《数学魔术：使用物理 reasoning 解决问题》(真价/零售 PDF)

English | January 24th, 2023 | ISBN: 0691242054 | 201 pages | True PDF | 6.84 MB

Everybody knows that mathematics is indispensable to physics—imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist.

Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can. Did you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that soap film holds the key to determining the cheapest container for a given volume? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? Levi demonstrates how to use physical intuition to solve these and other fascinating math problems. More than half the problems can be tackled by anyone with precalculus and basic geometry, while the more challenging problems require some calculus. This one-of-a-kind book explains physics and math concepts where needed, and includes an informative appendix of physical principles.

The Mathematical Mechanic will appeal to anyone interested in the little-known connections between mathematics and physics and how both endeavors relate to the world around us.

每个人都明白数学对于物理的重要性——想象一下如果没有数学支撑，爱因斯坦和牛顿的理论将会是什么样子。但有多少人意识到物理学可以用来解决许多惊人的、令人赞叹的优雅数学问题呢？马克·莱维在这一本有趣的书中展示了这一点，为读者准备了一系列有趣的问题和让人费解的谜题，这些谜题既能娱乐又能激发他们内心中的物理学家。 莱维将数学和物理彻底打乱，揭示了物理学如何简化证明并提供更快的解决方案以及新的定理，并且如何通过物理解决方案展示结论是正确的独特方式，而这些结论通过漫长的数学计算从未能做到。你知道吗？可以通过旋转一个装满水的鱼缸来推导出勾股定理吗？或者肥皂泡可以揭示确定给定体积最便宜容器的关键？又或是数据集的最佳拟合线可以用由一根杆和弹簧制成的机械装置找到？莱维展示了如何利用物理直觉解决这些以及其他有趣的数学问题。超过一半的问题只需要高中预修课和基本几何学就可以解决，而更具挑战性的问题则需要一些微积分的知识。这本独一无二的书籍解释了所需的物理学和数学概念，并包括了一个信息丰富的附录介绍物理原理。 《数学机械师》这本书将吸引那些对数学与物理学之间的未知联系以及这两者如何与我们周围的世界相关联感兴趣的读者。

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