Search results
Results from the WOW.Com Content Network
With the Cartesian equation it is easier to check whether a point lies on the circle or not. With the parametric version it is easier to obtain points on a plot. In some contexts, parametric equations involving only rational functions (that is fractions of two polynomials) are preferred, if they exist.
Volcano plot showing metabolomic data. The red arrows indicate points-of-interest that display both large magnitude fold-changes (x axis) and high statistical significance (-log 10 of p value, y axis). The dashed red line shows where p = 0.05 with points above the line having p < 0.05 and points below the line having p > 0.05.
The statements above presume the knowledge of the axis direction of the parabola, in order to construct the points ,. The following property determines the points Q 1 , Q 2 {\displaystyle Q_{1},Q_{2}} by two given points and their tangents only, and the result is that the line Q 1 Q 2 {\displaystyle Q_{1}Q_{2}} is parallel to the axis of the ...
Another simple Lissajous figure is the parabola ( b / a = 2, δ = π / 4 ). Again a small shift of one frequency from the ratio 2 will result in the trace not closing but performing multiple loops successively shifted only closing if the ratio is rational as before. A complex dense pattern may form see below.
The green path in this image is an example of a parabolic trajectory. A parabolic trajectory is depicted in the bottom-left quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the parabolic trajectory is shown in red.
At umbilic points, both principal curvatures are equal and every tangent vector can be considered a principal direction. These typically occur in isolated points. At hyperbolic points, the principal curvatures have opposite signs, and the surface will be locally saddle shaped. At parabolic points, one of the principal curvatures is zero ...
where for every direction in the base space, S n, the fiber over it in the total space, SO(n + 1), is a copy of the fiber space, SO(n), namely the rotations that keep that direction fixed. Thus we can build an n × n rotation matrix by starting with a 2 × 2 matrix, aiming its fixed axis on S 2 (the ordinary sphere in three-dimensional space ...
In this position, the hyperbolic paraboloid opens downward along the x-axis and upward along the y-axis (that is, the parabola in the plane x = 0 opens upward and the parabola in the plane y = 0 opens downward). Any paraboloid (elliptic or hyperbolic) is a translation surface, as it can be generated by a moving parabola directed by a second ...