digital piano
https://www.roland.com/ca/products/fp-30x/
https://www.korg.com/us/products/digitalpianos/d1/
Compare weather anywhere
// print painting
https://www.stuffedsafari.com/Hansa-Stuffed-Animals-and-Plush-Animals-s/14.htm
https://www.christmascentral.com/set-of-3-handcrafted-plush-mallard-duck-stuffed-animals-13-5/
// goose
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The surface integral of the function $f$ over the surface $S$ is denoted by
\[ \int\int_S f dS \]
$dS$ is the area of an infinitesimal piece of the surface $S$.
Average over the sphere is
\[ <f> = \frac{1}{4\pi} \int_0^{2\pi} d\phi \int_0^{\pi} f \sin(\theta)d\theta ,\]
where $dS=\sin(\theta)d\theta d\phi$. This can be seen as a weight average, the weight is surface area.
\[ <\cos^2(\theta)>=1/3 \]
\[<\sin(\theta)>=2/3.\]
From: https://dynesty.readthedocs.io/en/stable/examples.html.
