Neal Strassner

Quantum Computing on the Sixty-Ring: Every Gate a Setting, Every Gradient a Quarter Turn, and a Checksum on the Classical Half

Every tool of quantum computing is one of three moves on two sliding rings marked with the sixty last digits of the Fibonacci numbers. A setting is a value read off one placement of the rings. A fold is a product turned into a sum by the half-angle law. A turn is a shift of posit...

The Harmonic Oscillator on the Two Rings: Geometry in Place of Operator Mechanics, with a Check on Every Step

The simple harmonic oscillator is solved by geometry on the two-ring instrument and the Fibonacci 60-ring of the companion papers, with every step checked as it is made, in lengths a student can draw. The route it replaces is the operator mechanics that Freericks and Doughty (arX...

The Moment Ladder: Exact Integer Checksums that Certify, Locate, and Fill

A string of digits, a frame, a tile of a matrix product, any list of integers, carries a ladder of exact totals: the plain sum T, the position-weighted sum W, the quadratic sum Q, the cubic C, and onward. This paper states the laws of that ladder and proves them by algebra and by...

Two Sliding Rings: A Self-Checking Instrument that Reads Sine, Cosine and Tangent at One Setting

Two identical rings, each marked with the sixty repeating last digits of the Fibonacci numbers, are slid over each other until they cross on an angle. At that one setting the distance between the centres, halved, is the cosine and the distance between the crossings, halved, is th...

The Golden Octave: Why the Fibonacci Ring's Dial Sings Only Whole Tones, and Falls Silent Only at φ

On the Fibonacci 60-ring, two equal circles can be made to cross at an integer setting k, placing their two crossing points a fixed number of divisions apart. Read those two points as musical pitches — the ring carries five octaves of twelve chromatic notes — and a striking patte...

The Cosine Ruler and the Selection Law: A Computing Instrument Built on the Fibonacci 60-Ring

This paper introduces a single instrument and the law that governs it. Place two equal circles sotheir boundaries cross on a 60-division ring; one integer setting, k, then fixes the distance betweentheir centers exactly, by the relation d = 2R·cos(6k°). As k runs from 1 to 14, th...