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Infinite Powers

Infinite Powers

How Calculus Reveals the Secrets of the Universe

OKUYACAKLARIMA EKLE
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Infinite Powers (How Calculus Reveals the Secrets of the Universe)
Basım
English · United States of America · Houghton Mifflin Harcourt · 2 Nisan 2019 · Karton kapak · 9781328879981
“Marvelous . . . an array of witty and astonishing stories . . . to illuminate how calculus has helped bring into being our contemporary world.”—The Washington Post From preeminent math personality and author of The Joy of x, a brilliant and endlessly appealing explanation of calculus – how it works and why it makes our lives immeasurably better. Without calculus, we wouldn’t have cell phones, TV, GPS, or ultrasound. We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket. Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down‑to‑earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real‑world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous. Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS. As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.

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In contrast to a mild power function x or x², an exponential function like 2^x or 10^x describes a much more explosive kind of growth, a growth that snowballs and feeds on itself. Instead of adding a constant increment at each step as in linear growth, exponential growth involves multiplying by a constant factor.
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The pivotal moment in the history of calculus occurred in the middle of the seventeenth century when the mysteries of curves, motion, and change collided on a two-dimensional grid, the xy plane of Fermat and Descartes. Back then, Fermat and Descartes had no idea what a versatile tool they had created. They intended the xy plane as a tool for pure mathematics. Yet from the start, it too was a crossroads of sorts, a place where equations met curves, algebra met geometry, and the mathematics of the East met that of the West. Then, in the next generation, Isaac Newton built on their work as well as on the work of Galileo and Kepler and brought geometry and physics together in a great synthesis. Newton's spark set off the fire that lit the Enlightenment and caused a revolution in Western science and mathematics.
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Fermat had applied his embryonic version of differential calculus to physics. No one had ever done that before. And in so doing, he showed that light travels in the most efficient way--not the most direct way, but the fastest. Of all the possible paths light can take, it somehow knows, or behaves as if it knows, how to get from here to there as quickly as possible. This was an early clue that calculus was somehow built into the operating system of the universe.