Can a graph be drawn without its edges crossing? If so, we are talking about a planar graph. Knowing whether a graph is planar by looking at it was a rather hard task! That was until Kuratowski came up with this simple rule to find "undrawable" graphs in 1930. #MathType #math

#Fibonacci Numbers have fascinated mathematicians for centuries. The Fibonacci rabbit hole goes so deep that even to this day new insights are being gained from them and more properties, generalizations and applications in #NumberTheory are being discovered. #MathType #math

A Pythagorean Triple is a set of 3 positive integers that satisfy the formula of Pythagoras' theorem. Feel free to share some Pythagorean Triples you know in the comments below! #MathType #math #mathematics #mathematical #mathematician #mathproblems #mathfacts

The fine-structure constant, introduced in 1916 by Arnold Sommerfeld, quantifies the electromagnetic interaction between elementary charged particles, which allows us to characterize the spectral lines of the hydrogen atom. #MathType #math #mathematics #Physics

Here's Schwartz's Theorem, also known as the "equality of mixed partials". It's one of the classical #calculus results, and a relief for students. #MathType #math #mathematics #mathematical #mathematician #mathproblems #mathfacts #mathformula #mathiscool #mathiseverywhere

An object's #SolidAngle is the segment of a unit sphere that it covers when looking at the object from the center of the sphere. Although the Moon is much smaller than the Sun, both have very similar solid angles when viewed from any point on Earth. #MathType #math #mathfacts

Schrödinger equation can predict the wave function (state) of a system and its evolution in time. It's Newton's law analog for #QuantumMechanics #MathType #math #mathematics #mathematical #mathematician #mathproblems #mathfacts

Tijdeman's theorem states that only a finite number of consecutive powers can exist. Do you know how it was proved? #MathType #NumberTheory #math #mathematics #mathematical #mathematician #mathproblems #mathfacts

A group is an abstract mathematical structure consisting of a set with an inner operation. Groups are used in geometry to represent symmetry phenomena, which gives rise to numerous applications. #MathType #math #mathematics #mathematical #mathematician #mathproblems #mathfacts

The Euler-Bernoulli equation can be used in elasticity problems. It provides a way of calculating the load-carrying and deflection characteristics of beams. #MathType #math #mathematics #mathematical #mathematician #mathproblems #mathfacts

A parallelepiped is a three-dimensional figure that consists of six parallelograms. How would you get to this formula? #MathType #math #mathematics #mathematical #mathematician #mathproblems #mathfacts

The Mean Value Theorem is a classical elementary result proven by #Cauchy in 1823 using the ideas of modern calculus. #MathType #math #mathematics #mathematical #mathematician #mathproblems #mathfacts

In algebra, the center of a group is a fundamental structure that plays an important role in understanding the group's properties. Notably, the center of G is always an abelian and normal subgroup of G. #MathType #math #mathematics #mathematical #mathematician #mathfacts

Pascal's theorem is very useful in proving the collinearity of three intersections among six points on a circle. Did you know about it? #MathType #math #mathematics #mathematical #mathematician #mathproblems #mathfacts #mathformula #mathiscool #mathiseverywhere #numbers

You choose n elements in a specific order from a larger set. This is what we call a variation of m elements choose n. If you now have the freedom to choose the same element multiple times, then you are working with a variation with repetition of m elements choose n. #MathType

An astroid is a particular type of roulette curve. Specifically, it is the path traced by a point on a smaller circle rolling within a larger circle, four times its size. #MathType #NumberTheory #math #mathematics #mathematical #mathematician #mathproblems #mathfacts

Descartes' rule of sign is used to predict the number of real zeros of a polynomial function. In particular, zero changes imply 0 positive roots, while just one change means a single one. #MathType #math #mathematics #mathematical #mathematician #mathproblems #mathfacts

The #binomial distribution was first studied in the context of games of pure chance, and it's now widely used to analyze data in many fields. It models the number of successes when performing n trials of an experiment with a probability of success p. #MathType #math #mathfacts

In the realm of algebra and number theory, Euclid's Lemma captures a fundamental property of prime numbers: When a prime number divides the product of two integers, it inevitably divides at least one of these integers. Did you know about it? #MathType #math #mathfacts

Kepler’s laws, published by Johannes Kepler, are three scientific laws that describe the motion of planets around the Sun. The first Kepler law states, "The orbit of every planet is an ellipse with the Sun at one of the two foci”. #MathType #math #mathematics #mathfacts