Category: Visual Math
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Every Unsolved Circle Problem that Sounds Easy
Five Circle Problems That Are Way Harder Than They Look The Erdős-Oler Conjecture The Gauss Circle Problem The Kissing Number Problem Unequal Circle Packing Sendov’s Conjecture The Erdős-Oler Conjecture A unit circle is a circle whose radius (the distance from the center to the edge) is 1. An equilateral triangle read more
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Unsolved Math Problems in Calculus That Sound Easy
The Casas-Alvero Conjecture The Riemann Hypothesis Navier-Stokes Existence and Smoothness The Jacobian Conjecture The Casas-Alvero Conjecture If an integer k can be expressed as the product of two integers m and n, then m and n are called factors of k. A common factor of two integers is a factor shared read more
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Every Geometry Paradox That Shouldn’t Be Possible
The Missing Square Puzzle The Laves Paradox The Ebbinghaus Illusion The Klein Bottle The Penrose Stairs The Missing Square Puzzle The triangle puzzle with the missing square is one of the most well-known examples where geometric intuition fails. At first glance, the problem seems simple. Two triangular figures are composed of read more
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Every Core Math Concept Explained
Terminological precision in mathematics is not a mere formality but has profound consequences for the logical structure and understanding of mathematical theories. In the mathematical and scientific field, the concepts of principles and laws play a fundamental role in the formulation of knowledge. Although both terms are often used interchangeably in everyday language, in the read more
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Every Unsolved Problem in Discrete Mathematics that sounds Easy
The Riemann Hypothesis The Navier-Stokes Problem The P versus NP Problem The Collatz Conjecture The Goldbach Conjecture The Riemann Hypothesis The Riemann hypothesis is one of the unsolved cornerstones of analytic number theory. Formulated by Bernhard Riemann in 1859, it states that all non-trivial zeros of the Riemann zeta function, denoted read more
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Every Proof that √2 is Irrational but they get increasingly more complex (pt. 2)
Continued Fractions Tennenbaum’s Proof Rational Root Theorem Applying the Rational Root Theorem to √2 Continued Fractions A continued fraction is one possible way to represent a number, consisting of a collection of nested fractions. Here we will focus on the case where the numerators of the fractions are all equal read more
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Every Math Problem that Made Someone Famous
Andrew Wiles and Fermat’s Last Theorem Carl Friedrich Gauss and the 17 Gon Joseph Fourier and Fourier Series Leonhard Euler and the Bridges of Königsberg Isaac Newton and the Law of Universal Gravitation John Nash and the Nash Equilibrium Albert Einstein and General Relativity James Clerk Maxwell and Maxwell’s Equations Further read more
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Every Weird Paradox in Set Theory
The Paradox of Enumeration Cardinality of the Continuum Russell’s Paradox König’s Paradox Richard’s Paradox Skolem’s Paradox The Paradox of Enumeration The paradox of enumeration is one of the basic problems of sets, first encountered prior to the development of modern set theory. It is related to the cardinality, or quantity of read more
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Every Major Topic in Calculus Explained – Part 2
A Complete Guide to Integrals What Are Integrals? The Power Rule The Sum Rule Integration by Substitution Integration by Parts Integration by Partial Fractions Definite Integrals A Real-Life Application A Complete Guide to Integrals What Are Integrals? An integral is a mathematical operation that computes the area under a curve or read more
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Every Unsolved Math Problem Solved
The Poincaré Conjecture Trisecting an Angle The Classification of Finite Simple Groups The Four Color Theorem The Continuum Hypothesis Fermat’s Last Theorem Gödel’s Incompleteness Theorems The Prime Number Theorem Solving Polynomials by Radicals The Poincaré Conjecture Henri Poincaré. Public domain, via Wikimedia Commons In 2000, the Clay Mathematics Institute, a nonprofit read more
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