Category: Algebra
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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 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 read more
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Every Level of Geometry Explained
Level 1. Basic Geometry Level 2. Intermediate Geometry Level 3. Advanced Geometry Level 4. Analytic Geometry Level 5. Non-Euclidean Geometry Level 6. Topological Geometry Level 7. Projective Geometry Level 8. Differential Geometry Level 9. Algebraic Geometry Level 1. Basic Geometry The fundamental entities of geometry include the point, the line, and read more
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Every Proof that 0.999 equals 1 but they get increasingly more complex
If we have 1/3 = 0.333… and we multiply both sides of the equation by 3, we see that 3/3 is equal to 0.999… Since 3/3 is 1, we find that 1 equals 0.999… The above is one of the simplest and most popular demonstrations that can be found regarding the claim that 0.999… equals 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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The Fastest Way to Travel is not a Straight Line
What Is the Brachistochrone? The Challenge The Calculus of Variations Deriving the Solution The Cycloid What Is the Brachistochrone? One of the most fascinating problems in the history of mathematics is the brachistochrone problem, posed in the 17th century. It seeks to answer a seemingly simple question: what is the fastest 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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