Tag: mathematics
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Why Catalan’s Constant Still Puzzles Mathematicians
Catalan’s constant is a well-known mathematical constant defined by the infinite series: It is named after the Belgian mathematician Eugène Charles Catalan, who first gave an equivalent series and expressions in terms of integrals for this constant. Where Does Catalan’s Constant Appear? Is Catalan’s Constant Rational or Irrational? Computing Catalan’s Constant read more
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Every Unsolved Math Problem Explained
Notable Conjectures and Unsolved Problems in Mathematics Casas-Alvero Conjecture Riemann Hypothesis Navier–Stokes Existence and Smoothness Jacobian Conjecture Erdős–Oler Conjecture Gauss Circle Problem Kissing Number Problem Unequal Circle Packing Sendov’s Conjecture Tripod Packing Thomson Problem Levi–Hadwiger Conjecture Heesch Problem Kalai’s 3d Conjecture Casas-Alvero Conjecture If an integer k can be expressed as read more
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Euler's Number Explained in 30 seconds
Euler’s Number e Overview Applications Properties Overview The mathematical constant e is the base of the natural logarithm, a fundamental logarithmic function. It is also known as Euler’s number, named after the mathematician Leonhard Euler, who extensively studied this constant. e ≈ 2.71828 Applications The constant e is used in many read more
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Every Forbidden Operation in Math Explained
Ever wondered why you cannot take the logarithm of zero? We are diving into every forbidden math operation that just does not play by the rules. Division by Zero Logarithm of Zero Negative Output of Absolute Value Zero to a Negative Exponent Multiplying Infinity by Zero Adding Scalars and Vectors Determinant read more
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the Irrational Apéry’s Constant Explained
Apéry’s Constant Overview The Riemann Zeta Function Significance Irrationality Apéry’s Constant Overview Apéry’s constant is the value of the Riemann zeta function evaluated at the argument 3. It has an approximate value of 1.202. The Riemann Zeta Function The Riemann zeta function, denoted by ζ(s), is a function of a complex read more
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Every Weird Math Paradox Explained
The Hairy Ball Theorem The Dichotomy Paradox The Birthday Problem Gabriel’s Horn The Elevator Paradox The St. Petersburg Paradox Hilbert’s Hotel Russell’s Paradox The Banach-Tarski Paradox The Hairy Ball Theorem Hairy Ball Theorem. Public domain, via Wikimedia Commons Imagine a ball covered in hair, like a fuzzy tennis ball. The hairy read more
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The Greatest Accidental Math Breakthroughs
Non-Euclidean Geometry Napier’s Logarithms Fourier’s Mistake About Heat Newton and Calculus Euler and the Constant e from Finance Henri Poincaré and Chaos Theory Gauss and the Normal Curve Non-Euclidean Geometry For more than two millennia, Euclidean geometry stood as an unquestioned paradigm of physical space. Its fifth postulate, the parallel postulate, read more
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Pi Explained in 30 seconds π
Pi (π) is a fundamental mathematical constant that represents the ratio of a circle’s circumference to its diameter. It was first calculated by the ancient Greek mathematician Archimedes. Origin of the Symbol Discovery Applications Properties Origin of the Symbol The Greek letter π (pi) is the first letter of the Greek read more
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The Imaginary Unit i Explained in 30 Seconds
The imaginary unit i is defined by the rule i² = −1. It was introduced to solve equations that have no real number solutions. Definition and History Significance Definition and History The imaginary unit, denoted by the symbol i, is a mathematical constant representing √(−1). The concept of the imaginary unit read more
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Conway’s Constant Explained
Conway’s constant, approximately 1.303577, describes the growth rate of the look-and-say sequence. No matter which number you start with, the length of the sequence eventually grows by this same factor each step. The Look-and-Say Sequence The Constant (λ) The Look-and-Say Sequence Conway’s constant is a mathematical constant that arises in the read more
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