyday Mathematics
When Do Two Price Plans Switch Places?
Turn basic and usage fees into linear functions, then use their intersection to find where the cheaper plan changes.
Are 10% Off and 10% Points Really the Same?
Both appear to save ¥100 on a ¥1,000 purchase, but the base behind each “10%” is different. A middle-school mathematics look at a familiar shopping trap.
How to Measure a Tree or Building Without Climbing It
A stick and two shadows can reveal an unreachable height. An everyday measurement technique built from similar triangles.
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."
Mathematical Puzzles & Expression
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.
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 $k$.
Computers & Data Representation
Dating Was TCP; Marriage Became UDP
Fictional chats turn connections, ACKs, retransmission, ordering, and packet loss into a light-hearted guide to TCP and UDP.
Big-Endian and Little-Endian — Which Byte Comes First?
How does 0x12345678 appear in memory? A visual guide to byte order, floating-point data, and a checklist for avoiding decoding mistakes.
Nonlinear Analysis & SPICE
Nonlinear Equations Are Not Just One Kind of Problem
How is a polynomial different from nonlinear optimization? A map of nonlinear problems using two viewpoints: mathematical form and the purpose of the problem.
Why Doesn't SPICE Converge?
The mathematical meaning hidden in "Timestep too small". Analyzing Newton's method divergence and Predictor failures.
Drawing Tangent Lines with SPICE
Letting a circuit simulator solve pure math? A perverted way to find tangent lines using the ".SENS" command.
Exposing SPICE's Limits: .DISTO and B-Sources
A documentary of segfaults and silence when trying to make a simulator solve Taylor expansions. The moment perfect theory is defeated by internal implementation.