Category: Geometry
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Every Unsolved Geometry Problem that Sounds Easy – Part 2
Five More Geometry Problems That Are Way Harder Than They Look Tripod Packing The Thomson Problem The Levi-Hadwiger Conjecture Heesch’s Problem Kalai’s 3ᵈ Conjecture Tripod Packing Let’s start with a cube existing at some fixed location in 3D space. (This problem can be easier to comprehend if you think of the read more
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Every Complex Geometry Shape Explained 2
The Apollonian Gasket The Golden Spiral The Three-Torus The Mucube The Burning Ship Fractal 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 region is called a disc in math terms. Now draw a second read more
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Every Angle Unit Explained in 10 minutes
The Turn The Degree The Radian The Gradian Binary Angular Measurement The Turn An angle is formed between two rays that share an endpoint. The rays are called the angle’s sides, and the endpoint is called the angle’s vertex. Various units of measurement can be used to measure an angle. The read more
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Every Algebraic Curve 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 + b. Here read more
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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 read more
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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 read more
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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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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 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 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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