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The Descartes Systems Group Inc. (commonly referred to as Descartes) is a Canadian multinational technology company specializing in logistics software, supply chain management software, and cloud -based services for logistics businesses. Descartes is perhaps best known for its abrupt and unexpected turnaround in the mid-2000s after coming close ...
Complex number. A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i2 = −1. In mathematics, a complex number is an element of a number system ...
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.
Here the function is and therefore the three real roots are 2, -1 and -4. In algebra, a cubic equation in one variable is an equation of the form in which a is not zero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic ...
The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.
In algebraic terms, doubling a unit cube requires the construction of a line segment of length x, where x 3 = 2; in other words, x = , the cube root of two. This is because a cube of side length 1 has a volume of 1 3 = 1 , and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2.
René Descartes is credited as the father of analytical geometry, the bridge between algebra and geometry, crucial to the discovery of infinitesimal calculus and analysis. In the 17th century, Descartes introduced Cartesian co-ordinates which allowed the development of analytic geometry, bring the notation of equations to geometry.
Coordinate system. The spherical coordinate system is commonly used in physics. It assigns three numbers (known as coordinates) to every point in Euclidean space: radial distance r, polar angle θ (theta), and azimuthal angle φ (phi). The symbol ρ (rho) is often used instead of r.
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