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If we live in Leonhard Euler's universe of physical mathematics,

it makes sense to extend geometry outside the scale, speed and

spectrum of our vision, to our other senses, such as phonemes.

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http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/Waves2D_3D.pdf

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Phonemes are received in 3D receptors, in stereo, 2 ears shaped in geometric cones. This is optimized. Phoneme reception is an issue for medical research.

Parameters of distance, speed, time, scale, speed, and spectrum are indicated for phoneme classification in the brain. Pitch, tone, stress are triage issues.

3D and stereo oscilloscopes may be adapted to the problem of phoneme reception and classification in the brain, "cognitive computing"

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This Wall best on laptop.

May not work on mobile

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demonstrated sound and geometry.

Faraday waves on micro scale materials,

de broglie waves, quantum mechanics,

demonstrate geometry.

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Mathematical aspects of music

have been known since ancient

times. Singers use the voice

as a a musical instrument.

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The basic unit of Indo-European languages. A string of phonemes, "I scream, you scream" click black area, is illustrated in 2D.

Wikipedia has a discussion of the mathematics of torus 3D geometry and mathematics. Phonemes are formed in the

mouth region and transmitted through air as geometric shapes. The mathematics of Torus may be applied to each phoneme

so that each phoneme is mathematically and geometrically defined. However, as can be seen by cyamatics and Youtube

demos on plates and water, the boundaries of geometric sounds fluctuate. In addition it is likely that each individual has

slightly different formation of phonemes. So the geometric boundaries are probabilities. This latter quality is similar to

problems in quantum physics, coupled with a Big Data problem, hundreds of millions of speakers whose phonemes vary,

like snowflakes vary. https://www.internationalphoneticassociation.org/ International Phonetic Alphabet and related

approaches focus on the formation of phonemes in the mouth. The geometry of the formed phonemes and radiation

of phonemes through the air appears to be an unsolved problem for quantum physics, mathematics, ML, Big Data etc.

Spherical sound chambers to measure phonemes radiating from speaker may measure phonemes data.

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The mathematical analysis of Torus on Wikipedia

illustrates how phonemes in the International

Phonetic Alphabet may be mathematically and

geometrically defined.