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Kunstweg
Bürgi's Kunstweg is a set of algorithms invented by Jost Bürgi at the end of the 16th century.Staudacher, S., 2014. Jost Bürgi, Kepler und der Kaiser. Verlag NZZ, Zürich. They can be used for the calculation of sines to an arbitrary precision. Bürgi used these algorithms to calculate a Canon Sinuum, a table of sines in steps of 2 arc seconds. It is thought that this table had 8 sexagesimal places. Some authors have speculated that this table only covered the range from 0 to 45 degrees, but nothing seems to support this claim. Such tables were extremely important for navigation at sea. Johannes Kepler called the Canon Sinuum the most precise known table of sines.Max Caspar, ''Johannes Kepler Gesammelte Werke'', Band XVIII, page 149-150, Letter from Kepler to Landgraf Philipp von Hessen, december 1623Bayerische Akademie der Wissenschaften/ref> Bürgi explained his algorithms in his work Fundamentum Astronomiae which he presented to Emperor Rudolf II. in 1592. The principles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kunstweg (Jost Bürgi)
Bürgi's Kunstweg is a set of algorithms invented by Jost Bürgi at the end of the 16th century.Staudacher, S., 2014. Jost Bürgi, Kepler und der Kaiser. Verlag NZZ, Zürich. They can be used for the calculation of sines to an arbitrary precision. Bürgi used these algorithms to calculate a Canon Sinuum, a table of sines in steps of 2 arc seconds. It is thought that this table had 8 sexagesimal places. Some authors have speculated that this table only covered the range from 0 to 45 degrees, but nothing seems to support this claim. Such tables were extremely important for navigation at sea. Johannes Kepler called the Canon Sinuum the most precise known table of sines.Max Caspar, ''Johannes Kepler Gesammelte Werke'', Band XVIII, page 149-150, Letter from Kepler to Landgraf Philipp von Hessen, december 1623Bayerische Akademie der Wissenschaften/ref> Bürgi explained his algorithms in his work Fundamentum Astronomiae which he presented to Emperor Rudolf II. in 1592. The principles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jost Bürgi
Jost Bürgi (also ''Joost, Jobst''; Latinisation of names, Latinized surname ''Burgius'' or ''Byrgius''; 28 February 1552 – 31 January 1632), active primarily at the courts in Kassel and Prague, was a Swiss clockmaker, a maker of astronomical instruments and a mathematician. Life Bürgi was born in 1552 Lichtensteig, Toggenburg, at the time a subject territory of the Abbey of St. Gall (now part of the canton of St. Gallen, Switzerland). Not much is known about his life or education before his employment as astronomer and clockmaker at the court of William IV in Kassel in 1579; it has been theorized that he acquired his mathematical knowledge at Strasbourg, among others from Swiss mathematician Conrad Dasypodius, but there are no facts to support this. Although an autodidact, he was already during his lifetime considered as one of the most excellent mechanical engineers of his generation. His employer, William IV, Landgrave of Hesse-Kassel, in a letter to Tycho Brahe praise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canon Sinuum (Bürgi)
The ''Canon Sinuum'' was a historic table of sines thought to have given the sines to 8 sexagesimal places between 0 and 90 degrees in steps of 2 arc seconds. Some authors believe that the table was only between 0 and 45 degrees. It was created by Jost Bürgi at the end of the 16th century. Such tables were essential for navigation at sea. Johannes Kepler called the ''Canon Sinuum'' the most precise known table of sines. This table is thought to be lost. The ''Canon Sinuum'' was computed by Bürgi's algorithms explained in his work Fundamentum Astronomiae presented to Emperor Rudolf II. in 1592.Staudacher, S., 2014. Jost Bürgi, Kepler und der Kaiser. Verlag NZZ, Zürich. These algorithms made use of differences and were one of the early uses of difference calculus. The largest trigonometrical table actually contained in the Fundamentum Astronomiae is a table giving the sines for every minute of the quadrant and to 5 to 7 sexagesimal places. The manuscript of Fundamentum A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fundamentum Astronomiae
''Fundamentum Astronomiae'' is a historic manuscript presented by Jost Bürgi to Emperor Rudolf II in 1592. It describes Bürgi's trigonometry based algorithms called Kunstweg which can be used to calculate sines at arbitrary precision.Staudacher, S., 2014. Jost Bürgi, ''Kepler und der Kaiser''. Verlag NZZ, Zürich. General Bürgi took special care to avoid his method becoming public in his time. However, Henry Briggs (mathematician) (1561-1630) was acquainted with the method, likely via a link to John Dee who knew Christoph Rothmann, a colleague of Bürgi at the court. Method Bürgi used these algorithms, including multiplication table in sexagesimal system, to compute a '' Canon Sinuum'', a table of sines to 8 sexagesimal places in steps of 2 arc seconds. Such tables were extremely important for navigation at sea. Bürgi's method only uses additions and halving, his procedure is elementary and it converges from the standard method. Johannes Kepler called the Canon Sinuum t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sine
