Mathematics

The mathematical proof of this seemingly counterintuitive relation — The concept that 0.999… (0.9 repeating) is equal to 1 might seem counterintuitive, but it’s a fact that’s supported by several standard mathematical proofs. Here’s a simple demonstration of it: Consider the equation: 1/3 = 0.333… We know that this is true, as one divided by three gives you a…

Why Conscious Reasoning Should Never Supersede Instinct — For a high-level talk on this topic check out the NonTrivial Podcast. Mathematics as Rigor Our worldviews are largely based on how we think things work. Our experiences settle into ideas, and we use those ideas to make decisions. Our perceptions don’t exist merely as isolated concepts, rather we fashion them into narratives…

Here it is expressed in numbers — Improve nothing a day for a year is 1[365] = 1

How about distilled? From Merriam-Webster: Distilled: to extract the essence of. Also from Merriam-Webster: Distillate: something concentrated or extracted as if by distilling. In 2015 FQXi held the essay contest, Trick or Truth: The Mysterious Connection Between Physics and Mathematics; I shall draw from the essays by David Hestenes and…

In this article, I will present a comprehensive approach to further expanding upon my previous work by incorporating simulation capabilities into the development of a dynamic model for a self-balance robot, specifically a Segway. The model will be described using second-order motion equations based on Lagrangian mechanics. While our focus…

The great Persian mathematicians — Trigonometry in former science always merged with astronomy. Tusi was the first to write a work on trigonometry independently of astronomy. Tusi, in his Treatise on the Quadrilateral, gave an extensive exposition of spherical trigonometry, distinct from astronomy. …

“Legacy Chronicles: Rediscovering the Past” Dear [Newsletter Subscribers], Welcome to the inaugural edition of “Legacy Chronicles: Rediscovering the Past,” your go-to newsletter that combines the captivating stories of forgotten figures with intriguing highlights from “This Week in History.” …

Math is more than just numbers and equations — it’s a beautiful art form that has captured the attention of some of the world’s greatest minds throughout history. And while teaching this subject isn’t always a breeze, using math quotes can help inspire your students to see the beauty in…

From the perspective of mathematical logic, we start with languages, i.e. the language of groups, the language of sets, the language of Number Theory, etc.. These include all of the necessary symbols of the logic needed, whether it be propositional, first-order, second-order, or what have you. They also include non-logical…