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The axis of symmetry of a two-dimensional figure is a line such that, if a perpendicular is constructed, any two points lying on the perpendicular at equal distances from the axis of symmetry are identical. Another way to think about it is that if the shape were to be folded in half over the axis, the two halves would be identical as mirror ...
The pencil of conic sections with the x axis as axis of symmetry, one vertex at the origin (0, 0) and the same semi-latus rectum can be represented by the equation = + (),, with the eccentricity. For e = 0 {\displaystyle e=0} the conic is a circle (osculating circle of the pencil),
Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis. [1] For example, a baseball bat without trademark or other design, or a plain white tea saucer , looks the same if it is rotated by any angle about the line passing lengthwise through its center, so it is axially ...
Knowledge of such symmetries may help solve the differential equation. A Line symmetry of a system of differential equations is a continuous symmetry of the system of differential equations. Knowledge of a Line symmetry can be used to simplify an ordinary differential equation through reduction of order. [8]
Determine the symmetry of the curve. If the exponent of x is always even in the equation of the curve then the y-axis is an axis of symmetry for the curve. Similarly, if the exponent of y is always even in the equation of the curve then the x-axis is an axis of symmetry for the curve.
The dimensions of a symmetrical paraboloidal dish are related by the equation =, where F is the focal length, D is the depth of the dish (measured along the axis of symmetry from the vertex to the plane of the rim), and R is the radius of the rim. They must all be in the same unit of length. If two of these three lengths are known, this ...
If the discriminant is negative, then the parabola opens in the opposite direction, never crossing the -axis, and the equation has no real roots; in this case the two complex-valued roots will be complex conjugates whose real part is the value of the axis of symmetry.
In crystallography, a screw axis symmetry is a combination of rotation about an axis and a translation parallel to that axis which leaves a crystal unchanged. If φ = 360° / n for some positive integer n , then screw axis symmetry implies translational symmetry with a translation vector which is n times that of the screw displacement.