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concept:euclidean-algorithm

Euclidean Algorithm

Ancient algorithm from Euclid's Elements (circa 300 B.C.) that computes greatest common divisor; shown to structurally parallel Bjorklund's rhythm generation algorithm.

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Thinkers (3)

thinker
  • H. S. M. Coxeter
    cites
    Mathematician cited for historical account of mathematics-music interaction; author of 'Music and Mathematics' (1962).
  • Euclid of Alexandria
    introduces
    Ancient Greek mathematician (circa 300 B.C.) who described the Euclidean algorithm in Elements, Book VII, Proposition 2.
  • Pythagoras
    cites
    Ancient Greek mathematician and philosopher; referenced as originator of intimate relationship between mathematics and music, historically focused on pitch and scales.

Communities (2)

community

Concepts (1)

concept
  • Bjorklund's Algorithm
    associated_with
    Algorithm developed for timing systems in neutron accelerators; generates binary sequences where pulses are distributed as evenly as possible among intervals.

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

  • Euclidean Rhythmsframework0.785
    Family of musical rhythms generated via Bjorklund's algorithm, where k onsets are distributed evenly across n time units; denoted E(k,n).
  • Genetic Algorithmframework0.775
    Evolutionary search algorithm used to evolve embryo populations through development, selection, and mutation stages across 1000 generations.
  • Euclidean Geometry Assumptionconcept0.773
    The implicit assumption of linear steering methods, which the paper argues is inappropriate for neural activation spaces
  • Bjorklund's algorithm has identical structure to Euclidean algorithmclaim0.756
    Key theoretical insight: both algorithms use repeated subtraction (division) to recursively partition sequences; this structural identity justifies the term 'Euclidean rhythm'.
  • Forward Algorithmmethod0.750
    Used to update pain beliefs online from observations of happiness
  • Evolutionary Algorithmsmethod0.745
    Machine learning approach using evolutionary processes to generate and select designs, used to blur the designed vs. evolved distinction
  • RL algorithmsconcept0.744
    The different reinforcement learning algorithms used across conditions, to ensure the alignment result is not algorithm-specific.
  • Algorithm 1: Finding Localist Alignment Matrixmethod0.740
    Algorithm that extracts a localist (axis-aligned) approximation from any learned orthogonal rotation matrix for baseline comparison.