Category: Complex Numbers
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Every Weird Number That Shouldn't Exist Explained
Thanks for watching! Chapters: 0:00 Zero 1:40 Negative Numbers 2:40 Imaginary Numbers 3:39 Infinitesimals 4:44 Surreal Numbers 5:55 Quaternions 7:00 Octonions 8:32 Transfinite Ordinals 9:28 Irrational Numbers One useful way to organize the major number systems is as a ladder with seven levels: Natural numbers, N Integers, Z Rational numbers, Q Real numbers, R Complex… read more
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Math Has Exactly 7 Levels of Numbers
Thanks for watching! Levels: 0:00 Intro 0:24 Level 1: Natural Numbers 1:14 Level 2: Integers 2:21 Level 3: Rationals 3:38 Level 4: Real Numbers 5:07 Level 5: Complex Numbers 7:16 Level 6: Quaternions 8:41 Level 7: Octonions 9:17 Why There Is No Level 8 One useful way to organize the major number systems is as… 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 circle, C₂, that touches… 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, animals, or days. Whatever… 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 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 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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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 done with negative numbers… read more
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