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A cardioid microphone exhibits an acoustic pickup pattern that, when graphed in two dimensions, resembles a cardioid (any 2d plane containing the 3d straight line of the microphone body). In three dimensions, the cardioid is shaped like an apple centred around the microphone which is the "stalk" of the apple.
The part of the Mandelbrot set connected to the main cardioid at this bifurcation point is called the p/q-limb. Computer experiments suggest that the diameter of the limb tends to zero like 1 q 2 {\displaystyle {\tfrac {1}{q^{2}}}} .
The lemniscate is symmetric to the line connecting its foci F 1 and F 2 and as well to the perpendicular bisector of the line segment F 1 F 2. The lemniscate is symmetric to the midpoint of the line segment F 1 F 2. The area enclosed by the lemniscate is a 2 = 2c 2. The lemniscate is the circle inversion of a hyperbola and vice versa.
The outer coin makes two rotations rolling once around the inner coin. The path of a single point on the edge of the moving coin is a cardioid.. The coin rotation paradox is the counter-intuitive math problem that, when one coin is rolled around the rim of another coin of equal size, the moving coin completes not one but two full rotations after going all the way around the stationary coin ...
Construction of the limaçon r = 2 + cos(π – θ) with polar coordinates' origin at (x, y) = ( 1 / 2 , 0). In geometry, a limaçon or limacon / ˈ l ɪ m ə s ɒ n /, also known as a limaçon of Pascal or Pascal's Snail, is defined as a roulette curve formed by the path of a point fixed to a circle when that circle rolls around the outside of a circle of equal radius.
Specifically, with respect to a fixed circle with center O and radius k the inverse of a point Q is the point P for which P lies on the ray OQ and OP·OQ = k 2. The inverse of the curve C is then the locus of P as Q runs over C. The point O in this construction is called the center of inversion, the circle the circle of inversion, and k the ...
the point's distance from a reference point called the pole, and; the point's direction from the pole relative to the direction of the polar axis, a ray drawn from the pole. The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth. [1]
The midpoint of the line segment joining the foci is called the center of the hyperbola. [6] The line through the foci is called the major axis. It contains the vertices,, which have distance to the center. The distance of the foci to the center is called the focal distance or linear eccentricity.