*PM : the topologist's sine curve has the fixed point property, id = 9274 new !-- WP guess : the topologist's sine curve has the fixed point property-- Status:
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:No, this is not the best basis for approximating sine curves . the best basis is obviously the sine curves themselves, wherein every Fourier series has only 1 term.
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:The article on the topologist's sine curve might be tangentially ( no pun intended ) relevant here . talk ) 14 : 54, 14 June 2010 ( UTC)
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*PM : the topologist's sine curve has the fixed point property, id = 9274 new !-- WP guess : the topologist's sine curve has the fixed point property-- Status:
15.
Other formulas may be specially created to solve a particular problem; for example, using the equation of a sine curve to model the movement of the tides in a bay.
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The converse is not always true : examples of connected spaces that are not path-connected include the extended long line " L " * and the " topologist's sine curve ".
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The graph to the right illustrates the sine curve using Doppler spectroscopy to observe the radial velocity of an imaginary star which is being orbited by a planet in a circular orbit.
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** The cubic polynomial can be a good approximation of the sine curve in the [ 0, pi / 2 ] interval, but I couldn't find the ideal coefficients for this either.
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Moreover, the path components of the topologist's sine curve " C " are " U ", which is open but not closed, and C \ setminus U, which is closed but not open.
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The graph of the equation of time is closely approximated by the sum of two sine curves, one with a period of a year and one with a period of half a year.
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