Category: Complex Numbers
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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 Number Set Explained
Natural Numbers Integers Rational Numbers Real Numbers Complex Numbers Natural Numbers The story starts at the beginning of mathematics itself. Evidence of humans counting things goes back to the Paleolithic era, tens of thousands of years ago, with tally marks etched on various surfaces. Early humans could have been counting fruits, read more
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Every Weird Number System Explained Part 2
Base 10 may seem like a natural choice for humans based on our number of fingers, but it has its inconveniences. One major detail is that 1/3, which is one of the simplest fractions, can’t be represented without a repeating decimal. This extends to any fraction which is 1 divided by a positive multiple of read more
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Every Method to Complete the Square Explained
Completing the Square: Why It’s Actually About Squares If you’ve ever taken an algebra class, you’ve probably been asked to solve for x. Before you get to quadratic equations, you usually start with linear equations, which are equations that can be put in the form ax + b = 0 for a ≠ 0. Once 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 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 read more
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Complex & Imaginary Numbers Explained
From Squaring to Square Roots The Imaginary Unit The Complex Plane Operations on Complex Numbers Polynomial Equations and Complex Roots A Brief History of Complex Numbers Modeling Rotations From Squaring to Square Roots To start, consider multiplying a number by itself. For example, 4 × 4 = 16. This can be read more
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Where the Quadratic Formula Actually Comes From (Derived Step by Step)
What Are Complex Numbers? A Note on the Names Solving Quadratic Equations with Complex Numbers Working with Imaginary Solutions A Quick Aside on the Definition of i Deriving the Quadratic Formula What Are Complex Numbers? Complex numbers often arise when we are solving quadratic equations. We’ll begin with a simple read more
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Every Important Math Constant Explained
Pi (π) Euler’s Number (e) The Imaginary Unit (i) Pythagoras’s Constant (√2) Theodorus’s Constant (√3) The Golden Ratio (φ) The Euler-Mascheroni Constant (γ) The First Feigenbaum Constant (δ) The Second Feigenbaum Constant (α) Apéry’s Constant (ζ(3)) Conway’s Constant (λ) Khinchin’s Constant (K) The Glaisher-Kinkelin Constant (A) Zero (0) Aleph-Null (ℵ₀) Catalan’s read more
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