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The curve that has a catacaustic forming a circle. Approximates the Archimedean spiral. [11] Atomic spiral: 2002 = This spiral has two asymptotes; one is the circle of radius 1 and the other is the line = [12] Galactic spiral: 2019
A Doyle spiral of type (8,16) printed in 1911 in Popular Science as an illustration of phyllotaxis. [1] One of its spiral arms is shaded. In the mathematics of circle packing, a Doyle spiral is a pattern of non-crossing circles in the plane in which each circle is surrounded by a ring of six tangent circles.
An Archimedean spiral is, for example, generated while coiling a carpet. [5] A hyperbolic spiral appears as image of a helix with a special central projection (see diagram). A hyperbolic spiral is some times called reciproke spiral, because it is the image of an Archimedean spiral with a circle-inversion (see below). [6]
The Archimedean spiral (also known as Archimedes' spiral, the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes. The term Archimedean spiral is sometimes used to refer to the more general class of spirals of this type (see below), in contrast to Archimedes' spiral (the specific arithmetic spiral of ...
The representation of the Fermat spiral in polar coordinates (r, φ) is given by the equation = for φ ≥ 0. The parameter is a scaling factor affecting the size of the spiral but not its shape. The two choices of sign give the two branches of the spiral, which meet smoothly at the origin.
The Archimedean spiral is shown in red, and corresponds to the values 0 ≤ θ ≤ 8π of the angle parameter, while the Involute of the circle is shown in black, and corresponds to the values 0 ≤ θ ≤ 17π/2 of the angle parameter. The x-axis extends from -25 to +28 and the y-axis from -26.4 to +23.4, and there are tick marks at -20, -10 ...
The golden spiral is a logarithmic spiral that grows outward by a factor of the golden ratio for every 90 degrees of rotation (pitch angle about 17.03239 degrees). It can be approximated by a "Fibonacci spiral", made of a sequence of quarter circles with radii proportional to Fibonacci numbers.
Animation depicting evolution of a Cornu spiral with the tangential circle with the same radius of curvature as at its tip, also known as an osculating circle.. To travel along a circular path, an object needs to be subject to a centripetal acceleration (for example: the Moon circles around the Earth because of gravity; a car turns its front wheels inward to generate a centripetal force).
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