Symmetry The Many Symmetries of Tessellations ft. Harry’s Tiles Tessellations History You Can (Literally) Count On Me The History of the Abacus Fractal (Not Only Frozen) Fractals All Around A Discussion of Fractals Ramanujan It’s Time for a Breakdown (of Numbers) Now it’s time for a breakdown… (cue En Vogue’s My Lovin’ (You’re Never Gonna […]
From the Big bang to the Heat death of the universe It’s not because you’re stupid or weren’t concentrating in school Two envelopes with different amounts of money in them. Choose the better one with a higher chance than fifty-fifty! Natural numbers were created by God, everything else is the work of men — Kronecker […]
This post presents a novel method for approximating 1st roots of cubic polynomials that avoids the lengthy gradient and height calculation iterations associated with Newton’s and some of my own previously posted methods. It particularly addresses the task of approximating cubic polynomial roots in ‘difficult to get to’ locations – namely where root gradients are […]
Tensors Are The Facts Of The Universe — Lillian Lieber As the popular saying goes, necessity is the mother of invention — and when it comes to math, nature never ceases to provide us with a source for this necessity. Any experienced engineer can confirm: a very real necessity for engineers of all disciplines is to precisely model physical objects & […]
The beginner’s guide to proving the Fundamental Theorem of Calculus, with both a visual approach for those less keen on algebra, and an algebraic, slightly more rigorous approach, for those keen on exactness. By the end, I hope you feel a bit more like a mathematician 🙂 Introduction, motivation and ‘hello!’ Hello! We are going to understand one of the most […]
After hearing about Eugene Wigner’s article, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” for many years, I recently decided to read and digest the article for myself. (If you’re so inclined, you can read about the results here.) Continuing this exploration of the philosophy of mathematics led me to Mario Livio’s intriguing book, Is God […]
My intention for this article is to provide a look into how the decimal expansion of some fractions yields the Fibonacci sequence. Let us first take a look at the decimal expansion of 1/89: Now, for a quick refresher on the Fibonacci sequence. You start with the numbers 0 and 1, and every number after […]
Understanding Pierre de Fermat’s observation about prime numbers If p is a prime and a is any integer not divisible by p, then p divides aᵖ⁻¹ – 1. This property of numbers discovered by Pierre de Fermat in 1640 essentially says the following: Take any prime p and any number a not divisible by that […]
Cantor’s Archive is an official directory of stories published in Cantor’s Paradise, a community-driven publication of math-, science- and technology-related essays. Why Cantor’s Archive? Cantor’s Archive includes stories published in Cantor’s Paradise which are older than 1 years old. The Story Medium ceased supporting publications in mid-2021. Medium’s founder and CEO Ev Williams resigned from […]
As I finished reading The Fault in Our Stars by John Green, perhaps what stood out the most was the phrase, “Some infinities are bigger than other infinities.” As Hazel Grace looked back at the time that Augustus Waters and her had left together, she had struck a reference to a seemingly enigmatic idea — that there […]
Many philosophers and logicians have analysed the forms of arguments and shown us that the same forms occur across many different cases. They’ve also shown us that when it comes to what are called argument-forms, the semantic content of the premises doesn’t (really) matter as long as the argument-form (which involves the proper use of the symbols for the premises […]
If you are looking for the answer to the question “which one is best suited philosophy of mathematics?” I’m afraid this article can’t give it to you. But I do encourage you to work on it. In fact, to develop a good answer to the question “what the entire mathematical reasoning is about?” you will […]
I was born on the 2nd of August, exactly 33 years before my father was born. I always taught the fact of sharing the birthday with my dad was something really unique. I don’t even have two friends who were born on the same day. I never really thought about the math of two people […]
From the Big bang to the Heat death of the universe It’s not because you’re stupid or weren’t concentrating in school Two envelopes with different amounts of money in them. Choose the better one with a higher chance than fifty-fifty! Natural numbers were created by God, everything else is the work of men — Kronecker […]