banach inverse mapping theorem
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Banach inverse mapping theorem
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"Both Leonardo and Newton had fecund imaginations from which poured forth a stream of discoveries, gadgets, engineering marvels, and farsighted contrivances. Newton invented the reflecting telescope, Leonardo the helicopter; Newton, the binomial theorem, Leonardo, the parachute, submarine, and tank. Newton's discover ies were expressed in equations. Leonardo's in drawings. Leonardo made many contributions to science, both in theory and application, but he is principally featured in art history classes. Newton wrote lengthy exegeses on alchemy, the mysteries of the Trinity, and the authority of the Bible, yet he is considered history's premier physicist.... Each man transformed the science of his day from one that held an essentially static view of the universe into one that included motion. The subject of motion consumed them both and their greatest contributions to humankind grew out of an intense curiosity about it. Newton's ambitious desire to explain celes tial movements resulted in the formulation of his three famous laws of motion and his discovery of the inverse square law of gravitation. Leonardo's compelling studies of the muscular movements of men and horses, exemplified in his cartoons for his Battle of Anghiari, are the most detailed anatomical descriptions of men and animals in motion that have ever been produced."