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 exactly 42 minutes. Every…
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 through 39 and every output is prime. I explore why…
Statistical Physics: Ensembles
Ensembles in statistical physics are collections of macroscopically identical but essentially independent systems. I explain the three main types: microcanonical, canonical, and grand canonical ensembles, their defining properties, and when…
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. Conducted under the INSPIRE-SHE Scholarship Program, the research examines temperature,…
Irrational Numbers and The Proofs of their Irrationality
How do you prove a number is irrational? You can't check infinitely many decimal places. You need a proof. I present the classic proofs of irrationality for square root of…
The Area of a Disk
The area of a disk is pi times radius squared. You memorized this in middle school. But do you know why it's true? Most people don't. I show you the…
Triangle Inequality
The triangle inequality sounds obvious. No side of a triangle can be longer than the other two sides combined. But proving it rigorously is where things get interesting. I cover…
Welcome 2012 – The National Mathematical Year in India
India declared 2012 as the National Mathematical Year to celebrate Srinivasa Ramanujan's 125th birth anniversary. The government honored one of history's greatest self-taught mathematicians whose contributions to number theory, infinite…
Claim for a Prime Number Formula
Dr. SMRH Moosavi has claimed to derive a general formula for finding the nth prime number. I present his claim, the formula, and the surrounding mathematical context. Whether this constitutes…
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 you a genuine mathematical formula that works for any date…
Equations: A Basic Introduction
Equations are the reason we can solve problems in seconds that would take hours of guesswork. I cover the basics: what equations are, how they work, types of equations, and…
WordPress URL Shortening: The Complete Guide to Native and Third-Party Solutions
Long URLs are a pain when sharing links on social media, emails, or podcasts. WordPress has a built-in shortlink system most people don't know about, plus several third-party solutions that…