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An example of how geometry does not accurately represent the universe comes in the Banach-Tarski paradox which have consqequences such as that a marble can be cut up into finitely many pieces and reassembled into a planet, or a telephone could be cut up and reassembled as a water lily. These transformations are not possible with real objects made of atoms, but it is possible with their geometric shapes.

It is common to use idealized models in physics to simplify things. Massless ropes, point particles, ideal gas and particle in a box are among the many simplified models used in physics.

Throughout history, more and more accurate mathematical models have been developed. Newton's laws accurately describe many everyday fenomena, but at certain limits relativity theory and quantum mechanics must be used, even these do not apply to all situations and need further refinement. It is possible to obtain the less accurate models in approproate limits, for example relativistic mechanics reduce to Newtonian mechanics when the speed much less than the speed of light. Quantum mechanics reduce to classical physics when the quantum numbers are high. If we say that a tennisball is a particle and calculate its de Broglie wavelength is will turn out to be insignificantly small so it is seen that classical physics is better to use than quantum mechanics in this case.

The laws of physics are represented with simple equations such as Newton's laws, Maxwells equation and the Schrödinger equation. These laws are such as a basis for making mathematical models of real situations. Many real situations are very complex and thus modeled approximate on a computer, a model that is computationally feasible to compute is made from the basic laws or from approximate models made from the basic laws. For example molecules can be modeled by molecular orbital models that are approximate solutions to the Schrödinger equation. In engineeringEngineering is the application of science to the needs of humanity. This is accomplished through knowledge, mathematics, and practical experience applied to the design of useful objects or processes. Professional practitioners of engineering are called en, physics models are often made by mathematical methods such as finite element analysisFinite element analysis (FEA) is the application of the finite element method (FEM) to the analysis of static or dynamic physical objects and systems. In it, the object or system is represented by a geometrically similar model consisting of multiple, link.