Mathematics

An introduction to the mathematics of the universe - a first-principles learning journey through number theory and beyond, written to stand on its own as an educational resource for anyone curious about it, regardless of any interest in Binary Unified Theory. This is deliberately separate from the Experiments and Observations sections, which report real simulation results.

How this section works: the mathematics here is explored on its own terms, not as a search for evidence. Most of it will never touch Binary Unified Theory at all, and that is fine - it does not need to. Only on the rare occasion a genuine, well-earned connection turns up will it be mentioned, briefly, honestly, and clearly marked as exceptional rather than as the point of the piece.

Primes: From Euclid's Proof to the Forest Floor

Euclid's original infinitude proof, periodical cicadas and a real computation of why prime life cycles minimize overlap, which polygons can be built by hand, the Ulam spiral, and Stirling's approximation built up from Taylor series into a genuine tool for bounding how many primes exist.

first principles · real citations · every figure computed directly

Fibonacci Numbers and the Golden Ratio

Corrects the popular history (Fibonacci is Leonardo of Pisa, and the sequence is older still), and separates what's real about these numbers in nature from what's myth. Binet's formula derived two independent ways, the golden ratio's continued fraction, Zeckendorf's theorem, and why consecutive Fibonacci numbers are the worst case for the Euclidean algorithm.

first principles · real citations · honest about the nautilus myth

More topics are added as the series continues.