Fractal Geometry :: Mathematics Math Geometric Essays

Fractal GeometryIn the past, maths has been concerned largely with readys and functions to which the methods of classical calculus could be applied. slews or functions that ar not sufficiently smooth or regular have tended to be named as pathological and not worthy of canvass. They were regarded as individual curiosities and solely rarely were thought of as a class to which a world-wide theory might be applicable. However, in recent years this placement has changed. Irregular sets provide a much better representation of some natural phenomena than do the figures of classical geometry. Fractal geometry provides a general framework for the study of such irregular sets. (Falconer) The word fractal was coined in 1975 by mathematician Benoit B. Mandelbrot to describe an intricate-looking set of curves, many of which were not yet seen before the creation of the computer. Fractals often evidence self-similarity, which means that various copies of an object can be found in the orig inal object at smaller size scales. This continues for many magnifications standardised an endless nesting of Russian dolls within dolls. (Pickover) Fractals appear everywhere in nature, in galaxies and landscapes, in earthquakes and geological cracks, in aggregates and colloids, and even in the human body. Fractal geometry is an serious tool in the analysis of phenomena, ranging from rhythms in music melodies to the human beat and DNA sequences. Many professions including, mathematics, astronomy, physics, chemistry, engineering, and biology use fractal geometry. (Bunde)Waclaw Sierpinski was born on treat 14, 1882, in Warsaw, Poland. Sierpinski attended the University of Warsaw in 1899, when all classes were taught in Russian. He graduated in 1904 and went on to teach mathematics and physics at a girls school in Warsaw. He left teaching in 1905 to get his doctorate at the Jagiellonian University in Cracow. After receiving his doctorate in 1908, Sierpinski went on to teach at th e University of Lvov. During his years at Lvov, he wrote deuce-ace books and many research papers. These books were The Theory of Irrational numbers (1910), Outline of Set Theory (1912), and The Theory of Numbers (1912). In 1919, Sierpinski accepted a air as a professor at the University of Warsaw, and this is where Waclaw Sierpinski (The Mactutor)he would spend the relievo of his life. Throughout his career, Sierpinski wrote 724 papers and an amazing 50 books. Sierpinski studied many areas of mathematics, including, chimerical numbers, set theory, fractal geometry, and theory of numbers.