Verified Claims
8
Atlas Hub
Euclidyne v2
A warm, instrument-lab atlas of the Euclidean algorithm and its valid extensions: arithmetic, geometry, gear-ratio design, rational maps, locks, and rhythms. Unsupported mechanical claims stay clearly labeled.
Analogy Only
2
False Claims
3
Wing
Core Algorithm
The exact arithmetic backbone: Euclid, Bézout, inverses, and step-count behavior.
c. 300 BCE
Ancient, Still Useful
Euclid's algorithm is one of the oldest named algorithms that is still used directly in modern software.
Core Algorithm
Quick Calculator
The preserved exact-text fast path for Euclid, Bézout, and modular inverse results.
Core Algorithm
Algorithm Explorer
Interactive Euclid and Extended Euclid tables with synced equations and callouts.
Core Algorithm
Fibonacci Race
A side-by-side comparison between your input and Fibonacci worst-case behavior.
Core Algorithm
Centered Euclid Race
A comparison lab for two Euclid variants and how quickly they shrink the same pair.
Wing
Ratios and Geometry
Continued fractions, dissections, rational landscapes, and gear-ratio design.
phi
Special, Not Generic
The golden spiral story depends on self-similarity. Arbitrary Euclidean rectangle cuts do not automatically inherit it.
Ratios And Geometry
Rectangle Reactor
A dissection lab that keeps the geometry true and labels the golden special case correctly.
Ratios And Geometry
Gear Ratio Forge
A gear-design lab that uses Euclid-style reduction honestly: for choosing ratios, not pretending the train runs Euclid by itself.
Ratios And Geometry
Rational Sky
A shared rational-data playground with multiple visual lenses on the same reduced fractions.
Ratios And Geometry
Quadratic Surd Loop
A quadratic-irrational lab with period loops, convergents, and a Pell teaser.
Wing
Applications and Reality Checks
Locks, rhythms, and the mechanical claims that survive contact with the evidence.
x..x..
Math That You Can Hear
Euclidean rhythm patterns show up in multiple traditional musical families because they spread beats as evenly as possible.
Applications And Reality Checks
Modular Lock Lab
A lock-and-key view of modular inverses with coprime gating.
Applications And Reality Checks
Rhythm Sequencer
A pulse-distribution lab with transport controls and an audible Euclidean pattern.
Applications And Reality Checks
Meshing Reality Check
A debunk lab showing that the ratio stays fixed while contact conditions change.