Download 100 Essential Things You Didn't Know You Didn't Know about by John D. Barrow PDF

By John D. Barrow

A desirable exploration of math’s connection to the arts.
At first look, the worlds of math and the humanities will possibly not appear like cozy pals. yet as mathematician John D. Barrow issues out, they've got a powerful and normal affinity—after all, math is the examine of all styles, and the area of the humanities is wealthy with trend. Barrow whisks us via a hundred thought-provoking and sometimes whimsical intersections among math and plenty of arts, from the golden ratios of Mondrian’s rectangles and the curious fractal-like nature of Pollock’s drip work to ballerinas’ gravity-defying leaps and the subsequent iteration of monkeys on typewriters tackling Shakespeare. For these folks with our ft planted extra firmly at the flooring, Barrow additionally wields daily equations to bare what number guards are wanted in an artwork gallery or the place you have to stand to examine sculptures. From song and drama to literature and the visible arts, Barrow’s witty and obtainable observations are certain to spark the imaginations of math nerds and paintings aficionados alike. eighty five illustrations

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But this is a big problem. 5r) = √(5gr). As you start to move in a circular arc at the bottom you will therefore feel a downward force equal to your weight plus the outward circular motion force, and this is equal to: Net downward force at the bottom = Mg + MVb2 /r > Mg + 5Mg = 6Mg Therefore, the net downward force on the riders at the bottom will exceed six times their weight (an acceleration of 6-g). Most riders, unless they were offduty astronauts or high-performance pilots wearing gsuits, would be rendered unconscious by this force.

The skeptic points out that when a projectile, in this case the human body, is launched from the ground (and air resistance can be neglected) then its center of mass1 will follow a parabolic trajectory: nothing the projectile can do will change that. However, there is some fine print to the laws of mechanics: it is only the center of mass of the projectile that must follow a parabolic trajectory. If you move your arms around, or tuck your knees into your chest, you can change the location of parts of your body relative to your center of mass.

If we allow a stream of grains to fall vertically downward onto a tabletop then a pile will steadily grow. The falling grains will have haphazard trajectories as they tumble over the others. Yet, steadily, the unpredictable falls of the individual grains will build up a large orderly pile. Its sides steepen gradually until they reach a particular slope. After that, they get no steeper. The special “critical” slope will continue to be maintained by regular avalanches of all sizes, some involving just one or two grains but other rarer events producing a collapse of the whole side of the pile.

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