Hidden Harmonies

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A squared plus b squared equals c squared may seem simple, but it opens a vibrant world of mathematics, guided by acclaimed authors Robert and Ellen Kaplan. With wit and clarity, they explore the Pythagorean theorem's journey from ancient Babylon to modern times, highlighting figures like Leonardo da Vinci, Albert Einstein, and even President James Garfield, as well as the enigmatic Pythagoras, who likely did not originate the theorem. The authors delve into the theorem's numerous proofs, which range from two hundred to possibly four thousand, and its extensive applications, from ancient Egyptian surveying to contemporary astronomical measurements. The theorem's generalizations are remarkable, applying to shapes beyond squares and extending into any number of dimensions, even infinity. One of its most fascinating aspects is how it led to the discovery of irrational numbers, a concept that unsettled Pythagoras's followers. Like the authors' previous works, this book makes the excitement of mathematics accessible and engaging, showcasing its beauty and complexity.