Category: Geometry
-
Every Weird Number System Explained
Decimal (Base 10) Roman Numerals Binary (Base 2) Hexadecimal (Base 16) Golden Ratio Base Decimal (Base 10) Assuming you’ve heard of numbers before, you probably know about the decimal system, also known as base 10. It involves 10 digits that can be put together to represent a number. For example, consider the number 243. That’s… read more
Written by
-
Every Level of Geometry Explained
Level 1. Basic Geometry Level 2. Intermediate Geometry Level 3. Advanced Geometry Level 4. Analytic Geometry Level 5. Non-Euclidean Geometry Level 6. Topological Geometry Level 7. Projective Geometry Level 8. Differential Geometry Level 9. Algebraic Geometry Level 1. Basic Geometry The fundamental entities of geometry include the point, the line, and the plane. It is… read more
Written by
-
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
Written by
-
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
Written by
-
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
Written by
-
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
Written by
-
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
Written by
-
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
Written by
-
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
Written by
-
Every Unsolved Geometry Problem that Sounds Easy
Five Geometry Problems That Look Simple but Remain Unsolved Square Packing Bellman’s Lost in a Forest Problem Ulam’s Packing Conjecture Lebesgue’s Universal Covering Problem Moser’s Worm Problem Kobon’s Triangle Problem Five Geometry Problems That Look Simple but Remain Unsolved Square Packing A unit square is a square with a side length of one unit. Suppose… read more
Written by
