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Let f(x) be a real-valued function of a real variable, then f is even if the following equation holds for all x and -x in the domain of f: = Geometrically speaking, the graph face of an even function is symmetric with respect to the y-axis, meaning that its graph remains unchanged after reflection about the y-axis
The origin of a Cartesian coordinate system. In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space. In physical problems, the choice of origin is often arbitrary, meaning any choice of origin will ultimately give the same ...
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 ...
For a human observer, some symmetry types are more salient than others, in particular the most salient is a reflection with a vertical axis, like that present in the human face. Ernst Mach made this observation in his book "The analysis of sensations" (1897), [ 27 ] and this implies that perception of symmetry is not a general response to all ...
The standard orientation, where the xy-plane is horizontal and the z-axis points up (and the x- and the y-axis form a positively oriented two-dimensional coordinate system in the xy-plane if observed from above the xy-plane) is called right-handed or positive. 3D Cartesian coordinate handedness. The name derives from the right-hand rule.
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 ...
In Newton's theory of mechanics, given two bodies, each with mass m, starting at the origin and moving along the x-axis in opposite directions, one with speed v 1 and the other with speed v 2 the total kinetic energy of the system (as calculated from an observer at the origin) is 1 / 2 m(v 1 2 + v 2 2) and remains the same if the ...
Suppose a system of Cartesian coordinates is used such that the vertex of the parabola is at the origin, and the axis of symmetry is the y axis. The parabola opens upward. It is shown elsewhere in this article that the equation of the parabola is 4fy = x 2, where f is the focal length. At the positive x end of the chord, x = c / 2 and y ...