Mathematics on Thoughtful Wanderings
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Recent content in Mathematics on Thoughtful WanderingsHugo -- gohugo.iolaw9723@gmail.com (Lawrence Pilch)law9723@gmail.com (Lawrence Pilch)Mon, 17 Sep 2018 00:00:00 +0000The Beauty of Strange Attractors
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Mon, 17 Sep 2018 00:00:00 +0000law9723@gmail.com (Lawrence Pilch)https://lpdata.me/post/the-beauty-of-strange-attractors/Dynamic systems are those where something changes over time according to a set of rules. They are found in many fields of study including, physics, chemistry, geology, biology and economics. Examples include, the planets orbiting around the sun, the vibration of an airplane wing, and the diffusion of drugs in your body.
In mathematics, the something that changes over time can be points in a plane that change according to the rules of a function, which in a general form looks like this:Who's a Buffon?
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Fri, 27 Apr 2018 00:00:00 +0000law9723@gmail.com (Lawrence Pilch)https://lpdata.me/post/whos-a-buffon/I wanted to try a simple interactive visualization using RStudio’s Shiny package and thought Buffon’s needle problem would work well. Around 1732, Georges-Louis Leclerc, Comte de Buffon, a French mathematician, first posed and solved the question that essentially boils down to asking what is the probability that a needle dropped on a floor of parallel lines crosses a line? He discovered that if the length of the needle is less than or equal to the width of the lines the probability is: