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The prime symbol , double prime symbol , triple prime symbol , and quadruple prime symbol are used to designate units and for other purposes in mathematics, science, linguistics and music. Although the characters differ little in appearance from those of the apostrophe and single and double quotation marks, the uses of the prime symbol are quite different. While an apostrophe is now often used in place of the prime, and a double quote in place of the double prime (due to the lack of prime symbols on everyday writing keyboards), such substitutions are not considered appropriate in formal materials or in typesetting. Designation of units The prime symbol is commonly used to represent feet (ft), and the double prime is used to represent inches (in). The triple prime , as used in watchmaking, represents a ( of a "French" inch, or '' pouce'', about ). Primes are also used for angles. The prime symbol is used for arcminutes ( of a degree), and the double prime for arcseconds ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
4′33″
''4′33″'' is a Modernism (music), modernist composition by American experimental music, experimental composer John Cage. It was composed in 1952 for any instrument or combination of instruments; the score instructs performers not to play their instruments throughout the three movements. It is divided into three movements, lasting 30 seconds, two minutes and 23 seconds, and one minute and 40 seconds, respectively, although Cage later stated that the movements' durations can be determined by the musician. As suggested by the title, the composition lasts four minutes and 33 seconds. It is marked by silence except for ambient sound, which is intended to contribute to the performance. # ''4′33″'' was conceived around 1947–48, while Cage was working on the piano cycle ''Sonatas and Interludes.'' Many prior musical pieces were largely composed of silence, and silence played a notable role in his prior work, including ''Sonatas and Interludes''. His studies on Zen Buddhism du ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arcsecond
A minute of arc, arcminute (abbreviated as arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of a degree. Since one degree is of a turn, or complete rotation, one arcminute is of a turn. The nautical mile (nmi) was originally defined as the arc length of a minute of latitude on a spherical Earth, so the actual Earth's circumference is very near . A minute of arc is of a radian. A second of arc, arcsecond (abbreviated as arcsec), or arc second, denoted by the symbol , is a unit of angular measurement equal to of a minute of arc, of a degree, of a turn, and (about ) of a radian. These units originated in Babylonian astronomy as sexagesimal (base 60) subdivisions of the degree; they are used in fields that involve very small angles, such as astronomy, optometry, ophthalmology, optics, navigation, land surveying, and marksmanship. To express even smaller angles, standard SI prefixes can be employed; the milliarcse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Cage
John Milton Cage Jr. (September 5, 1912 – August 12, 1992) was an American composer and music theorist. A pioneer of indeterminacy in music, electroacoustic music, and Extended technique, non-standard use of musical instruments, Cage was one of the leading figures of the post-war avant-garde. Critics have lauded him as one of the most influential composers of the 20th century. He was also instrumental in the development of modern dance, mostly through his association with choreographer Merce Cunningham, who was also Cage's romantic partner for most of their lives. Cage's teachers included Henry Cowell (1933) and Arnold Schoenberg (1933–35), both known for their radical innovations in music, but Cage's major influences lay in various Eastern world, East and South Asia, South Asian cultures. Through his studies of Indian philosophy and Zen Buddhism in the late 1940s, Cage came to the idea of Aleatoric music, aleatoric or Indeterminism#Philosophy, chance-controlled music, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pouce
The traditional French units of measurement prior to metrication were established under Charlemagne during the Carolingian Renaissance. Based on contemporary Byzantine and ancient Roman measures, the system established some consistency across his empire but, after his death, the empire fragmented and subsequent rulers and various localities introduced their own variants. Some of Charlemagne's units, such as the king's foot () remained virtually unchanged for about a thousand years, while others important to commercesuch as the French ell () used for cloth and the French pound () used for amountsvaried dramatically from locality to locality. By the 18th century, the number of units of measure had grown to the extent that it was almost impossible to keep track of them and one of the major legacies of the French Revolution was the dramatic rationalization of measures as the new metric system. The change was extremely unpopular, however, and a metricized version of the traditional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apostrophe
