Editing Hyperbolic coordinates (section)

==Applications in physical science==
Fundamental physical variables are sometimes related by equations of the form ''k'' = ''x y''. For instance, ''V'' = ''I R'' ([[Ohm's law]]), ''P'' = ''V I'' ([[electrical power]]), ''P V'' = ''k T'' ([[ideal gas law]]), and ''f'' λ = ''v'' (relation of [[wavelength]], [[frequency]], and velocity in the wave medium). When the ''k'' is constant, the other variables lie on a hyperbola, which is a [[horocycle]] in the appropriate ''Q'' quadrant.

For example, in [[thermodynamics]] the [[isothermal process]] explicitly follows the hyperbolic path and [[work (thermodynamics)|work]] can be interpreted as a hyperbolic angle change. Similarly, a given mass ''M'' of gas with changing volume will have variable density &delta; = ''M / V'', and the ideal gas law may be written ''P = k T'' &delta; so that an [[isobaric process]] traces  a hyperbola in the quadrant of absolute temperature and gas density.

For hyperbolic coordinates in the [[theory of relativity]] see the [[#History|History]] section.