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Descartes is perhaps best known for its abrupt and unexpected turnaround in the mid-2000s after coming close to bankruptcy in the wake of the dot-com bubble collapse. It is also known as one of the earliest logistics technology companies to adopt an on-demand business model and sell its software as a service (SaaS) via the Internet.
History. The curve was first proposed and studied by René Descartes in 1638. Its claim to fame lies in an incident in the development of calculus.Descartes challenged Pierre de Fermat to find the tangent line to the curve at an arbitrary point since Fermat had recently discovered a method for finding tangent lines.
René Descartes (/ d eɪ ˈ k ɑːr t / day-KART or UK: / ˈ d eɪ k ɑːr t / DAY-kart; French: [ʁəne dekaʁt] ⓘ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650): 58 was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science.
Descartes's theorem. Descartes's theorem on the "total defect" of a polyhedron states that if the polyhedron is homeomorphic to a sphere (i.e. topologically equivalent to a sphere, so that it may be deformed into a sphere by stretching without tearing), the "total defect", i.e. the sum of the defects of all of the vertices, is two full circles (or 720° or 4 π radians).
If this definition is used, the cube root of a negative number is a negative number. The three cube roots of 1. If x and y are allowed to be complex, then there are three solutions (if x is non-zero) and so x has three cube roots. A real number has one real cube root and two further cube roots which form a complex conjugate pair.
Descartes' theorem generalizes to mutually tangent great or small circles in spherical geometry if the curvature of the th circle is defined as = , the cotangent of the oriented intrinsic radius. Then: [44] [19]
Doubling the cube is the construction, using only a straightedge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.
Expected fraction of seats won, s vs fraction of votes received, v (solid black) according to the cube rule, with a plot of the seat:vote ratio (dashed red) The cube rule or cube law is an empirical observation regarding elections under the first-past-the-post system. The rule suggests that the party getting the most votes is over-represented ...
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