By Mark Levi

Everybody is familiar with that arithmetic is fundamental to physics--imagine the place we might be this day if Einstein and Newton did not have the mathematics to again up their principles. yet what number of people observe that physics can be utilized to supply many wonderful and strikingly based suggestions in arithmetic? Mark Levi exhibits how during this pleasant e-book, treating readers to a bunch of pleasing difficulties and mind-bending puzzlers that would amuse and encourage their internal physicist.

Levi turns math and physics the other way up, revealing how physics can simplify proofs and result in faster strategies and new theorems, and the way actual options can illustrate why effects are actual in methods long mathematical calculations by no means can. do you know it really is attainable to derive the Pythagorean theorem via spinning a fish tank choked with water? Or that cleaning soap movie holds the most important to picking out the most cost effective box for a given quantity? Or that the road of most sensible healthy for a knowledge set are available utilizing a mechanical contraption made of a rod and comes? Levi demonstrates how one can use actual instinct to unravel those and different attention-grabbing math difficulties. greater than part the issues should be tackled through an individual with precalculus and simple geometry, whereas the tougher difficulties require a few calculus. This unique booklet explains physics and math suggestions the place wanted, and comprises an informative appendix of actual principles.

The Mathematical Mechanic will entice someone attracted to the little-known connections among arithmetic and physics and the way either endeavors relate to the realm round us.

Show description

Read or Download The Mathematical Mechanic: Using Physical Reasoning to Solve Problems PDF

Best Physics books

To Explain the World: The Discovery of Modern Science

A masterful observation at the historical past of technological know-how from the Greeks to trendy occasions, by means of Nobel Prize-winning physicist Steven Weinberg—a thought-provoking and critical e-book by way of some of the most distinct scientists and intellectuals of our time. during this wealthy, irreverent, and compelling heritage, Nobel Prize-winning physicist Steven Weinberg takes us throughout centuries from old Miletus to medieval Baghdad and Oxford, from Plato’s Academy and the Museum of Alexandria to the cathedral institution of Chartres and the Royal Society of London.

Game Physics

Create bodily sensible 3D portraits environments with this advent to the guidelines and methods at the back of the method. writer David H. Eberly comprises simulations to introduce the foremost difficulties concerned after which progressively unearths the mathematical and actual suggestions had to remedy them. He then describes the entire algorithmic foundations and makes use of code examples and dealing resource code to teach how they're carried out, culminating in a wide selection of actual simulations.

Quantum Theory of Solids (Oxford Classic Texts in the Physical Sciences)

This booklet develops the topic from the elemental ideas of quantum mechanics. The emphasis is on a unmarried assertion of the guidelines underlying a few of the approximations that experience for use and care is taken to split sound arguments from conjecture. This e-book is written for the scholar of theoretical physics who desires to paintings within the box of solids and for the experimenter with a data of quantum idea who's now not content material to take different people's arguments without any consideration.

Quantum Enigma: Physics Encounters Consciousness

In attempting to comprehend the atom, physicists outfitted quantum mechanics, the main profitable concept in technology and the foundation of one-third of our economic system. they discovered, to their embarrassment, that with their idea, physics encounters realization. Authors Bruce Rosenblum and Fred Kuttner clarify all this in non-technical phrases with support from a few fanciful tales and anecdotes concerning the theory's builders.

Additional resources for The Mathematical Mechanic: Using Physical Reasoning to Solve Problems

Show sample text content

DoCarmo. Differential Geometry of Curves and Surfaces. Englewood Cliffs, NJ: Prentice-Hall, 1976. P. G. Doyle and J. L. Snell. Random Walks and electrical Networks. Washington, DC: Mathematical organization of the US, 1984. See pages 65–69 for additional information and references. R. P. Feynman. QED. Princeton, NJ: Princeton college Press, 1985. R. L. Foote. Geometry of the Prytz planimeter. Rep. Math. Phys. 42(1–2) (1998), pp. 249–271. 184 BIBLIOGRAPHY [GF] I. M. Gelfand and S. V. Fomin. Calculus of diversifications. Englewood Cliffs, NJ: Prentice-Hall, 1963. H. Hofer and E. Zehnder. Symplectic Invariants and Hamiltonian Dynamics. Birkhäuser complicated Texts/Basler Lehrbucher. Basel: Birkhäuser Verlag, 1994. B. Yu. Kogan. The purposes of Mechanics to Geometry. Chicago: college of Chicago Press, 1974. M. Levi. minimum perimeter triangles. Am. Math. per 30 days 109 (2002), pp. 890–899. M. Levi. A “bicycle wheel” facts of the Gauss-Bonnet theorem, twin cones and a few mechanical manifestations of the Berry section. Expo. Math. 12 (1994), pp. 145–164. Yu. I. Lyubich and L. A. Shor. The Kinematic strategy in Geometrical difficulties, trans. V. Shokurov. Moscow: Mir Publishers, 1980. M. Levi and W. Weckesser. Non-holonomic results in averaging. Erg. Th. & Dynam. Sys. 22 (2002), pp. 1497–1506. J. Milnor. Morse idea. Annals of arithmetic reviews, No. fifty one. Princeton, NJ: Princeton collage Press, 1963. R. Nevanlinna and V. Paatero. advent to complicated research. windfall, RI: AMS Chelsea Publishing, 2007. G. Polya. arithmetic and believable Reasoning, vol. 1. Princeton, NJ: Princeton collage Press, 1990. M. R. Spiegel. complicated Variables. Schaum’s define sequence. ny: McGraw-Hill, 1968. J. Stewart. Calculus: suggestions and Contexts. Pacific Grove, CA: Brooks/Cole, 2001. A. E. Taylor. a geometrical theorem and its purposes to biorthogonal platforms. Bull. Am. Math. Soc. fifty three (1947), pp. 614–616. T. F. Tokieda. Mechanical principles in geometry. Am. Math. per month one hundred and five (8) (1998), pp. 697–703. L. F. Toth. Lagerungen in der Ebene auf der Kugel und im Raum. Berlin: Springer-Verlag, 1953. V. A. Uspenski. a few purposes of Mechanics to arithmetic. big apple: Pergamon Press, 1961.

Rated 4.29 of 5 – based on 13 votes