Tag: youtube
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Every Particle in Physics Explained
Every Fundamental Particle in the Standard Model Explained What is everything made of? The Standard Model of particle physics describes the smallest known building blocks of matter and the forces that govern their interactions. It includes particles such as electrons, quarks, and neutrinos, along with the particles that carry the electromagnetic, strong, and weak… read more
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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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Every Proof of the Pythagorean Theorem Explained
The Pythagorean theorem is one of the oldest and most famous results in mathematics. More than 370 proofs of the theorem are known, and mathematicians have continued finding new ones for over 2,000 years. Some proofs use nothing more than geometry and rearrangement. Others use algebra, trapezoids, or even calculus. In this article, we will… 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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Math Has Exactly 5 Perfect Shapes
Take a three-dimensional shape in which every face is the same regular polygon, such as an equilateral triangle, square, or regular pentagon, and the same number of faces meet at every corner. A shape this perfectly symmetrical is called a Platonic solid, named after the ancient Greek philosopher Plato. Only five Platonic solids exist: Tetrahedron… read more
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Every Unsolved Prime Number Problem
Brocard’s Conjecture Twin, Cousin, and Sexy Primes Palindromic Primes Euclid Numbers Goldbach’s Conjecture Brocard’s Conjecture A prime number is a positive whole number that has exactly two divisors: 1 and itself. Pick a prime number greater than 2, like 3. Then take the next prime number after that, in this case 5. Then take the… read more
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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 cubes as Minecraft blocks,… 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 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 turn is the simplest… 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 m represents the slope… read more
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