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Bach Mass B Minor Canon

Submitted by Ulrich Seidel on

J. S. Bach probably is one of the composers with most affinity to mathematics. He developed the art of fugue in a programmatic way in his work “The Art of Fugue”. So he used all kinds of techniques that are characteristic for composing fugues and canons. Canons are a special case of fugues. In the most strictest form they consist of just one melody that starts to different times in at least two voices. The canon melody repeats several times in a loop, at least one time for each voice. There are many ways to vary the melody with transformations that are well known from geometry: translation (transposition), rotation, scaling, mirror transformations. Bach liked composing canons and fugues so much that he used this technique even implicit. His great mass in B Minor ends with the Dona nobis pacem, where a canon melody is varied and hard to discover. The animation shows how the canon is constructed and a little excerpt of the beginning and the end of that movement.

MathLapse: String vs Beads

Submitted by Eli Parra on

“Stringing” a 3-dimensional integer lattice of “beads” with a Hamiltonian path (one that crosses every vertex but only once) as a visual showcase of 1-1 correspondence with the integers.

This is a bit like the Aleph-Null version of how Space-filling curves were discovered after Cantor’s surprising proof that the continuum of unit interval has the same cardinality as that of the unit cube.

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