There are many fascinating figures and shapes out there. The hyperboloid of revolution is a captivating three-dimensional surface generated by revolving a hyperbola around its axis. The resulting shape resembles an hourglass. Did you know about it?

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LU decomposition factors a matrix as a product of a lower triangular matrix and an upper triangular matrix. It is a method used by computers to solve systems of linear equations, to invert a matrix or compute its determinant.

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The fundamental lemma of the calculus of variations is a key result in the field of mathematical analysis. It is a simple but profound statement, and its proof involves a series of steps. How would you prove it?

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Jordan's lemma explains the behavior of a contour integral on the semicircular upper arc and is frequently used along the residue theorem to evaluate such integrals. It is named after the French mathematician Camille Jordan.

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The fundamental lemma of the calculus of variations is a key result in the field of mathematical analysis. It is a simple but profound statement, and its proof involves a series of steps. How would you prove it?

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The Nagell-Lutz theorem, named after Elisabeth Lutz and Trygve Nagell, describes rational torsion points on elliptic curves over the integers. It is a result of the diophantine geometry of elliptic curves.

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The scalar product, also referred to as the dot or inner product, is an algebraic operation performed between two vectors. While the input consists of vectors, the output is a scalar quantity, not another vector.

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An elegant example of the conservation of angular momentum, the rotational equivalent of linear momentum, is when a figure skater does a pirouette. Their rotational speed increases as their moment of inertia decreases by drawing in their arms and legs.

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Prepare to put your skills to the test! 🧩🔎

The task is simple, but the answer may be complex. Let’s find the solution and share your answer in the comments below! 👇

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A parallelepiped is a three-dimensional figure that consists of six parallelograms. How would you get to this formula?

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John Wallis was the English mathematician who coined the terms 'number line' and 'momentum', the first to use '∞' for infinity and fractional powers for roots. While calculating integrals (before calculus), he found this curious way to obtain pi.

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Stefan Banach formalized the notion of complete normed space, now known as Banach space. Amongst theorems that bear his name is the Fixed Point Theorem, fundamental in #FunctionalAnalysis and #DifferentialEquations .

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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.

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🧮 Attention, puzzle enthusiasts and math whizzes!

We have an intriguing challenge for you. Can you determine the value of r with the information provided?

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The central limit theorem states that as the sample size of a random variable increases, the distribution of sample means becomes more and more normal, regardless of the underlying distribution of the population. It is fundamental in probability theory and #statistics . #MathType

The Fermi golden rule describes the transition rate from one eigenstate of a quantum system to a group of eigenstates in a continuum, as the consequence of a weak perturbation.

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MathType MathType

shall we place g(x) into that little product under ∫ integral sign?

to replace h(x) sitting there unsupervised?

❤️❤️❤️

MathType

MathType Source: Matemáticas Básicas para el acceso a la Universidad. Ed. Pirámide.
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