Tag: mathematics
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Every Scale used to Measure Natural Phenomena Explained
Hurricanes and the Saffir-Simpson Scale Earthquakes and the Richter Scale The Moment Magnitude Scale Tsunamis and the Imamura-Iida Scale Tornadoes and the Fujita-Pearson Scale Volcanic Eruptions and the VEI The Role of Mathematical Models Hurricanes and the Saffir-Simpson Scale Hurricanes, cyclones, and typhoons are the same meteorological phenomenon: a storm system characterized by a closed… read more
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Every Proof that √2 is Irrational but they get increasingly more complex
Four Proofs That √2 Is Irrational Proof by Contradiction Prime Factorization Proof Infinite Descent Proof Reciprocal Proof Four Proofs That √2 Is Irrational The square root of 2, or 2^(1/2), is irrational. That is, it’s a real number that cannot be expressed as the ratio of two integers. Its decimal expansion is non-terminating and non-repeating.… 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 ABCD is made of… read more
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Every Complex Geometry Shape Explained – Full Video
The Apollonian Gasket The Golden Spiral The Torus The Mucube The Burning Ship Fractal The Sierpiński Triangle The Tesseract The Klein Bottle The Mandelbrot Set The Weierstrass Function Seifert Surfaces The Apollonian Gasket Let’s start by drawing a circle named C₁. Note that we’re not including the inside region as part of the circle. That… 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 tour through some of… read more
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Every Higher Dimensional Geometry Shape Explained
Every Higher-Dimensional Geometry Shape Explained Hypercubes Hyperspheres and Hyperballs Polytopes Simplexes Hyperplanes Hypercubes In one-dimensional (1D) space, a line segment is bounded by two points. In 2D space, a square is bounded by four line segments (if we include the inside region as part of the square). In 3D space, a cube is bounded by… read more
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Every Massive Number Explained
The Biggest Numbers in Mathematics Googol The Shannon Number Skewes’ Numbers Graham’s Number TREE(3) Rayo’s Number The Biggest Numbers in Mathematics Googol A googol is 10¹⁰⁰. Written out, this is a 1 followed by 100 zeros. It is also known as ten duotrigintillion. The word “googol” was originally invented by Milton Sirotta in 1920 when… read more
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Every Greek Letter in Math Explained
Every Greek Letter Used in Mathematics, Explained α (Alpha) β (Beta) Γ/γ (Gamma) Δ/δ (Delta) ε (Epsilon) ζ (Zeta) η (Eta) θ (Theta) ι (Iota) κ (Kappa) λ (Lambda) μ (Mu) ν (Nu) ξ (Xi) ο (Omicron) π/Π (Pi) ρ (Rho) Σ/σ (Sigma) τ (Tau) υ (Upsilon) φ (Phi) χ (Chi) ψ (Psi) Ω/ω (Omega)… read more
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Newton Discovers Gravity & publishes Principa Mathematica
In 1666, Isaac Newton was sitting in his garden when he observed an apple falling straight down. He wondered why it always falls down and not sideways or up. Then it hit him. Maybe the same invisible force pulling the apple to the ground is also what keeps the moon from flying off into space.… read more
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He Measured the Entire Earth Using Shadows 2,200 Years Ago
Over 2,200 years ago, a librarian named Eratosthenes performed one of the most extraordinary scientific experiments in history. Using nothing more than a vertical stick, a shadow, and a brilliant idea, he calculated the circumference of the Earth with astonishing accuracy. The Experiment Eratosthenes experiment. Public domain, via Wikimedia Commons Eratosthenes noticed that at noon… read more
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