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Bach Mass B Minor Canon

Enviado por Ulrich Seidel el

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

Enviado por Eli Parra el

“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.

Fractal Fugues

Enviado por Jeffrey Ventrella el

Fractal Fugues are self-similar structures made from a simple motif which generates copies of itself. These copies are transformed in the dimensions of time and pitch.

Science Spaces: An Open Workshop Concept to Create Science Exhibits

Enviado por Bianca Violet el

We introduce and outline a workshop concept called Science Spaces aimed at High School students, which combines mathematics and natural sciences with art to strengthen creativity, imagination, and perceptual abilities. The workshop guides the participants through the process of designing and implementing a public exhibition.

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