Category: Algebra
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Amazing Things You Can Do in Geometric Algebra Explained
Geometric Algebra Explained: Vectors, Bivectors, and the Geometric Product Vectors and Scalars Scalar Multiplication and Vector Addition The Dot Product The Wedge Product The Geometric Product Geometric Algebra Explained: Vectors, Bivectors, and the Geometric Product Geometric algebra opens up a whole new world of possibilities in math and physics. It read more
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Every Proof That There Are Infinitely Many Primes Explained
What Is a Prime Number? Euclid’s Proof Factorial Proof Erdős’s Proof What Is a Prime Number? Think of a natural number. That is, a number used for counting, like six. Next, think of another natural number, like two. If we calculate 6 / 2, the result is 3. Since 3 is read more
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The Basic Math Iceberg Explained
The Math Iceberg Explained, Part 1 Counting Addition Subtraction Multiplication Division Equations Basic Geometry Order of Operations Decimals Factors Fractions Powers and Radicals Data Plots Variables Cartesian Coordinates Functions Additional Context on Number Systems Counting Counting is a method of finding what number of something you have. The number zero indicates 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 Equation That Changed History Explained
Timeline of Equations That Changed the World 6th Century BC: Thales’ Theorem 6th Century BC: Pythagorean Theorem 300 BC: Euclid’s Theorem 250 BC: Archimedes’ Principle of Flotation 200 BC: Conic Sections First Century AD: Heron’s Formula 1202: Fibonacci Sequence 1609: Kepler’s Laws of Planetary Motion 1614: Logarithms 1637: Cartesian Plane 1637: read more
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Every Unsolved Problem in Discrete Mathematics that sounds Easy
The Riemann Hypothesis The Navier-Stokes Problem The P versus NP Problem The Collatz Conjecture The Goldbach Conjecture The Riemann Hypothesis The Riemann hypothesis is one of the unsolved cornerstones of analytic number theory. Formulated by Bernhard Riemann in 1859, it states that all non-trivial zeros of the Riemann zeta function, denoted read more
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Every Math Problem that Made Someone Famous
Andrew Wiles and Fermat’s Last Theorem Carl Friedrich Gauss and the 17 Gon Joseph Fourier and Fourier Series Leonhard Euler and the Bridges of Königsberg Isaac Newton and the Law of Universal Gravitation John Nash and the Nash Equilibrium Albert Einstein and General Relativity James Clerk Maxwell and Maxwell’s Equations Further read more
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Every Unsolved Math Problem Solved
The Poincaré Conjecture Trisecting an Angle The Classification of Finite Simple Groups The Four Color Theorem The Continuum Hypothesis Fermat’s Last Theorem Gödel’s Incompleteness Theorems The Prime Number Theorem Solving Polynomials by Radicals The Poincaré Conjecture Henri Poincaré. Public domain, via Wikimedia Commons In 2000, the Clay Mathematics Institute, a nonprofit read more
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Every Important Graph in Math Explained
Linear Graphs Quadratic Graphs Circles Ellipses Hyperbolas Sine and Cosine Exponential Functions Logarithmic Functions Linear Graphs A linear graph is a line-shaped graph that can be written as y = mx + b. Here, m is the slope: for every one unit you go to the right, you rise by m read more
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Every Equation in Math and Physics You Need to Know
Every Crucial Equation in Math and Physics Seventeen Equations That Built the Modern World The Pythagorean Theorem Logarithms Calculus The Law of Gravity The Square Root of −1 Euler’s Polyhedra Formula The Fourier Transform The Wave Equation Maxwell’s Equations The Second Law of Thermodynamics The Normal Distribution Relativity The Schrödinger Equation read more
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