Category: Number Theory
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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 read more
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Every Number Set Explained
Natural Numbers Integers Rational Numbers Real Numbers Complex Numbers Natural Numbers The story starts at the beginning of mathematics itself. Evidence of humans counting things goes back to the Paleolithic era, tens of thousands of years ago, with tally marks etched on various surfaces. Early humans could have been counting fruits, 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 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 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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Every Unsolved Math Problem that Sounds Easy – Part 2
Six Deceptively Simple Unsolved Problems in Mathematics Mersenne Primes Perfect Numbers The Rational Distance Problem The Moving Sofa Problem The Inscribed Square Problem The Ramsey Theory Problem Six Deceptively Simple Unsolved Problems in Mathematics Mersenne Primes One unsolved problem in mathematics concerns whether or not there are infinitely many Mersenne primes. 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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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 Proof that √2 is Irrational but they get increasingly more complex (pt. 2)
Continued Fractions Tennenbaum’s Proof Rational Root Theorem Applying the Rational Root Theorem to √2 Continued Fractions A continued fraction is one possible way to represent a number, consisting of a collection of nested fractions. Here we will focus on the case where the numerators of the fractions are all equal read more
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