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Mathematics and Mechanics - The Interplay - Volume I: The Basics (Hardcover, 1st ed. 2021)
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Mathematics and Mechanics - The Interplay - Volume I: The Basics (Hardcover, 1st ed. 2021)
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Mathematics plays an important role in mechanics and other human
endeavours. Validating examples in this first volume include, for
instance: the connection between the golden ratio (the "divine
proportion" used by Phidias and many other artists and enshrined in
Leonardo's Vitruvian Man, shown on the front cover), and the
Fibonacci spiral (observable in botany, e.g., in the placement of
sunflower seeds); is the coast of Tuscany infinitely long?; the
equal-time free fall of a feather and a lead ball in a vacuum; a
simple diagnostic for changing your car's shocks; the Kepler laws
of the planets; the dynamics of the Sun-Earth-Moon system; the
tides' mechanism; the laws of friction and a wheel rolling down a
partially icy slope; and many more. The style is colloquial. The
emphasis is on intuition - lengthy but intuitive proofs are
preferred to simple non-intuitive ones. The mathematical/mechanical
sophistication gradually increases, making the volume widely
accessible. Intuition is not at the expense of rigor. Except for
grammar-school material, every statement that is later used is
rigorously proven. Guidelines that facilitate the reading of the
book are presented. The interplay between mathematics and mechanics
is presented within a historical context, to show that often
mechanics stimulated mathematical developments - Newton comes to
mind. Sometimes mathematics was introduced independently of its
mechanics applications, such as the absolute calculus for
Einstein's general theory of relativity. Bio-sketches of all the
scientists encountered are included and show that many of them
dealt with both mathematics and mechanics.
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