#MathType

The Mandelbrot Set reveals infinitely intricate fractal geometry from an astonishingly simple quadratic recurrence relation by collecting every complex parameter where iterating from zero stays permanently bounded within an absolute value of two. #Math #Fractals #MathType #STEM

The Laplace transform, named after Pierre-Simon Laplace, transforms a function of a real variable t (normally time) to a function of a complex variable s (complex frequency). It is often used in engineering, like in circuit analysis. #MathType

The Dirac Equation describes all spin-½ massive particles and also implies the existence of Antimatter. Paul Dirac predicted the possibility of antielectrons in 1928 with this equation, but it wasn't until 1932 that Carl D. Anderson discovered positrons. #MathType #math

Cauchy’s Integral Formula is a central statement in complex analysis. It says that given a holomorphic function f(z) defined on a closed curve C, if we know the values of f(z) on the boundary curve, we know everything about the function inside C. #MathType

The mathematician Emmy Noether announced an important theorem in physics that explains the connection between symmetry and conservation laws. It is a profound reinterpretation of the Euler-Lagrange equation. #MathType

Laplace transform converts a function that depends on a real variable t into a function that depends on a complex variable s. This mathematical tool finds widespread application in engineering, particularly in circuit analysis. #MathType #math #mathematics #mathfacts

The Fourier series is a great technique to break any function into simple sine waves, which can then be pieced together for an approximation of arbitrary precision. This is key in any technology involving signal processing of EM waves e.g. radio, wifi. #MathType #mathfacts

The Handshaking Lemma proves the sum of all vertex degrees equals twice the edges in a graph, meaning odd-degree vertices must come in pairs. Did you know Euler proved this in 1736 solving the Konigsberg bridge problem? #Math #GraphTheory #MathType #STEM

Laplace transform converts a function that depends on a real variable t into a function that depends on a complex variable s. This mathematical tool finds widespread application in engineering, particularly in circuit analysis. #MathType #math #mathematics #mathfacts

Rolle's theorem states that for a differentiable function with real values, if it takes the same value at two distinct points, then there exists at least one point between them where the first derivative is zero. #MathType #math #mathematics #mathfacts

Lambert's W function, also called product logarithm, is defined as the inverse of the function f(x)=x e^x. It's a multivalued complex function that can't be expressed in terms of elementary functions. It's useful in #combinatorics and #biochemistry. #MathType #math #mathfacts

The Fourier series is a great technique to break any function into simple sine waves, which can then be pieced together for an approximation of arbitrary precision. This is key in any technology involving signal processing of EM waves e.g. radio, wifi. #MathType #mathfacts

The #quaternion number system is an extension of the complex numbers. They're widely used in pure mathematics, but also find applications in areas like computer animation and quantum mechanics. #MathType

L'Hôpital's Rule was actually devised by Johann Bernoulli. It appeared in the first-ever #Calculus textbook by Guillaume de L'Hôpital, thanks to an agreement: Bernoulli would inform L'Hôpital only of his latest findings in exchange for an annual payment of 300 Francs. #MathType

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 #Analysis

Lami's Theorem is a straightforward application of the sine rule to #Mechanics dating back to the 17th century. This rule is still used in structural analysis in #CivilEngineering to keep those buildings standing! #MathType #math #mathematics #mathfacts

The #Laurent series, named after the mathematician Pierre Alphonse Laurent, is the representation of a complex function as a power series that includes terms of negative degree. Laurent series is used when a #Taylor series cannot be applied. #MathType #math #mathfacts

Information entropy is a basic quantity associated with a random variable expressing the average level of "information" of the variable's possible outcomes. It can be written as a function of a logarithm of any base. #MathType #math #mathfacts

In the process of solar radiation creation, mass is converted to energy in accordance with Einstein's Mass–energy equivalence, this means solar mass is constantly lost. The amount of mass the Sun loses every second can be calculated. #MathType

The Cauchy–Bunyakovsky–Schwarz inequality is one of the most famous and used inequalities in mathematics. Particular cases of it include Cauchy's inequality for the dot product and Holder's inequality for square-integrable functions. #MathType