An atlas is a collection of maps; it is typically a map of Earth or a region of Earth, but there are atlases of the other planets (and their satellites) in the Solar System. Furthermore, atlases of anatomy exist, mapping out the human body or other organisms. Atlases have traditionally been bound into book form, but today many atlases are in multimedia formats. In addition to presenting geographic features and political boundaries, many atlases often feature geopolitical, social, religious and economic statistics. They also have information about the map and places in it.
The word atlas dates from 1636, first in reference to the English translation of Atlas, sive cosmographicae meditationes de fabrica mundi (1585) by Flemish geographer Gerhardus Mercator, who might have been the first to use this word in this way. A picture of the Titan Atlas holding up the world appeared on the frontispiece of this and other early map collections.
The first work that contained systematically arranged woodcut maps of uniform size, intended to be published in a book, thus representing the first modern atlas, was De Summa totius Orbis (1524–26) by the 16th-century Italian cartographer Pietro Coppo. Nonetheless, this distinction is conventionally awarded to the Flemish cartographer Abraham Ortelius who in 1570 published the collection of maps Theatrum Orbis Terrarum.
The Atlas Computer was a joint development between the University of Manchester, Ferranti, and Plessey. The first Atlas, installed at Manchester University and officially commissioned in 1962, was one of the world's first supercomputers, considered to be the most powerful computer in the world at that time. It was said that whenever Atlas went offline half of the United Kingdom's computer capacity was lost. It was a second-generation machine, using discrete germanium transistors. Two other Atlas machines were built: one for British Petroleum and the University of London, and one for the Atlas Computer Laboratory at Chilton near Oxford.
A derivative system was built by Ferranti for Cambridge University. Called the Titan, or Atlas 2, it had a different memory organisation and ran a time-sharing operating system developed by Cambridge University Computer Laboratory. Two further Atlas 2s were delivered: one to the CAD Centre in Cambridge (later called CADCentre, then AVEVA), and the other to the Atomic Weapons Research Establishment (AWRE), Aldermaston.
In mathematics, particularly topology, one describes a manifold using an atlas. An atlas consists of individual charts that, roughly speaking, describe individual regions of the manifold. If the manifold is the surface of the Earth, then an atlas has its more common meaning. In general, the notion of atlas underlies the formal definition of a manifold and related structures such as vector bundles and other fibre bundles.
The definition of an atlas depends on the notion of a chart. A chart for a topological space M (also called a coordinate chart, coordinate patch, coordinate map, or local frame) is a homeomorphism from an open subset U of M to an open subset of Euclidean space. The chart is traditionally recorded as the ordered pair
.
An atlas for a topological space M is a collection of charts on M such that
. If the codomain of each chart is the n-dimensional Euclidean space and the atlas is connected, then M is said to be an n-dimensional manifold.
Frequency is a 2000 American science fiction thriller film. It was co-produced and directed by Gregory Hoblit and written and co-produced by Toby Emmerich. The film stars Dennis Quaid and Jim Caviezel as father and son, Frank and John Sullivan respectively. It was filmed in Toronto and New York City. The film gained mostly favorable reviews following its release via DVD format on October 31, 2000.
In Queens, New York during October 1999, John Sullivan (Caviezel), a 36-year-old homicide detective, breaks up with his girlfriend Samantha (Melissa Errico) with the reason partially attributed to the trauma caused by the death of his fireman father Frank (Quaid). Still living in the same house where he grew up, he discovers his father's Heathkit single-sideband ham radio and begins transmitting radio signals. Because of highly localized electro-temporal spatial effects caused by unusual aurora borealis activity, John somehow makes contact with his father exactly 30 years in the past on the day before Frank's death in a warehouse fire. The ensuing conversation results in Frank thinking John is a stalker. Before the connection cuts out, John is able to shout out the circumstances that led to Frank's death. The next day as little things brought up in their conversation prove true, Frank believes and heeds John's words, escaping the fire to safety. The father and son reconnect on the HAM radio set later that evening, with Frank sharing his dreams and his hopes for his son, and John recounting the details of the Mets-Orioles World Series, which is just beginning in Frank's timeline in 1969. John also reveals to Frank that he now dies of lung cancer in 1989 due to his smoking habit.
In statistics the frequency (or absolute frequency) of an event is the number
of times the event occurred in an experiment or study. These frequencies are often graphically represented in histograms.
Cumulative frequency refers to the total of the absolute frequencies of all events at or below a certain point in an ordered list of events.
The relative frequency (or empirical probability) of an event refers to the absolute frequency normalized by the total number of events:
The values of for all events
can be plotted to produce a frequency distribution.
In the case when for certain i, pseudocounts can be added.
The following are some commonly used methods of depicting frequency:
A histogram is a representation of tabulated frequencies, shown as adjacent rectangles or squares (in some situations), erected over discrete intervals (bins), with an area proportional to the frequency of the observations in the interval. The height of a rectangle is also equal to the frequency density of the interval, i.e., the frequency divided by the width of the interval. The total area of the histogram is equal to the number of data. A histogram may also be normalized displaying relative frequencies. It then shows the proportion of cases that fall into each of several categories, with the total area equaling 1. The categories are usually specified as consecutive, non-overlapping intervals of a variable. The categories (intervals) must be adjacent, and often are chosen to be of the same size. The rectangles of a histogram are drawn so that they touch each other to indicate that the original variable is continuous.