For 2D or 3D Cartesian coordinate systems, there are simple formulas based on the Pythagorean theorem that allow one to calculate distance between two points. But what if the surface is curved, like that of the Earth? In other words, how do you get the shortest distance between two cities along the surface of the... Continue Reading →

# From Da Vinci to a Constraint Problem

I was going through a copy of Leonardo da Vinci's notebooks, and the following short passage caught my attention. To heat the water for the stove of the Duchess, take four parts of cold water and 3 parts of hot water. "Cold water" and "hot water" are both vague terms. But given that this was... Continue Reading →

# Why Only Five Platonic Solids in Our Geo-Bio-Chemical World?

The DNA-surrounding capsid of the cold virus and the atomic arrangement of a certain allotrope of boron consists of 20 triangles arranged in a three dimensional shape known as a icosahedron. If you form a three-dimensional structure with 8 triangles, you get an octahedron. An example is the molecular structure of the electrical insulator and... Continue Reading →