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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 robust and normal affinity—after all, math is the learn of all styles, and the realm of the humanities is wealthy with development. Barrow whisks us via a hundred thought-provoking and infrequently 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 new release of monkeys on typewriters tackling Shakespeare. For these folks with our toes planted extra firmly at the floor, Barrow additionally wields daily equations to bare what percentage guards are wanted in an artwork gallery or the place you have to stand to examine sculptures. From track and drama to literature and the visible arts, Barrow’s witty and obtainable observations are bound to spark the imaginations of math nerds and artwork aficionados alike. eighty five illustrations

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N). Now imagine a very unusual cake: one with an 49 infinite number of tiers. 17 + + . ) (1/n2) = π3/6 = The remarkable thing about this infinite sum of terms is that it is a finite number. 64. 1 Next, we have to ice it. For this we need to know how much icing to make, so we should calculate the total outside surface areas. ) The total area to be iced is the sum of the areas of all the tiers in the infinite tower: Total Surface Area = 2π × (1 +½ + ⅓ + ¼ + . ) = 2π × Σ 50 1 (1/n) This sum is infinite.

This means that Alice believes that Bob’s assumption – “that Alice believes that Bob’s assumption is incorrect” – is correct. But this again creates a contradiction because it means that Alice does believe that Bob’s assumption is incorrect! We have displayed a belief that it is not logically possible to hold. This conundrum turns out to be farreaching. It means that if the language we are using contains simple logic, then there must always be 35 statements that it is impossible to make consistently in that language.

I talked about the ancient and modern conceptions of the vacuum (the vuoto of the title) in science and music, and of zero in mathematics; and Einaudi performed piano pieces that showed the influence of silence, and hence timing, in musical composition and performance. No conversation about “nothing” and music could fail to mention John Cage’s famous 4'33" (“Four minutes, thirty-three seconds”) and Einaudi was able to provide the first-ever performance of this work at the Rome auditorium. It was composed in 1952 – the score says “for any instrument or combination of instruments” – and consists of 4'33" of silence in three movements.

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100 Essential Things You Didn't Know You Didn't Know about Math and the Arts by John D. Barrow

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