The Number Mysteries: A Mathematical Odyssey through Everyday Life (MacSci)
Format: PDF / Kindle (mobi) / ePub
Every time we download music, take a flight across the Atlantic or talk on our cell phones, we are relying on great mathematical inventions. In The Number Mysteries, one of our generation's foremost mathematicians Marcus du Sautoy offers a playful and accessible examination of numbers and how, despite efforts of the greatest minds, the most fundamental puzzles of nature remain unsolved. Du Sautoy tells about the quest to predict the future―from the flight of asteroids to an impending storm, from bending a ball like Beckham to forecasting population growth. He brings to life the beauty behind five mathematical puzzles that have contributed to our understanding of the world around us and have helped develop the technology to cope with it. With loads of games to play and puzzles to solve, this is a math book for everyone.
pairs of points there are that differ in one coordinate. Keep this in mind as we move to a shape for which we don’t have a picture. Descartes’s dictionary has shapes and geometry on one side and numbers and coordinates on the other. The problem is that the visual side runs out if we try to go beyond three-dimensional shapes, since there isn’t a fourth physical dimension in which we can see higher-dimensional shapes. The beauty of Descartes’s dictionary is that the other side of the dictionary
need to think of a sheet of card stock being placed on each point and then look at how all these cards intersect or cut into one another. Each card needs to be angled so that it is perpendicular to the line running from the center of the shape to the vertex. For example, if you replace the vertices of a dodecahedron with faces, you get the icosahedron: Figure 3.6 By playing this trick with the Archimedean solids, the procedure produces 13 new dice. The classic soccer ball has 60 vertices, and
of those guesses; there doesn’t appear to be a clever way to make these guesses other than trying one after another until one set of guesses leads you to a consistent answer. Packing Problem You run a moving company. All your packing crates are of the same height and width, exactly the same as the internal dimensions of your truck (well, just a little smaller so that they just squeeze in). But the crates are of different lengths. Your truck is 150 feet long, and the crates available for packing
years, then what is the explanation? Figure 5.8 Yet again, it turns out that mathematics has the answer. A simple equation tells us how many lemmings there will be from one season to the next. We start by assuming that, because of environmental factors such as food supply and predators, there’s a maximum population that can be sustained. We’ll call that N. We’ll say that L is the number of lemmings that survived from the previous season, and that after the births in the new season, the
Beyond the threshold where the chaos kicks in, 3.5699, it’s almost impossible to predict how the population will vary. The equation controlling the population numbers can start out very predictable, but with just a small change in lemming fecundity, chaos can suddenly erupt. Figure 5.12 When lemming numbers increase in the spring by a factor of 3.5699 or more, the population variations become chaotic. How to Play the Fishy Formula Game This is a game for two players. Download the PDF from the