Examination Strategies : Tactics & Tips
Every student or graduate knows how hard the first experience of passing exams is. Preliminary preparation starves the nervous system and the physical condition of…
Complete Elementary Analysis of Nested radicals
This is a continuation of the series of summer projects sponsored by department of science and technology, government of India. In this project work, I…
Hopalong Orbits Visualizer: Stunning WebGL Experiment
I just discovered Barry Martin’s Hopalong Orbits Visualizer — an excellent abstract visualization, which is rendered in 3D using Hopalong Attractor algorithm, WebGL and Mrdoob’s…
Study Notes on Real Sequences (Definitions and Examples)
In this study note, I have discussed and explained about real sequences — a very important topic in Real Analysis and Calculus. I will cover…
Tunnel through the Earth
Drop a ball through a tunnel drilled straight through Earth. It won’t fall forever—it’ll oscillate back and forth, popping out on the other side in…
Euler’s (Prime to) Prime Generating Equation
The greatest number theorist in mathematical universe, Leonhard Euler had discovered some formulas and relations in number theory, which were based on practices and were…
Statistical Physics: Ensembles
Ensembles in Chemical Sciences and Statistical Physics are a collection of a number of macroscopically identical but essentially independent systems. The System, here, is defined…
Analysis of Meteorological Data of Pantnagar Weather Station
This paper presents a statistical analysis of 20 years of meteorological data (1989-2008) from the Pantnagar weather station in Uttarakhand, India. The research was conducted…
Irrational Numbers and The Proofs of their Irrationality
How do you prove a number is irrational? You can’t just look at a number and declare it irrational. You can’t check infinitely many decimal…
The Area of a Disk
The area of a disk with radius \( R \) is \( \pi R^2 \). You probably memorized this in middle school. But do you…
Triangle Inequality
The triangle inequality is one of those results that sounds obvious until you try to prove it rigorously. Here’s the geometric intuition: no side of…
On Ramanujan’s Nested Radicals
In 1911, a 23-year-old clerk from Madras posed a problem in the Journal of the Indian Mathematical Society that stumped professional mathematicians for months. The…