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Every Coordinate System Explained
Cartesian Coordinate System The Cartesian Plane in Two Dimensions Slope of a Line Equations of Lines Vectors Conic Sections Three-Dimensional Cartesian Plane Quadric Surfaces Polar Coordinate System Main Differences with Cartesian Coordinates Conversion Between Polar and Cartesian Coordinates Degrees vs Radians Cylindrical Coordinate System Main Differences Conversion Spherical Coordinate System Main read more
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The 3 Tests That Make or Break an Infinite Series
If you’re into mathematics, you may have heard of an operation called addition, where you simply combine two values together. Summation is the addition of a sequence of values or terms to get a result or sum. For example, 1 + 2 + 3 = 6. But what if a summation keeps going forever? An read more
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Fibonacci and the Birth of Modern Math
Leonardo de Pisa Fundamentally Changed Math Discovering the Fibonacci Series Ancient Indian Discoveries in Sanskrit Texts The Golden Number (Phi, φ) The Golden Spiral From Roman Numerals to Hindu-Arabic Numbers Fascinating Facts About the Fibonacci Sequence Leonardo de Pisa Fundamentally Changed Math mathematics is related to Natural Sciences the result of read more
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Every Binary Operation and Logic Gate Explained
The binary system is the foundation of all computing. Without it, there would be no computers, cell phones, internet, or modern technology as we know it. What Is the Binary System? Converting Between Decimal and Binary Binary Arithmetic Operations Boolean Algebra and Logic Gates Basic Logic Gates Derived Logic Gates Properties 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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Every Non-Newtonian Fluid Explained
What Is a Non-Newtonian Fluid? Time-Independent Non-Newtonian Fluids Time-Dependent Non-Newtonian Fluids The Mathematical Challenge Rheological Models Real-World Applications and Open Problems What Is a Non-Newtonian Fluid? A non-Newtonian fluid is one whose viscosity does not remain constant under different rates of deformation. Unlike Newtonian fluids such as water or air, where read more
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Every Weird Number Set Explained
The Extended Real Number Line The Hyperreal Numbers Increasing Dimensions: Why Not Three Components? Quaternions The Extended Real Number Line We all know and love the real numbers. But infinity is not a real number, at least not in the mathematical sense of the term. Since this is math, though, we read more
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Every Real Function Explained
Every Type of Mathematical Function 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 read more
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Every Scale used to Measure Natural Phenomena Explained
Hurricanes and the Saffir-Simpson Scale Earthquakes and the Richter Scale The Moment Magnitude Scale Tsunamis and the Imamura-Iida Scale Tornadoes and the Fujita-Pearson Scale Volcanic Eruptions and the VEI The Role of Mathematical Models Hurricanes and the Saffir-Simpson Scale Hurricanes, cyclones, and typhoons are the same meteorological phenomenon: a storm system read more
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Every Proof that √2 is Irrational but they get increasingly more complex
Four Proofs That √2 Is Irrational Proof by Contradiction Prime Factorization Proof Infinite Descent Proof Reciprocal Proof Four Proofs That √2 Is Irrational The square root of 2, or 2^(1/2), is irrational. That is, it’s a real number that cannot be expressed as the ratio of two integers. Its decimal expansion read more
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