
Place for Open and Interactive Mathematics - selvan
https://imaginary.org/
======
indigochill
I wish the pieces had descriptions explaining the connection between the math
and the visual in more detail. Particularly, I was looking at this one:
[https://imaginary.org/hands-on/the-harmonic-
series-2-3d-scul...](https://imaginary.org/hands-on/the-harmonic-
series-2-3d-sculptures)

As an amateur musician, I find the idea of 3d-printing chords a fascinating
concept, but the print here looks like it's formed into a cube shape and it's
not at all clear to me how one gets to a cube from what I assume are three
sinusoidal waves (one for each note in the triad).

~~~
MrEldritch
I think what they're doing with those sculptures is that they're taking three
sine waves of different frequencies A, B, and C, and that the sculpture is the
path that the point (cos(A t), cos(B t), cos(C t)) takes over the combined
period of all three frequencies. That's why it's cube-shaped; x, y, and z each
vary from -1 to 1 over the respective periods of each component. Like a 3D
Lissajous figure; see this
([https://gfycat.com/angelicdismalamazonparrot](https://gfycat.com/angelicdismalamazonparrot))
for a 2D example.

But I also agree that I shouldn't _have_ to be guessing like this, and that
it'd be better if they had more explanation.

