A Wandering Mathematician personal notes

Envelopes of Solids of Revolution

Flank milling is a manufacturing process in which material is removed from the workpiece using a cutter rotating at high speed. Since the cutter rotates much faster than the feed rate of the tool, the cutter can be thought of as a solid of revolution, and the envelope swept by this solid becomes the final surface of the workpiece. Numerous book... Read more

The Miracle of Data-Driven Modelling

A typical problem in machine learning is to fit a collection of labelled data points $(\bold{x}^1, y^1), \ldots, (\bold{x}^p, y^p)$ using some model function \[y = f(\bold{x}).\] Each point $\bold{x} = (x_1, \ldots, x_N)$ is a vector in $\R^N$, where $N$ could easily be about millions. For example, a black and white picture with a regular came... Read more