Thermodynamics

Temperature Scales

The most widely adopted temperature scale is the Celsius or centigrade scale. Nowadays, we use these terms as synonyms, but, in fact, they were not such, originally.

Gradient Descent

Gradient Descent for Machine Learning, Explained

In typical machine learning problems, there is always an input and a desired output. However, the machine doesn’t really know that.

Philosophy

The Demons of the Mathematicians

There is a rich history of mathematicians, philosophers, and other thinkers invoking demons (real or imaginary) in their reasonings. The tradition goes back at least to the iconic ancient Greek philosopher Socrates.

Babylonian

A Modern Look at Square Roots in the Babylonian Way

Revisiting the Babylonian method for square roots: why and how does it work?

Philosophy

Professor E. Brian Davies’s Mathematical Empiricism

This commentary is on the relevant parts of Davies’s book, Science in the Looking Glass. The following is not a book review.

Algorithm

The Power of Binary Search

Binary search is ubiquitous. Even if you are not aware of it, you have most likely used some (approximate) version of binary search one way or another

Geometry

Geometrical Beauty: The Properties of the Tautochrone Curve

When a Sliding Bead at Rest Reaches Its Minimum Independently of Its Where It Started

Entropy

What, Exactly, is Entropy?

Entropy is a bit of a buzzword in modern science. Usually it is used as a synonym for “disorder,” but it is so much more interesting than that.

Graph Theory

City Planning Using Graph Theory

Strongly Connected Components Algorithm

Kinematics

Finding the Shape of the Surface of Water Rotating in a Bucket

A Simple Application of the Basics of Newtonian Physics in Accelerated Reference Frames

Electromagnetism

An Unorthodox Lecture on Electric Currents

An introduction to the concept of an electrical current

Newton

The Genius of Isaac Newton

A Modern Derivation of Newton’s Revolutionary Proof of the Inverse-Square Law