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Descartes' rule of signs. In mathematics, Descartes' rule of signs, described by René Descartes in his La Géométrie, counts the roots of a polynomial by examining sign changes in its coefficients. The number of positive real roots is at most the number of sign changes in the sequence of polynomial's coefficients (omitting zero coefficients ...
In number theory, a Descartes number is an odd number which would have been an odd perfect number if one of its composite factors were prime.They are named after René Descartes who observed that the number D = 3 2 ⋅7 2 ⋅11 2 ⋅13 2 ⋅22021 = (3⋅1001) 2 ⋅ (22⋅1001 − 1) = 198585576189 would be an odd perfect number if only 22021 were a prime number, since the sum-of-divisors ...
t. e. René Descartes (/ deɪˈkɑːrt / day-KART or UK: / ˈdeɪkɑːrt / DAY-kart; French: [ʁəne dekaʁt] ⓘ; [note 3][11] 31 March 1596 – 11 February 1650) [12][13]: 58 was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathematics was paramount ...
Regulae ad directionem ingenii, or Rules for the Direction of the Mind is an unfinished treatise regarding the proper method for scientific and philosophical thinking by René Descartes. Descartes started writing the work in 1628, and it was eventually published in 1701 after Descartes' death. [1] This treatise outlined the basis for his later ...
Descartes' rule of signs asserts that the difference between the number of sign variations in the sequence of the coefficients of a polynomial and the number of its positive real roots is a nonnegative even integer. It results that if this number of sign variations is zero, then the polynomial does not have any positive real roots, and, if this ...
All results described in this article are based on Descartes' rule of signs. If p(x) is a univariate polynomial with real coefficients, let us denote by # + (p) the number of its positive real roots, counted with their multiplicity, [1] and by v(p) the number of sign variations in the sequence of its coefficients.
René Descartes. Cartesian doubt is a form of methodological skepticism associated with the writings and methodology of René Descartes (March 31, 1596–February 11, 1650). [1][2]: 88 Cartesian doubt is also known as Cartesian skepticism, methodic doubt, methodological skepticism, universal doubt, systematic doubt, or hyperbolic doubt.
v. t. e. The wax argument or the sheet of wax example is a thought experiment that René Descartes created in the second of his Meditations on First Philosophy. He devised it to analyze what properties are essential for bodies, show how uncertain our knowledge of the world is compared to our knowledge of our minds, and argue for rationalism. [1][2]