Category: Paradoxes
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Every Fractal Dimension Explained
Fractals are geometric objects that have a fascinating property: they are self-similar. This means that their structure repeats itself at different scales, no matter how close or far away you are looking. Imagine an object whose shape repeats itself over and over again, just at different sizes. These structures are not just abstract objects but read more
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Fibonacci and the Birth of Modern Math
Leonardo de Pisa Fundamentally Changed Math Discovering the Fibonacci Series Ancient Indian Discoveries in Sanskrit Texts The Golden Number (Phi, φ) The Golden Spiral From Roman Numerals to Hindu-Arabic Numbers Fascinating Facts About the Fibonacci Sequence Leonardo de Pisa Fundamentally Changed Math mathematics is related to Natural Sciences the result of read more
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Complex Geometry Puzzles Explained
Five Geometry Puzzles That Will Test Your Problem-Solving Skills Triangle and Five Rectangles Wood Piece Puzzle Inscribed Triangle Problem Wertheimer’s Car Riddle Shaded Area Problem Five Geometry Puzzles That Will Test Your Problem-Solving Skills Triangle and Five Rectangles Here’s a simple problem to start off, posted to the subreddit r/askmath. Rectangle read more
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Every Weird Geometry Paradox Explained Part 1
Every Geometry Paradox Explained String Girdling Earth Coin Rotation Paradox Staircase Paradox Sphere Eversion Banach-Tarski Paradox Every Geometry Paradox Explained Geometry is not always as straightforward as it seems. Some of its most surprising results look like errors at first glance but hold up completely under scrutiny. Here is a read more
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Every Proof That There Are Infinitely Many Primes Explained
What Is a Prime Number? Euclid’s Proof Factorial Proof Erdős’s Proof What Is a Prime Number? Think of a natural number. That is, a number used for counting, like six. Next, think of another natural number, like two. If we calculate 6 / 2, the result is 3. Since 3 is 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 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 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, read more
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Every Weird Math Paradox Explained – Part 2
Simpson’s Paradox The Monty Hall Problem The Sleeping Beauty Problem Cantor’s Paradox The Ant on a Stretching Rope Berry’s Paradox The Absent-Minded Driver Hooper’s Paradox Bertrand’s Paradox Simpson’s Paradox Simpson’s Paradox is often presented as a compelling demonstration of why we need statistics education in our schools. It was first noted read more
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Why aleph‑null + aleph‑null = aleph‑null (The Math of Infinity)
Aleph-Null: The Smallest Infinity Aleph-null (ℵ₀) is a cardinal number in set theory that represents the cardinality, or size, of the set of natural numbers {1, 2, 3, …}. It is the first transfinite cardinal number and is used to describe the size of infinite sets. Arithmetic with Aleph-Null Comparing Infinite read more
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