Tag: math education
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Every Weird Number Set Explained
The Extended Real Number Line The Hyperreal Numbers Increasing Dimensions: Why Not Three Components? Quaternions The Extended Real Number Line We all know and love the real numbers. But infinity is not a real number, at least not in the mathematical sense of the term. Since this is math, though, we can make up new… read more
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Every Real Function Explained
Every Type of Mathematical Function Explained Linear Functions Quadratic Functions Polynomials of Degree n Rational Functions Radical Functions Exponential Functions Logarithmic Functions Trigonometric Functions Inverse Trigonometric Functions Hyperbolic Functions The Absolute Value Function Constant Functions Floor and Ceiling Functions The Sign Function Piecewise Functions Linear Functions Linear functions have the form f(x) = mx +… read more
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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 Complex Geometry Shape Explained
Every Complex Geometry Shape Explained Sierpinski Triangle Tesseract Klein Bottle Mandelbrot Set Weierstrass Function Seifert Surface Every Complex Geometry Shape Explained Geometry is not just about simple shapes. Some of the most fascinating objects in mathematics are staggeringly complex, emerging from surprisingly simple rules. Here is a tour through some of the most remarkable ones.… read more
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Amazing Things You Can Do in Geometric Algebra Explained
Geometric Algebra Explained: Vectors, Bivectors, and the Geometric Product Vectors and Scalars Scalar Multiplication and Vector Addition The Dot Product The Wedge Product The Geometric Product Geometric Algebra Explained: Vectors, Bivectors, and the Geometric Product Geometric algebra opens up a whole new world of possibilities in math and physics. It extends the familiar ideas… read more
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