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These patternsrecur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracksand stripes.[1] Early Greek philosophersstudied pattern, with Plato, Pythagorasand Empedoclesattempting to explain order in nature.
e. In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical objects as a straightedge, a taut string, or a ray of light. Lines are spaces of dimension one, which may be embedded in spaces of dimension two, three, or higher.
Any cylindrical map projection can be used as the basis for a spherical spiral: draw a straight line on the map and find its inverse projection on the sphere, a kind of spherical curve. One of the most basic families of spherical spirals is the Clelia curves, which project to straight lines on an equirectangular projection.
If a straight line falls on two straight lines in such a manner that the interior angles on the same side are together less than two right angles, then the straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. Other mathematicians have devised simpler forms of this property.
[clarification needed] Straight lines are also strongly influenced by tone, color, and repetition concerning the rest of the image. Compared to straight lines, curves provide a greater dynamic influence in a picture. They are also generally more aesthetically pleasing, as the viewer associates them with nature and softness.
Curve. A parabola, one of the simplest curves, after (straight) lines. In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago ...
A section of the Mandelbrot set following a logarithmic spiral. 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"). [ 1 ][ 2 ] More than a century later, the ...
A contour line (also isoline, isopleth, isoquant or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. [1][2] It is a plane section of the three-dimensional graph of the function parallel to the -plane. More generally, a contour line for a function of ...