Tag: mathematics
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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 elements, of certain infinite… 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 the accumulation of a… read more
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The Constant Zero Explained
Zero is a fundamental concept in mathematics that represents the absence of quantity or magnitude. It is one of the most important and widely used constants in various branches of mathematics and science. The Additive Identity Zero Across Mathematics The History and Significance of Zero The Additive Identity Zero is the additive identity, meaning that… read more
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Every Form of Energy Explained
Thermal Energy Chemical Energy Nuclear Energy Electrical Energy Dark Energy Electromagnetic Energy Sound Energy Hydropower Wind Energy Geothermal Energy Solar Energy Seismic Energy Mechanical Wave Energy Magnetic Energy Phase Change Energy Gravitational Potential Energy Elastic Potential Energy The Big Picture Thermal Energy Thermal Energy. fir0002 flagstaffotos [at] gmail.com Canon 20D + Tamron 28-75mm f/2.8, GFDL… read more
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Every Major Topic in Calculus Explained – Part 1
A Complete Walkthrough of Calculus What Is Calculus? Functions Limits Derivatives Derivative Rules Derivatives of All Six Trigonometric Functions A Real-Life Application of Derivatives A Complete Walkthrough of Calculus What Is Calculus? Calculus is the branch of mathematics involving the study of the continuous rate of change of quantities, particularly in the context of functions… read more
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Every Dark Scandal in Math
The Murder of Hypatia The Nobel Affair The Burning of the Library of Alexandria The MIT Card Counters in Las Vegas The Air Force Cheating Scandal André Bloch’s Murders P versus NP Alan Turing Newton and Leibniz’s Calculus Wars The Drowning of Hippasus Galois’s Duel and Death The Eudaemons Cardano versus Tartaglia Cantor Driven to… read more
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Every Infinity Paradox Explained
Hilbert’s Hotel Cantor’s Diagonal Argument Thompson’s Lamp Gabriel’s Horn The Ross-Littlewood Paradox The Dartboard Paradox The St. Petersburg Paradox The Riemann Series Theorem Hilbert’s Hotel Hilbert’s Hotel is a thought experiment proposed by German mathematician David Hilbert in 1925. It involves a hotel with an infinite sequence of rooms: 1, 2, 3, and so on… read more
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Every Equation in Math and Physics You Need to Know
Every Crucial Equation in Math and Physics Seventeen Equations That Built the Modern World The Pythagorean Theorem Logarithms Calculus The Law of Gravity The Square Root of −1 Euler’s Polyhedra Formula The Fourier Transform The Wave Equation Maxwell’s Equations The Second Law of Thermodynamics The Normal Distribution Relativity The Schrödinger Equation Heisenberg’s Uncertainty Principle The… read more
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The First Irrational Number – Square Root of 2 Explained
√2 is a fundamental mathematical constant also known as Pythagoras’s constant. It represents the length of the diagonal of a square with side length 1: √2 ≈ 1.41421… This special number was first studied in depth by the ancient Greek mathematician Pythagoras and his followers. Why Is √2 Important? Where Else Does √2 Appear? Why… read more
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γ, the Euler–Mascheroni Constant Explained
The Euler–Mascheroni constant, denoted by γ (gamma), is approximately equal to: γ ≈ 0.57721… This constant appears in various areas of mathematics, especially in number theory and analysis. It is defined as the limiting difference between the harmonic series and the natural logarithm: γ = lim(n→∞) (1 + 1/2 + 1/3 + … + 1/n… read more
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