Category: Calculus
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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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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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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 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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Unsolved Math Problems in Calculus That Sound Easy
The Casas-Alvero Conjecture The Riemann Hypothesis Navier-Stokes Existence and Smoothness The Jacobian Conjecture The Casas-Alvero Conjecture If an integer k can be expressed as the product of two integers m and n, then m and n are called factors of k. A common factor of two integers is a factor shared 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 Major Topic in Calculus Explained – Part 2
A Complete Guide to Integrals What Are Integrals? The Power Rule The Sum Rule Integration by Substitution Integration by Parts Integration by Partial Fractions Definite Integrals A Real-Life Application A Complete Guide to Integrals What Are Integrals? An integral is a mathematical operation that computes the area under a curve or read more
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Every Major Topic in Calculus Explained – Part 1
A Complete Walkthrough of Calculus What Is Calculus? Functions Limits Derivatives Derivative Rules Derivatives of All Six Trigonometric Functions A Real-Life Application of Derivatives A Complete Walkthrough of Calculus What Is Calculus? Calculus is the branch of mathematics involving the study of the continuous rate of change of quantities, particularly in read more
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