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In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mutually tangent circles.
Solution of a travelling salesperson problem: the black line shows the shortest possible loop that connects every red dot. The travelling salesman problem, also known as the travelling salesperson problem (TSP), asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns ...
According to his theory, a probability assertion is akin to a bet, and a bet is coherent only if it does not expose the wagerer to loss if their opponent chooses wisely. To explain his meaning, de Finetti created a thought-experiment to illustrate the need for principles of coherency in making a probabilistic statement.
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Descartes' second model on light uses his theory of the elements to demonstrate the rectilinear transmission of light as well as the movement of light through solid objects. He uses a metaphor of wine flowing through a vat of grapes, then exiting through a hole at the bottom of the vat.
He dismissed Descartes' theory of light because he rejected Descartes’ understanding of space, which derived from it. [6] With the publication of Opticks in 1704, [ 7 ] Newton for the first time took a clear position supporting a corpuscular interpretation, though it would fall on his followers to systemise the theory.
In the Netherlands, where Descartes had lived for a long time, Cartesianism was a doctrine popular mainly among university professors and lecturers.In Germany the influence of this doctrine was not relevant and followers of Cartesianism in the German-speaking border regions between these countries (e.g., the iatromathematician Yvo Gaukes from East Frisia) frequently chose to publish their ...
Theory reductionism: the suggestion that a newer theory does not replace or absorb an older one, but reduces it to more basic terms. Theory reduction itself is divisible into three parts: translation, derivation, and explanation. [4] Reductionism can be applied to any phenomenon, including objects, problems, explanations, theories, and meanings.