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  2. Seven Bridges of Königsberg - Wikipedia

    en.wikipedia.org/wiki/Seven_Bridges_of_Königsberg

    In the history of mathematics, Euler's solution of the Königsberg bridge problem is considered to be the first theorem of graph theory and the first true proof in the theory of networks, [4] a subject now generally regarded as a branch of combinatorics.

  3. Euler's theorem - Wikipedia

    en.wikipedia.org/wiki/Euler's_theorem

    In 1736, Leonhard Euler published a proof of Fermat's little theorem [1] (stated by Fermat without proof), which is the restriction of Euler's theorem to the case where n is a prime number. Subsequently, Euler presented other proofs of the theorem, culminating with his paper of 1763, in which he proved a generalization to the case where n is ...

  4. Eulerian path - Wikipedia

    en.wikipedia.org/wiki/Eulerian_path

    This is known as Euler's Theorem: A connected graph has an Euler cycle if and only if every vertex has even degree. The term Eulerian graph has two common meanings in graph theory. One meaning is a graph with an Eulerian circuit, and the other is a graph with every vertex of even degree. These definitions coincide for connected graphs. [2]

  5. Euler's theorem in geometry - Wikipedia

    en.wikipedia.org/wiki/Euler's_theorem_in_geometry

    In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by [1] [2] = or equivalently + + =, where and denote the circumradius and inradius respectively (the radii of the circumscribed circle and inscribed circle respectively).

  6. Contributions of Leonhard Euler to mathematics - Wikipedia

    en.wikipedia.org/wiki/Contributions_of_Leonhard...

    Euler proved Newton's identities, Fermat's little theorem, Fermat's theorem on sums of two squares, and made distinct contributions to the Lagrange's four-square theorem. He also invented the totient function φ(n) which assigns to a positive integer n the number of positive integers less than n and coprime to n.

  7. Pentagon officials discussing how to respond if Trump issues ...

    www.aol.com/pentagon-officials-discussing...

    Pentagon officials are holding informal discussions about how the Department of Defense would respond if Donald Trump issues orders to deploy active-duty troops domestically and fire large swaths ...

  8. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

  9. Moral Injury: The Grunts - The Huffington Post

    projects.huffingtonpost.com/moral-injury/the...

    Can we imagine ourselves back on that awful day in the summer of 2010, in the hot firefight that went on for nine hours? Men frenzied with exhaustion and reckless exuberance, eyes and throats burning from dust and smoke, in a battle that erupted after Taliban insurgents castrated a young boy in the village, knowing his family would summon nearby Marines for help and the Marines would come ...