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"Nicomachus's theorem" #mathtype 1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + 8³ + 9³ = 2025 45² = 2025

The following identity, sometimes called Nicomachus's theorem, states that the sum of n cubes is equal to the square of the nth triangular number, i.e., the square of the sum of n natural numbers from 1 to n. #MathType #math #mathematics #mathematical #mathematician #mathfacts

By utilizing this algorithm, we can construct a set of orthonormal vectors from a set of linearly independent vectors that span the same space. #MathType #math #mathematics #mathematical #mathematician #mathproblems #mathfacts

The Bernoulli distribution is a fundamental concept in probability theory that models a random experiment with two possible outcomes. This distribution is helpful in analyzing the probability of binary events. #MathType #math #mathematics #mathematician #mathfacts

The Planck units of measurement are a system defined based on 5 physical universal constants. In this system, those constants are normalized to 1, greatly simplifying the key equations of #Physics #MathType #NumberTheory #math #mathematics #mathematical #mathematician #mathfacts

Aren’t rings fascinating? Let’s explore Krull’s Separation Lemma, a profound result that pertains to these captivating algebraic structures. It was proved by Wolfgang Krull in 1928. #MathType #NumberTheory #math #mathematics #mathematical #mathfacts

The Fundamental Theorem of Arithmetic states that every positive integer greater than 1 can be represented uniquely as a product of prime numbers. Without this property, an irreducible number (only divisible by itself or the unit) would not need to be prime. #MathType #math

Matrices are fundamental mathematical objects that have numerous applications in various fields. Tell us, what do you use them for? #MathType #math #mathematics #mathfacts

Trigonometry is fun, but non-euclidean fun is better! Just remember: the angles of a triangle on a sphere add up to more than 180 degrees and its sides divided by the radius are just angles. #MathType #math #mathematics #mathematician #mathproblems #mathfacts

The Extreme Value Theorem is a fundamental result in calculus. It guarantees that a continuous function on a closed interval has both a maximum and a minimum value. #MathType #math #mathematics #mathfacts

The beta function is also called the beta integral or the Euler integral of the first kind. Many complex integrals can be reduced to expressions that involve the beta function, and it has a close connection to the gamma function. #MathType #math #mathematics #mathfacts

Absolute continuity has important implications in calculus and analysis, particularly in the exploration of integration and differentiation. Functions that possess absolute continuity exhibit a range of desirable properties. which ones you know? #MathType #math #mathfacts

Convolution in math is an operator applied on two functions which results in another function that reflects how the shape of one is modified by the other. It can also act on periodic functions and be defined for the discrete domain. #MathType #math #mathematics #mathfacts

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The folium of Descartes is a mathematical curve named after René Descartes. It is a single loop with one node and two asymptotes at the end and symmetrical about the line y=x. #MathType #math #mathematics #mathematical #mathfacts

The DFT transforms a sequence of N complex numbers (x) into another sequence of complex numbers (X). In digital signal processing, the function x(n) represents a signal that varies over time. #MathType #math #mathematics #mathematical #mathematician #mathproblems #mathfacts

The Iverson Bracket is a powerful generalization of the well-known Kronecker Delta, very useful for embedding logical conditions and truth values into your formulas #MathType #math #mathematics #mathematical #mathfacts

Lagrange’s four-square theorem asserts that any positive whole number can be written as the sum of four squares of integers. Leave an example in the comments! #MathType #NumberTheory #math #mathematics #mathproblems #mathfacts

When paired with the linearity of the integral, Cavalieri's quadrature formula allows computing the integrals of all polynomials. #MathType #math #mathematics #mathfacts

Wilhelm Wirtinger was an Austrian mathematician born in 1865. One of his contributions is Wirtinger's Inequality, widely used in many areas of #Analysis. Notably, he also had some remarkable students like Gödel and Schrödinger. #MathType #math #mathematics #mathfacts

In simpler terms, a torus of revolution can be envisioned as a donut-shaped object boasting a perfectly circular cross-section. Who doesn’t like donuts? 😜 #MathType #math #mathematics #mathematical #mathematician #mathproblems #mathfacts #mathformula

The Angle Bisector Theorem is a geometric result that sheds light on the distances between various points in relation to the angle's bisector. But first, how would you find the bisector of an angle graphically? #MathType #math #mathematics #mathproblems #mathfacts

In every finite undirected graph, the number of vertices that touch an odd number of edges is even. In a graph G, the sum of the degrees of the vertices is equal to twice the number of edges. #MathType #math #mathematics #mathematical #mathematician #mathproblems #mathfacts

The length of a vector, also known as its magnitude or norm, refers to the measure of its size or extent. It provides information about the vector's distance from the origin to its endpoint in a coordinate system. #MathType #math #mathematics #mathematical #mathfacts

The linear independence of vectors is a concept from linear algebra. A set of vectors is said to be linearly independent if no vector in the set can be expressed as a linear combination of the others. #MathType #math #mathematics #mathematician #mathproblems #mathfacts

The following identity, sometimes called Nicomachus's theorem, states that the sum of n cubes is equal to the square of the nth triangular number, i.e., the square of the sum of n natural numbers from 1 to n. #MathType #math #mathematics #mathematical #mathematician #mathfacts