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2. Hearing the shape of a drum - Wikipedia

   en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum

   The proof that both regions have the same eigenvalues uses the symmetries of the Laplacian. This idea has been generalized by Buser, Conway, Doyle, and Semmler [4] who constructed numerous similar examples. So, the answer to Kac's question is: for many shapes, one cannot hear the shape of the drum completely. However, some information can be ...

3. Combination tone - Wikipedia

   en.wikipedia.org/wiki/Combination_tone

   In pipe organs, [7] this is done by having two pipes, one pipe of the note being played, and another harmonically related, typically at its fifth, being sounded at the same time. The result is a pitch at a common subharmonic of the pitches played (one octave below the first pitch when the second is the fifth, 3:2, two octaves below when the ...

4. Elementary mathematics - Wikipedia

   en.wikipedia.org/wiki/Elementary_mathematics

   Elementary mathematics, also known as primary or secondary school mathematics, is the study of mathematics topics that are commonly taught at the primary or secondary school levels around the world. It includes a wide range of mathematical concepts and skills, including number sense , algebra , geometry , measurement , and data analysis .

5. Mathematical Tripos - Wikipedia

   en.wikipedia.org/wiki/Mathematical_Tripos

   The Tripos was an important institution in nineteenth century England and many notable figures were involved with it. It has attracted broad attention from scholars. See for example: Griffin, N.; Lewis, A. C. (1990). "Bertrand Russell's Mathematical Education". Notes and Records of the Royal Society. 44: 51–71. doi: 10.1098/rsnr.1990.0004.

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7. Harmonic series (music) - Wikipedia

   en.wikipedia.org/wiki/Harmonic_series_(music)

   For example, a perfect fifth, say 200 and 300 Hz (cycles per second), causes a listener to perceive a combination tone of 100 Hz (the difference between 300 Hz and 200 Hz); that is, an octave below the lower (actual sounding) note. This 100 Hz first-order combination tone then interacts with both notes of the interval to produce second-order ...

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9. Mathematical beauty - Wikipedia

   en.wikipedia.org/wiki/Mathematical_beauty

   For example, mathematical beauty arises in a Math Circle activity on symmetry designed for 2nd and 3rd graders, where students create their own snowflakes by folding a square piece of paper and cutting out designs of their choice along the edges of the folded paper. When the paper is unfolded, a symmetrical design reveals itself.