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A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called it an "eternal line" ("ewige Linie").
The spiral is started with an isosceles right triangle, with each leg having unit length.Another right triangle (which is the only automedian right triangle) is formed, with one leg being the hypotenuse of the prior right triangle (with length the square root of 2) and the other leg having length of 1; the length of the hypotenuse of this second right triangle is the square root of 3.
For <, spiral-ring pattern; =, regular spiral; >, loose spiral. R is the distance of spiral starting point (0, R) to the center. R is the distance of spiral starting point (0, R) to the center. The calculated x and y have to be rotated backward by ( − θ {\displaystyle -\theta } ) for plotting.
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 trace (purple) of the tangents of a conical spiral with a hyperbolic spiral as floor plan. The black line is the asymptote of the hyperbolic spiral. The collection of intersection points of the tangents of a conical spiral with the --plane (plane through the cone's apex) is called its tangent trace.
Golden spirals are self-similar. The shape is infinitely repeated when magnified. In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. [1] That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.
If you've been having trouble with any of the connections or words in Monday's puzzle, you're not alone and these hints should definitely help you out. Plus, I'll reveal the answers further down ...
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 ...