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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 i 2 = −1.
The adjective Cartesian refers to the French mathematician and philosopher René Descartes, who published this idea in 1637 while he was resident in the Netherlands.It was independently discovered by Pierre de Fermat, who also worked in three dimensions, although Fermat did not publish the discovery. [1]
In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3).It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.
In the first part of his work, Descartes ponders the relationship between the thinking substance and the body. For Descartes, the only link between these two substances is the pineal gland (art. 31), the place where the soul is attached to the body. The passions that Descartes studies are in reality the actions of the body on the soul (art. 25).
To explain his meaning, de Finetti created a thought-experiment to illustrate the need for principles of coherency in making a probabilistic statement. In his scenario, when someone states their degree-of-belief in something, one places a small bet for or against that belief and specifies the odds, with the understanding that the other party to ...
The Necker cube is an optical illusion that was first published as a rhomboid in 1832 by Swiss crystallographer Louis Albert Necker. [1] It is a simple wire-frame, two dimensional drawing of a cube with no visual cues as to its orientation, so it can be interpreted to have either the lower-left or the upper-right square as its front side.
Existentialism asserts that people make decisions based on subjective meaning rather than pure rationality. The rejection of reason as the source of meaning is a common theme of existentialist thought, as is the focus on the anxiety and dread that we feel in the face of our own radical free will and our awareness of death. Kierkegaard advocated ...
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements.Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions from these.