Real Sequences: Definitions, Theorems, and Examples
Real sequences form the backbone of real analysis and advanced calculus. I've taught this topic to dozens of students, and…
Blog
2,366+ articles on WordPress, SEO, business growth, and making money online.
If I haven’t tested it myself, I don’t write about it. 18 years of building sites, breaking things, and figuring out what actually works.
You’ll find tutorials, tool reviews, marketing strategies, and the occasional honest take that might save you from an expensive mistake.
What if We Dig a 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…
Euler’s (Prime to) Prime Generating Equation
Euler discovered a simple formula that generates 40 consecutive prime numbers: n squared plus n plus 41. Plug in 0…
Ensembles in Statistical Mechanics: Complete Theory and Examples
Ensembles are the trick that makes statistical mechanics computable: instead of tracking 10^23 particles, you average over imaginary copies of…
Analysis of Meteorological Data of Pantnagar Weather Station
This paper presents a statistical analysis of 20 years of meteorological data from the Pantnagar weather station in Uttarakhand, India.…
Introduction to Object Oriented Ontology
Object Oriented Ontology (OOO) challenges the idea that humans are the center of philosophical inquiry. It argues that objects exist…
Area of a Disk – Why is it Ï€r²?
The area of a disk is pi times radius squared. You memorized this in middle school. But do you know…
Triangle Inequality: Concepts, Theorems, and Examples
The triangle inequality sounds obvious. No side of a triangle can be longer than the other two sides combined. But…
National Mathematical Year 2012: What India Promised Ramanujan and What It Actually Delivered
In December 2011, India declared 2012 as National Mathematical Year to honor Ramanujan's 125th birthday. I wrote at the time…
The Quest for a Prime Number Formula: Why It’s Harder Than You Think
Mathematicians have spent centuries trying to find a formula that generates all prime numbers. Euler's n²+n+41 works for 40 values…
Find the Day of a Date using this Calendar Formula
You can figure out what day of the week any date falls on. No calendar needed. Just arithmetic. I'll teach…
Equations: A Basic Introduction
Equations are the reason we can solve problems in seconds that would take hours of guesswork. I cover the basics:…