The apostrophe (, ) is a punctuation mark, and sometimes a diacritical mark, in languages that use the Latin alphabet and some other alphabets. In English, the apostrophe is used for two basic purposes: * The marking of the omission of one or more letters, e.g. the contraction (grammar), contraction of "do not" to "don't" * The marking of Possessive, possessive case of nouns (as in "the eagle's feathers", "in one month's time", "the twins' coats") It is also used in a few exceptional cases for the #Use in forming some plurals, marking of plurals, e.g. "p's and q's" or Oakland A's. The same mark is used as a single quotation mark. It is also substituted informally for other marks for example instead of the prime symbol to indicate the units of foot (unit), foot or minutes of arc. The word ''apostrophe'' comes from the Ancient Greek language, Greek (hē apóstrophos [prosōidía], '[the accent of] turning away or elision'), through Latin language, Latin and French language, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quotation Mark
Quotation marks are punctuation marks used in pairs in various writing systems to identify direct speech, a quotation, or a phrase. The pair consists of an opening quotation mark and a closing quotation mark, which may or may not be the same glyph. Quotation marks have a variety of forms in different languages and in different media. History The single quotation mark is traced to Ancient Greek practice, adopted and adapted by monastic copyists. Isidore of Seville, in his seventh century encyclopedia, , described their use of the Greek ''diplé'' (a Angle bracket, chevron): The double quotation mark derives from a marginal notation used in fifteenth-century manuscript annotations to indicate a passage of particular importance (not necessarily a quotation); the notation was placed in the outside margin of the page and was repeated alongside each line of the passage. In his edition of the works of Aristotle, which appeared in 1483 or 1484, the Milanese Renaissance humanis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Third (angle)
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane (mathematics), plane angle in which one Turn (geometry), full rotation is 360 degrees. It is not an SI unit—the SI unit of angular measure is the radian—but it is mentioned in the SI Brochure, SI brochure as an Non-SI units mentioned in the SI, accepted unit. Because a full rotation equals 2 radians, one degree is equivalent to radians. History The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, which follows through the ecliptic path over the course of the year, seems to advance in its path by approximately one degree each day. Some ancient calendars, such as the Iranian calendar, Persian calendar and the Babylonian calendar, used 360 days for a year. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angle
In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle. More generally angles are also formed wherever two lines, rays or line segments come together, such as at the corners of triangles and other polygons. An angle can be considered as the region of the plane bounded by the sides. Angles can also be formed by the intersection of two planes or by two intersecting curves, in which case the rays lying tangent to each curve at the point of intersection define the angle. The term ''angle'' is also used for the size, magnitude (mathematics), magnitude or Physical quantity, quantity of these types of geometric figures and in this context an a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourth (angle)
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees. It is not an SI unit—the SI unit of angular measure is the radian—but it is mentioned in the SI brochure as an accepted unit. Because a full rotation equals 2 radians, one degree is equivalent to radians. History The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, which follows through the ecliptic path over the course of the year, seems to advance in its path by approximately one degree each day. Some ancient calendars, such as the Persian calendar and the Babylonian calendar, used 360 days for a year. The use of a calendar with 360 days may be related to the use of sexagesimal numbers. Another ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foot (length)
The foot (standard symbol: ft) is a unit of length in the British imperial and United States customary systems of measurement. The prime symbol, , is commonly used to represent the foot. In both customary and imperial units, one foot comprises 12 inches, and one yard comprises three feet. Since an international agreement in 1959, the foot is defined as equal to exactly 0.3048 meters. Historically, the "foot" was a part of many local systems of units, including the Greek, Roman, Chinese, French, and English systems. It varied in length from country to country, from city to city, and sometimes from trade to trade. Its length was usually between 250 mm and 335 mm and was generally, but not always, subdivided into 12 inches or 16 digits. The United States is the only industrialized country that uses the (international) foot in preference to the meter in its commercial, engineering, and standards activities. The foot is legally recognized in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
