User:Create42000/Sandbox

please see wikipedia:en:user:Create42000

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$$\frac{\mathrm{d}}{\mathrm{d}t}(mr^2\sin^2\theta\dot{\varphi})=0.$$

N(p) = N(p-1) + N(p-2); recur backwards

$$ \left(\mathrm{PL}_j\right)_i = \frac{\left(X_{j\bullet[j]}\right)_i^2}{\sum_{k=1}^n\left(X_{j\bullet[j]}\right)_k^2} $$

Mahalanobis distance = (N − 1)(h − 1/N)

$$S_i^{(t)} = \left\{ \mathbf x_j : \big\| \mathbf x_j - \mathbf m^{(t)}_i \big\| \leq \big\| \mathbf x_j - \mathbf m^{(t)}_{i^*} \big\| \text{ for all }i^*=1,\ldots,k \right\} $$

$$\mathbf m^{(t+1)}_i = \frac{1}{|S^{(t)}_i|} \sum_{\mathbf x_j \in S^{(t)}_i} \mathbf x_j $$