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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] |
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] |
Degree (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] |
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] |
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] |
16th Century
The 16th century begins with the Julian year 1501 ( MDI) and ends with either the Julian or the Gregorian year 1600 ( MDC) (depending on the reckoning used; the Gregorian calendar introduced a lapse of 10 days in October 1582). The 16th century is regarded by historians as the century which saw the rise of Western civilization and the Islamic gunpowder empires. The Renaissance in Italy and Europe saw the emergence of important artists, authors and scientists, and led to the foundation of important subjects which include accounting and political science. Copernicus proposed the heliocentric universe, which was met with strong resistance, and Tycho Brahe refuted the theory of celestial spheres through observational measurement of the 1572 appearance of a Milky Way supernova. These events directly challenged the long-held notion of an immutable universe supported by Ptolemy and Aristotle, and led to major revolutions in astronomy and science. Galileo Galilei became a champion o ... [...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] |
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] |
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] |
Difference Calculus
A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. The difference operator, commonly denoted \Delta is the operator that maps a function to the function \Delta /math> defined by :\Delta x)= f(x+1)-f(x). A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations, specially in the solving methods. Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences. In numerical analysis, finite differences are widely used for approximating derivatives, and the term "fini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wrocław
Wrocław (; german: Breslau, or . ; Silesian German: ''Brassel'') is a city in southwestern Poland and the largest city in the historical region of Silesia. It lies on the banks of the River Oder in the Silesian Lowlands of Central Europe, roughly from the Baltic Sea to the north and from the Sudeten Mountains to the south. , the official population of Wrocław is 672,929, with a total of 1.25 million residing in the metropolitan area, making it the third largest city in Poland. Wrocław is the historical capital of Silesia and Lower Silesia. Today, it is the capital of the Lower Silesian Voivodeship. The history of the city dates back over a thousand years; at various times, it has been part of the Kingdom of Poland, the Kingdom of Bohemia, the Kingdom of Hungary, the Habsburg monarchy of Austria, the Kingdom of Prussia and Germany. Wrocław became part of Poland again in 1945 as part of the Recovered Territories, the result of extensive border changes and expulsions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemy's Table Of Chords
The table of chords, created by the Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's ''Almagest'', a treatise on mathematical astronomy. It is essentially equivalent to a table of values of the sine function. It was the earliest trigonometric table extensive enough for many practical purposes, including those of astronomy (an earlier table of chords by Hipparchus gave chords only for arcs that were multiples of ). Centuries passed before more extensive trigonometric tables were created. One such table is the '' Canon Sinuum'' created at the end of the 16th century. The chord function and the table A chord of a circle is a line segment whose endpoints are on the circle. Ptolemy used a circle whose diameter is 120 parts. He tabulated the length of a chord whose endpoints are separated by an arc of ''n'' degrees, for ''n'' ranging from to 180 by increments o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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