Mihajlo Pupin: The Serbian-American Genius Who Helped Build Modern Telecommunications

Mihajlo Pupin surrounded by transmission lines, loading coils, mathematical formulas, and a global telecommunications network symbolizing his role in the development of modern communication systems.

Introduction: Why Pupin Deserves a Place Among the Great Scientific Minds Mihajlo Idvorski Pupin was one of the most important scientist-inventors in the history of electrical engineering, telecommunications, and applied mathematical physics. He was a Serbian-American physicist, inventor, professor, writer, and public intellectual whose work helped extend the practical range of long-distance telephone communication through … Read more

How I Built NajduzaRec.rs: Mathematics, Algorithms and Educational Software

NajduzaRec.rs educational platform combining mathematics, algorithms, word generation and interactive learning applications

Mathematics Has Always Been More Than a Subject to Me Mathematics has never been merely a collection of formulas, rules and procedures to me. Long before I became a professional electrical engineer, mathematics had already become a way of thinking. I was always fascinated by logical structures, numerical patterns, elegant solutions and the ability of … Read more

The Wall of Death: The Physics Behind a Motorcycle Defying Gravity

Motorcyclist riding horizontally on the vertical Wall of Death, illustrating the normal force, gravity, friction and centripetal acceleration

How can a motorcycle travel horizontally along a vertical wooden wall without falling? The answer combines circular motion, Newton’s laws, static friction, torque, and the remarkable skill of the rider. A Childhood Question That Physics Eventually Answered When I was a child, I had the opportunity to witness one of the most spectacular motorcycle attractions … Read more

Nikola Tesla: Architect of the Modern World

Nikola Tesla standing before a giant Tesla coil with alternating current systems, wireless communication, Wardenclyffe Tower, and a modern illuminated city symbolizing how his inventions shaped today's technological world

Introduction: Why Tesla Still Matters  Few individuals in modern history have changed the technological direction of civilization as deeply as Nikola Tesla. He was not merely an inventor in the narrow sense, nor only an engineer, nor only a visionary. He was a rare figure whose imagination operated at the scale of systems: power generation, long-distance transmission, electric … Read more

The Number π Explained: History, Properties, Formulas, and Its Connection to e, i, and the Golden Ratio

Mathematical illustration of the number pi symbol connected to Euler's identity, the complex plane unit circle, a Fourier series formula, a sine wave, and the golden ratio spiral

Introduction Few symbols in mathematics are as universally recognized as π (pi). Whether one studies elementary geometry, advanced calculus, engineering, physics, statistics, signal processing, or number theory, π appears repeatedly in formulas describing circles, waves, probabilities, and even the structure of the universe itself. In previous articles, we explored three remarkable mathematical constants: Together with … Read more

The Golden Ratio Explained: Mathematics, Fibonacci Numbers, and the Golden Ratio Bridge

Golden ratio spiral with Fibonacci squares, showing phi 1.618 and its connection to mathematics, geometry, and patterns in nature

The Golden Ratio is one of the most fascinating numbers in all of mathematics. It appears in geometry, number theory, algebra, computer science, architecture, art, biology, and countless natural growth processes. For centuries, mathematicians, philosophers, artists, and scientists have been intrigued by its unique mathematical properties and its surprising appearance in the world around us. … Read more

RLC Circuit Transient Response with a DC Source: Complete Mathematical Derivation

Series RLC circuit connected to a DC voltage source showing resistor, inductor, capacitor, transient current i(t), damped oscillations, and capacitor charging during the transient response

Introduction The transient response of electrical circuits is one of the fundamental topics in circuit theory and electrical engineering. While RC and RL circuits are governed by first-order differential equations, an RLC circuit contains both energy-storage elements—a capacitor and an inductor—which leads to a second-order differential equation and considerably richer dynamic behavior. Depending on the … Read more

RL Circuit Transient Response with a DC Source: Complete Theoretical Analysis and Formula Derivation

Series RL circuit with DC voltage source U, switch S, resistor R, and inductor L, showing exponential current rise i(t) and the time constant τ during transient response

Introduction The transient behavior of electrical circuits is one of the fundamental topics in electrical engineering. While resistors react instantaneously to changes in voltage and current, inductors possess the unique ability to oppose sudden changes in current due to their magnetic field energy storage. As a consequence, whenever a DC source is connected to or … Read more

Transient Process in RC Circuits with a DC Source: Complete Analytical Derivation of Switching Behavior

RC circuit diagram showing a DC voltage source, switch, resistor, and capacitor with labeled components, illustrating capacitor charging and discharging transient processes over time

Abstract The transient response of resistor-capacitor (RC) circuits under direct current (DC) excitation represents a fundamental topic in electrical engineering and applied physics. This article provides a rigorous, and fully derived of the charging and discharging processes, emphasizing formulas, physical interpretation, and engineering relevance. Introduction RC circuits are first-order linear dynamic systems whose transient behavior … Read more

Bayes’ Theorem Explained: Why a 99% Accurate Test Can Still Be Wrong

Infographic explaining Bayes’ theorem showing why a 99 percent accurate test can result in only a 50 percent probability

Statistics surround us every day. We encounter percentages, probabilities, survey results, economic indicators, and medical studies in news reports, social media posts, advertisements, and political debates. Because numbers appear objective and scientific, many people accept them without questioning what they actually mean. However, statistics can be surprisingly misleading when presented without context. A single percentage … Read more