A theorem of Apollonius states that for a line segment tangent to the hyperbola at a point and intersecting the asymptotes at points and , then is constant, and right figure above; Wells The arguments supplied to functions in MeshFunctions and RegionFunction are x , y , f. Collection of teaching and learning tools built by Wolfram education experts: Weird Mathematica Plot behavior Ask Question. Sign up using Email and Password. The hyperbola can be constructed by connecting the free end of a rigid bar , where is a focus , and the other focus with a string.
The Double Cone Phil Ramsden.
Then it uses an adaptive algorithm to subdivide at most MaxRecursion times to generate smooth contours.
ContourPlot—Wolfram Language Documentation
Hilbert and Cohn-Vossenp. Unlimited random practice problems and answers with built-in Step-by-step solutions.
The corners of the quadrilaterals have coordinates corresponding to the values of the f i hypergola t and u take on values in a regular grid. In addition, the locus of the apex of a cone containing that hyperbola is the original ellipse.
Please try again later. The locus of the apex of a variable cone containing an ellipse fixed in three-space is a hyperbola through the foci of the ellipse. ContourPlot has the same options as Graphicswith the following additions and changes: Sign up or hypergola in Sign up using Google.
Circle, Ellipse, Hyperbola, and Astroid
After reading Mathematica’s explanation about Plot – it says that it generates more points if the function changes fast. At positions where f does not evaluate to a real matnematica, holes are left so that the background to the contour plot shows through. Please complete this field. Placed [ lspec… ].
Here the and coordinates for the quadrilaterals are given simply by t and u. This shows the same surface as before, but with the coordinates distorted by a quadratic transformation.
The answer is that Mathematica has decided that the graph will look good that way. As the bar is rotated about and is kept taut against the bar i.
The two-center bipolar coordinates equation with origin at a focus is. In some cases, it may be more efficient to use Evaluate to evaluate the f i and g i symbolically before specific numerical values are assigned to x and y. You may find value in DiscretePlot: To check your results, you should try increasing the settings for PlotPoints and Gyperbola.
The arc lengthcurvatureand tangential angle for the above parametrization are. I think that what you are seeing is an artefact common to most computer-based hypsrbola Ajasja Ajasja 1 12 Euclid and Aristaeus wrote about the general hyperbola, but only studied one branch of it. The eccentricity of the hyperbola which always satisfies is then defined as.
ContourPlot has attribute HoldAlland evaluates the f i and g i only after assigning specific numerical values to x and y. In each case, you can think of the surfaces as being formed by “distorting” or “rolling up” the – coordinate grid in a certain way.
MathGroup Archive: May 
You can also use the Wolfram Language to make parametric plots. ContourPlot treats the variables x and y as local, effectively using Block. HyperGroups HyperGroups 4, 13