Rose (mathematics)
In mathematics, a rose or rhodonea curve is a sinusoid plotted in polar coordinates.
General overview
Up to similarity, these curves can all be expressed by a polar equation of the form
or, alternatively, as a pair of Cartesian parametric equations of the form
If k is an integer, the curve will be rose-shaped with
Where k is even, the entire graph of the rose will be traced out exactly once when the value of theta,θ changes from 0 to 2π. When k is odd, this will happen on the interval between 0 and π. (More generally, this will happen on any interval of length 2π for k even, and π for k odd.)
If k is a half-integer (e.g. 1/2, 3/2, 5/2), the curve will be rose-shaped with 4k petals.
If k can be expressed as n±1/6, where n is a nonzero integer, the curve will be rose-shaped with 12k petals.
If k can be expressed as n/3, where n is an integer not divisible by 3, the curve will be rose-shaped with n petals if n is odd and 2n petals if n is even.
Rose
A rose (/ˈroʊz/) is a woody perennial flowering plant of the genus Rosa, in the family Rosaceae. There are over 100 species and thousands of cultivars. They form a group of plants that can be erect shrubs, climbing or trailing with stems that are often armed with sharp prickles. Flowers vary in size and shape and are usually large and showy, in colours ranging from white through yellows and reds. Most species are native to Asia, with smaller numbers native to Europe, North America, and northwest Africa. Species, cultivars and hybrids are all widely grown for their beauty and often are fragrant. Rose plants range in size from compact, miniature roses, to climbers that can reach seven meters in height. Different species hybridize easily, and this has been used in the development of the wide range of garden roses.
The name rose comes from French, itself from Latin rosa, which was perhaps borrowed from Oscan, from Greek ρόδον rhódon (Aeolic βρόδον wródon), itself borrowed from Old Persian wrd- (wurdi), related to Avestan varəδa, Sogdian ward, Parthian wâr.
Rose (symbolism)
Roses have been long used as symbols in a number of societies. Roses are ancient symbols of love and beauty. "Rose" means pink or red in a variety of languages (such as the Romance languages and Greek).
The Classical Era
The rose was sacred to a number of goddesses including Isis, whose rose appears in the late classical allegorical novel The Golden Ass as "the sweet Rose of reason and virtue" that saves the hero from his bewitched life in the form of a donkey. The ancient Greeks and Romans identified the rose with the goddess of love, Aphrodite (Greek name) and Venus (Roman name).
In Rome a wild rose would be placed on the door of a room where secret or confidential matters were discussed. The phrase sub rosa, or "under the rose", means to keep a secret — derived from this ancient Roman practice.
Islam and Sufism
The cultivation of geometrical gardens, in which the rose has often held pride of place, has a long history in Iran and surrounding lands. In the lyric ghazal, it is the beauty of the rose that provokes the longing song of the nightingale - an image prominent, for example, in the poems of Hafez.
Rosé
A rosé (from French rosé; also known as rosado in Portugal and Spanish-speaking countries and rosato in Italy) is a type of wine that incorporates some of the color from the grape skins, but not enough to qualify it as a red wine. It may be the oldest known type of wine, as it is the most straightforward to make with the skin contact method. The pink color can range from a pale "onion"-skin orange to a vivid near-purple, depending on the varietals used and winemaking techniques. There are three major ways to produce rosé wine: skin contact, saignée and blending. Rosé wines can be made still, semi-sparkling or sparkling and with a wide range of sweetness levels from bone-dry Provençal rosé to sweet White Zinfandels and blushes. Rosé wines are made from a wide variety of grapes and can be found all around the globe.
When rosé wine is the primary product, it is produced with the skin contact method. Black-skinned grapes are crushed and the skins are allowed to remain in contact with the juice for a short period, typically one to three days. The must is then pressed, and the skins are discarded rather than left in contact throughout fermentation (as with red wine making). The longer that the skins are left in contact with the juice, the more intense the color of the final wine.
Mathematics
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers),structure,space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.
Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics (producer)
Mathematics, also known as Allah Mathematics, (born: Ronald Maurice Bean) is a hip hop producer and DJ for the Wu-Tang Clan and its solo and affiliate projects.
Biography
Born and raised in Jamaica, Queens, New York, Mathematics was introduced to hip hop by his brother who used to bring home recordings of the genre's pioneers like Grandmaster Flash & The Furious Five, Treacherous Three and Cold Crush Brothers. He began his career in 1987 DJing block parties and park jams in Baisley Projects, going by the name Supreme Cut Master. In 1988, he became the full-time DJ for experienced rapper Victor C, doing countless shows in clubs and colleges in New York City.
In 1990, Mathematics linked up with GZA/Genius; he soon became one of the Wu-Tang Clan's founding members, but at the time GZA was struggling to build a career on the Cold Chillin' label. This partnership earned Mathematics a spot on his first official tour, The Cold Chillin Blizzard Tour (with popular acts such as Biz Markie, Big Daddy Kane, Kool G. Rap & DJ Polo and Marley Marl).
Mathematics (Cherry Ghost song)
"Mathematics" is the debut single from Manchester band Cherry Ghost. It was released as a digital download on March 26, 2007 and on CD and 7" vinyl on April 9, 2007. It went to #57 on the UK singles chart. "Mathematics" acquired the title "song of the week" on BBC Radio 2 in early 2007, and Zane Lowe of BBC Radio 1 declared the song "the hottest record in the world" in February 2007. Jimi Goodwin of Doves plays bass and drums on the single. The B-side "Junebug" is a Sparklehorse cover.
The song is also coincidentally appropriate for the band, as songwriter Simon Aldred has a B.Sc. in Pure Mathematics from the University of Leeds.
Two music videos were made for the song. The first, a self-produced video featuring a man in a bird costume, was posted in late 2006. The second, featuring Simon Aldred's family home movies, appeared on Heavenly Records' website in early 2008.
Track listings
All songs written by Simon Aldred except where noted.
Promo CD (HVN167CDRP):
