- Jun 13, 2020
Joukowsky transformation of a circle centered at (1,1) of radius 1 is a curve resembling a heart.
- May 31, 2020
We may generalize Euler–Lagrange equation to higher dimensional optimization problems: find a function defined inside a region to extremize a functional defined as an integral over that region, with the constraint that the value of the function is fixed on the boundary of the region.
- Mar 3, 2020
This article gives the formula for the normal vectors of a surface defined by a scalar field on Rn. The normal vector of the graph of the function y=f(x) at (x0,f(x0)) is (∇f(x0),−1). This also provides us a way to recover a scalar field from the normal vectors of its graph: normalizing the vectors so that the last component is −1, and then integrate the rest components.
- Jan 25, 2020
In this article, I introduce the barycentric coordinates: it is an elegant way to represent geometric shapes related to a simplex. By using it, given a simplex, we can construct a hyperellipsoid with the properties: its surface passes every vertex of the simplex, and its tangent hyperplane at each vertex is parallel to the hyperplane containing all other vertices.