Spiral in the context of "Archimedes"

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 Archimedes). It is the locus corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity. Equivalently, in polar coordinates (r, θ) it can be described by the equation$${\displaystyle r=b\cdot \theta }$$with real number b. Changing the parameter b controls the distance between loops.

From the above equation, it can thus be stated: position of the particle from point of start is proportional to angle θ as time elapses.

Spiral galaxies form a class of galaxy originally described by Edwin Hubble in his 1936 work The Realm of the Nebulae and, as such, form part of the Hubble sequence. Most spiral galaxies consist of a flat, rotating disk containing stars, gas and dust, and a central concentration of stars known as the bulge. These are often surrounded by a much fainter halo of stars, many of which reside in globular clusters.

Spiral galaxies are named by their spiral structures that extend from the center into the galactic disk. The spiral arms are sites of ongoing star formation and are brighter than the surrounding disc because of the young, hot OB stars that inhabit them.

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"). More than a century later, the curve was discussed by Descartes (1638), and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, "the marvelous spiral".

The logarithmic spiral is distinct from the Archimedean spiral in that the distances between the turnings of a logarithmic spiral increase in a geometric progression, whereas for an Archimedean spiral these distances are constant.

A whorl (/wɜːrl/ or /wɔːrl/) is an individual circle, oval, volution or equivalent in a whorled pattern, which consists of a spiral or multiple concentric objects (including circles, ovals and arcs).

In geometry, a spirangle is a spiral polygonal chain. Spirangles are similar to spirals in that they expand from a center point as they grow larger, but they are made out of straight line segments, instead of curves. Spirangle vectographs are used in vision therapy to promote stereopsis and help resolve problems with hand–eye coordination.

Spiral arms are a defining feature of spiral galaxies. They manifest as spiral-shaped regions of enhanced brightness within the galactic disc. Typically, spiral galaxies exhibit two or more spiral arms. The collective configuration of these arms is referred to as the spiral pattern or spiral structure of the galaxy.

The appearance of spiral arms is quite diverse. Grand design spiral galaxies exhibit a symmetrical and distinct pattern, comprising two spiral arms that extend throughout the galaxy. In contrast, the spiral structure of flocculent galaxies comprises numerous small fragments of arms that are not connected to each other. The appearance of spiral arms varies across the electromagnetic spectrum.

Tie-dye is a term used to describe a number of resist dyeing techniques and the resulting dyed products of these processes. The process of tie-dye typically consists of folding, twisting, pleating, or crumpling fabric or a garment, before binding with string or rubber bands, followed by the application of dye or dyes. The manipulations of the fabric before the application of dye are called resists, as they partially or completely prevent ('resist') the applied dye from coloring the fabric. More sophisticated tie-dye may involve additional steps, including an initial application of dye before the resist, multiple sequential dyeing and resist steps, and the use of other types of resists (stitching, stencils) and discharge.

Unlike regular resist-dyeing techniques, modern tie-dye is characterized by the use of bright, saturated primary colors and bold patterns. These patterns, including the spiral, mandala, and peace sign, and the use of multiple bold colors, have become widely recognized as symbols of the 1960s and 1970s counterculture movement. However tie-dye wasn't as pronounced in fashion even among the counterculture as it would be in later years and the present day. The vast majority of tie-dye garments and objects produced for wholesale distribution use these designs, with many being mass-produced.