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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 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.
Archimedes of Syracuse [a] (/ ˌ ɑːr k ɪ ˈ m iː d iː z / AR-kim-EE-deez; [2] c. 287 – c. 212 BC) was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. [3] Although few details of his life are known, he is considered one of the leading scientists in classical antiquity.
More precisely, this example works to explain a kind of math called chaos theory, which looks at how small changes made to a system’s initial conditions—like the extra gust of wind from a ...
The example shows trisection of any angle θ > 3π / 4 by a ruler with length equal to the radius of the circle, giving trisected angle φ = θ / 3 . Angle trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics .
For example, a linearly ordered group that is Archimedean is an Archimedean group. This can be made precise in various contexts with slightly different formulations. For example, in the context of ordered fields , one has the axiom of Archimedes which formulates this property, where the field of real numbers is Archimedean, but that of rational ...
An Archimedean point (Latin: Punctum Archimedis) is a hypothetical viewpoint from which certain objective truths can perfectly be perceived (also known as a God's-eye view) or a reliable starting point from which one may reason.
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]