Tag: math education
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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 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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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
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Unsolved Problems in Graph Theory Explained
Graph theory has uncovered many secrets of networks and relationships, but some problems remain unsolved. Here are three famous unsolved problems in graph theory, the Total Coloring Conjecture, the Hadwiger Conjecture, and the 1-Factorization Conjecture, and why they continue to puzzle mathematicians. Building Blocks of Graph Theory 1-Factorization Conjecture Unfriendly Partition Conjecture Hadwiger Conjecture Total… read more
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