Dive into a world of insightful articles on Education, Business, Technology, Social Media, E-commerce, Cryptocurrency, and Growth Hacking.
Whether you want to learn new skills, stay updated with industry trends, or grow your personal and professional ventures, I got you covered.
Discover in-depth tutorials, free tools, blogging guides, actionable marketing strategies, how-to articles, and innovative growth hacks. From mastering SEO to understanding the latest in AI and digital marketing, my blog is your ultimate resource hub.
Join thousands of readers who trust my blog for practical advice, expert insights, and tools to take your journey to the next level.
I was reading a book on ancient mathematics problems from Indian mathematicians. Here I wish to share one problem from Bhaskaracharya‘s famous creation Lilavati. Who was Bhaskaracharya? Bhaskara II, who is popularly known as Bhaskaracharya, was an Indian mathematician and astronomer from the 12th century. He’s especially known for the discovery of the fundamentals of…
Henry Poincaré was trying to save the Old classical theory of Physics by Suitable Adjustments & Modifications in it. When the experiments, like Michelson Morley Experiment, in search of the ether drift failed, it began to be increasingly realized that there was no such thing as an absolute or privileged frame of reference and that…
Pick any positive integer. If it’s even, halve it. If it’s odd, triple it and add one. Repeat. You’ll always end up at 1. That’s the Collatz Conjecture. It sounds like something you could prove in an afternoon. Mathematicians have been trying for nearly 90 years. Nobody’s succeeded. You might also hear it called the…
The Gamma function is one of the most important special functions in mathematics. It extends the factorial to non-integer values. The Beta function is its close relative, and together they show up everywhere: probability theory, complex analysis, physics, and engineering. This article covers both functions, their definitions, key properties, and the famous Dirichlet theorem that…
Bimolecular reactions make sense. Two molecules collide, bonds break, new bonds form. Simple. But unimolecular reactions? A single molecule just… reacts? Where does the energy come from? This puzzle bothered chemists for years until F.A. Lindemann proposed an elegant solution in 1922. The Problem with Unimolecular Reactions Collision theory explains bimolecular reactions beautifully. When two…
Two women sell marbles at a market. One charges 3 marbles for ₹1. The other charges 2 marbles for ₹1. They each have 30 unsold marbles at the end of the day. Instead of selling separately, they combine their marbles and ask a friend to sell all 60 at “5 for ₹2.” Seems fair, right?…
In 1904, the french Mathematician Henri Poincaré (en-US: Henri Poincare) posed an epoch-making question, which later came to be termed as Poincare Conjecture, in one of his papers, which asked: If a three-dimensional shape is simply connected, is it homeomorphic to the three-dimensional sphere? Henri Poincare – 1904 So what does it really mean? How…
Wondering what Cosmic Radiation & Cosmic Ray Showers are and how these are formed? If you are, you are at the perfect place. Cosmic radiation and cosmic ray showers are some of the most intriguing and fascinating phenomena in the universe. While the term “radiation” may have negative connotations, cosmic radiation is a natural occurrence…
Lord Rayleigh made an attempt to explain the energy distribution in black body radiation, which was completed by Jeans in 1900. The results obtained by then are known as Rayleigh-Jeans’ Rules on Black Body Radiation. The law covering these rules is called Rayleigh Jean’s Law. The black body emits radiation of continuously variable wavelengths right…
The problem of energy distribution in black body radiation stumped physicists for years. German physicist Max Planck finally cracked it. But he didn’t work in a vacuum. Before Planck, Wilhelm Wien and the duo of Lord Rayleigh and James Jeans made critical contributions. Their work (and their failures) paved the way for Planck’s quantum revolution.…
Derivative of x squared As we know, the derivative of x squared, i.e., differentiation of $ x^2$ , with respect to $ x$, is $ 2x$. i.e., $ \dfrac{d}{dx} x^2 = 2x$ A Curious Case Suppose we write $ x^2$ as the sum of $ x$ ‘s written up $ x$ times. i.e., $ x^2…
Here’s a problem that looks impossible at first glance. You’ve got infinitely many nested square roots, each level multiplied by an increasing integer. How do you even begin to evaluate something like that? Turns out, Ramanujan already solved this—and the answer is surprisingly clean. The Problem: An Infinite Sequence of Nested Radicals Consider this sequence…