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle \theta, the sine and cosine functions are denoted simply as \sin \theta and \cos \theta. More generally, the definitions of sine and cosine can be extended to any real value in terms of the lengths of certain line segments in a unit circle. More modern definitions express the sine and cosine as infinite series, or as the solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers. The sine and cosine functions are commonly used to model periodic phenomena such as sound and lig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arc Seconds
A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of Angular unit, angular measurement equal to of one Degree (angle), degree. Since one degree is of a turn (geometry), turn (or complete rotation), one minute of arc is of a turn. The nautical miles, nautical mile (nmi) was originally defined as the meridian arc, arc length of a minute of latitude on a spherical Earth, so the actual Earth circumference is very near . A minute of arc is of a radian. A second of arc, arcsecond (arcsec), or arc second, denoted by the symbol , is of an arcminute, of a degree, of a turn, and (about ) of a radian. These units originated in Babylonian astronomy as sexagesimal 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 milliarcsecond ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Navigation
Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, marine navigation, aeronautic navigation, and space navigation. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks. All navigational techniques involve locating the navigator's position compared to known locations or patterns. Navigation, in a broader sense, can refer to any skill or study that involves the determination of position and direction. In this sense, navigation includes orienteering and pedestrian navigation. History In the European medieval period, navigation was considered part of the set of '' seven mechanical arts'', none of which were used for long voyages across open ocean. Polynesian navigation is probably the earliest form of open-ocean navigation; it was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johannes Kepler
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of planetary motion, and his books ''Astronomia nova'', ''Harmonice Mundi'', and ''Epitome Astronomiae Copernicanae''. These works also provided one of the foundations for Newton's theory of universal gravitation. Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting (or Keplerian) telescope, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emperor Rudolf II
Rudolf II (18 July 1552 – 20 January 1612) was Holy Roman Emperor (1576–1612), King of Hungary and Croatia (as Rudolf I, 1572–1608), King of Bohemia (1575–1608/1611) and Archduke of Austria (1576–1608). He was a member of the House of Habsburg. Rudolf's legacy has traditionally been viewed in three ways:Hotson, 1999. an ineffectual ruler whose mistakes led directly to the Thirty Years' War; a great and influential patron of Northern Mannerist art; and an intellectual devotee of occult arts and learning which helped seed what would be called the Scientific Revolution. Determined to unify Christendom, he initiated the Long Turkish War (1593–1606) with the Ottoman Empire. Exhausted by war, his citizens in Hungary revolted in the Bocskai Uprising, which led to more authority given to his brother Matthias. Under his reign, there was a policy of toleration towards Judaism. Early life Rudolf was born in Vienna on 18 July 1552. He was the eldest son and successor of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Column
A column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above to other structural elements below. In other words, a column is a compression member. The term ''column'' applies especially to a large round support (the shaft of the column) with a capital and a base or pedestal, which is made of stone, or appearing to be so. A small wooden or metal support is typically called a ''post''. Supports with a rectangular or other non-round section are usually called ''piers''. For the purpose of wind or earthquake engineering, columns may be designed to resist lateral forces. Other compression members are often termed "columns" because of the similar stress conditions. Columns are frequently used to support beams or arches on which the upper parts of walls or ceilings rest. In architecture, "column" refers to such a structural element that also has certain proportional and decorative featur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximations
An approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix ''ad-'' (''ad-'' before ''p'' becomes ap- by assimilation) meaning ''to''. Words like ''approximate'', ''approximately'' and ''approximation'' are used especially in technical or scientific contexts. In everyday English, words such as ''roughly'' or ''around'' are used with a similar meaning. It is often found abbreviated as ''approx.'' The term can be applied to various properties (e.g., value, quantity, image, description) that are nearly, but not exactly correct; similar, but not exactly the same (e.g., the approximate time was 10 o'clock). Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws. In science, approximation can refer to u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
