# Mathober2025_OrthoPolynomials

# MetaLegendre

For My 26th Sketch of **Mathober2025**, MetaLegendre is coded with **SonicPi & Desmos.** For the 11th Prompt of *Orthogonal Polynomial,* uses a desmos sketch that half of the Legendre Polynomials are in 2D and the other half are in 3D. For the 27th Prompt of *Bidiminished,* the sound is control by the volume of *a* Metabidiminished Icosahedron.

## Poetry

```ocaml
Graphing
Through the Volume
Do the Patterns Resume?
As they await their crafting
```

## Video

%[https://youtu.be/VZydYSYSEcQ] 

## Code

### SonicPi (Sped Up 2.2x)

```ruby
#https://mathworld.wolfram.com/MetabidiminishedIcosahedron.html

#The volume of a Metabidiminished Icosahedron is represented with V
#The audio plays out the bidiminished


V = (1.0 / 6) * (5 + 2 * Math.sqrt(5))

def metabidi(units)
  vol = V * units
  return vol
end



live_loop :volume do
  use_random_seed Time.now.to_i / metabidi(2)
  with_fx :ping_pong do
    use_bpm metabidi(rrand_i(45,78))
    sample [:drum_bass_hard,:tabla_ghe2,:guit_em9].choose,beat_stretch: metabidi(dice(5)) , rate: metabidi(dice(3)), sustain: metabidi(dice(4))
  end
  sleep [metabidi(0.5),metabidi(0.75),metabidi(0.97)].choose
end
```

### Desmos

![](https://cdn.hashnode.com/res/hashnode/image/upload/v1761189520797/4125eab1-5cda-48f3-bf4d-0c04e3ca8b09.png align="center")