This space is closed and bounded and so compact by the Heine Borel theorem, but has similar properties to the topologist's sine curve & mdash; it too is connected but neither locally connected nor path-connected.
22.
Second question, does that change if instead of dx / dt being constant ds / dt is constant where s measures the distance along the sine curve ? talk ) 18 : 27, 26 June 2015 ( UTC)
23.
As mentioned in the introduction above, leading or lagging current represents a time shift between the current and voltage sine curves, which is represented by the angle by which the curve is ahead or behind of where it would be initially.
24.
As far as elliptic functions being complex . . . well I just thought you were looking for any mathematical functions that could approximate sine curves, and from a mathematical standpoint, the elliptic functions are far more simple than square waves, among periodic functions.
25.
I can't believe that the topologists sine curve could be a topological group-but I can't see any obvious reason why it is impossible to define a group structure on the points of the curve . . . Madmath789 21 : 47, 11 October 2006 ( UTC)
26.
Since a bezier spline can't correctly define a perfect sine function ( unless you use a indefinite number of control points ), then what's the best aproximation I can get of a sine curve ( [ 0, 2 & pi; ] ) using a bezier spline?
27.
A graph of measured radial velocity versus time will give a characteristic curve ( sine curve in the case of a circular orbit ), and the amplitude of the curve will allow the minimum mass of the planet to be calculated using the binary mass function.
28.
If I plotted the temperature of Sydney over one year on a graph with temperature as the Y axis and time ( in days ) as the X axis, I would get a sort of sine curve ( due to higher temperatures in summer and lower ones in winter ).
29.
When a conrod bigend rotates, its up-down movement ( as seen from the side of an inline 4 cylinder engine ) can be plotted on a graph ( with the position on the stroke on Y-axis, rotational position of the crank in degrees on X-axis ) with a clean Sine curve, and so this is called the sinusoidal movement.
30.
However the closure of a path connected set need not be path connected : for instance, the topologist's sine curve is the closure of the open subset " U " consisting of all points " ( x, y ) " with " x > 0 ", and " U ", being homeomorphic to an interval on the real line, is certainly path connected.
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