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Amazings.es , Microsiervos , Enchufa2 or Francis (th) E mule Science's News . For my part, I honor him by telling a story with which revolutionized the world of geometry.
I: Benoît Mandelbrot Mathematicians Benoît Mandelbrot always considered a special kind, including many who were excluded from the field of mathematics. But he always felt proud to be a bold new prisms trying to find those who see reality otherwise. Investigated the theory of games, the distribution of words in literature and even ventured successfully in economics, studying the distribution of large and small incomes in an economy.
These revolutionary ideas were flying at the head of Mandelbrot with its unorthodox way of thinking about mathematics. But all these studies became an article of conventional when Lewis F. Richardson fell into the hands of Mandelbrot. In this article, Richardson was intrigued by what the different compare available through the length of the coasts of countries such as Spain, Portugal and Belgium were discrepancies of up to 20% of each other. What was the reason for differences so great to measure something known by all? Why the English when they measured their border obtained a different value than the Portuguese obtained by measuring the same border?
In 1967, Mandelbrot introduced Article
How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension a puzzling scientific conference all attendees. Mandelbrot directly asked his colleagues what was the length of England, without obtaining a concise answer any of them. Some chose to simply say that it was not his field, while others ventured to look in the encyclopedia. But both answers Mandelbrot were unsatisfactory. The only accurate answer to that question was: infinite.
II: Measuring Britain with 200 km segment
surveyors, when they venture to measure the length of a coastline using a meter or rhythm of defined length. Say you use straight measuring 200km off the coast of the island of Great Britain. The result will be approximately 2.400Km, as shown in the image above.
Anyone can determine that this approach is crude and full of vague. Then we will consider a straight section measuring less, 50Km by example. In this case, the result of measuring the length of the coast will be superior to the previous case, 3,400 Km-long. The explanation is simple, because now we have had the opportunity to measure embers that had previously been completely overlooked. But is this approach sufficient? Probably not.
III: Measuring Britain segment 50Km
In 50 km we are ignoring many capes and bays that would increase the coastline. But where is the limit for this measurement? Common sense would suggest that at some point end up converging estimates reaching the true value of coastal length. And this would be true if the shoreline keep Euclidean geometry, the geometry that we have all learned, but the reality is that nature is not governed by Euclidean geometry.
Mandelbrot found that as the measurement scale becomes smaller, the length of the coastline increases without limit. Only when you reach the atomic scale can be completed this recursive process, and assuming that at some point find and indivisible elementary particles at that point all the modern theories.
IV: Fractal: Mandelbrot Set While
Mandelbrot in that article of 1967, the Congress in which he presented the article at no time mentioned the term fractal, this was the beginning of the concept of fractal geometry. It was not until 1975 that Mandelbrot introduced the term that revolutionized the field of mathematics that was intact from the ancient Greeks, geometry.
Sources and further information:
- How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension
- How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension
- Eureka: Scientific Breakthroughs That changed the world
- In pictures: Mandelbrot's fractals
- Benoît Mandelbrot
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