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David Rytz
David Rytz von Brugg (1 April 1801, in Bucheggberg – 25 March 1868, in Aarau) was a Swiss mathematician and teacher. Life Rytz von Brugg was son of a priest and studied mathematics at Göttingen and Leipzig. He had teaching positions at various cities, one of them 1835 until 1862 at Aarau, where he was ''„Professor der Mathematik an der Gewerbeschule zu Aarau“''.Alexander Ostermann, Gerhard Wanner: ''Geometry by Its History.'' 2012, S. 69 Merits Rytz von Brugg is famous for a geometrical method which is known as Rytz’s axis construction. This classical procedure retrieves the semi-axes of an Ellipse from any pair of conjugate diameters In geometry, two diameters of a conic section are said to be conjugate if each chord (geometry), chord parallel (geometry), parallel to one diameter is bisection, bisected by the other diameter. For example, two diameters of a circle are conjugate .... This method is known since 1845, when it was published within a paper by Leopo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aarau
Aarau (, ) is a List of towns in Switzerland, town, a Municipalities of Switzerland, municipality, and the capital of the northern Swiss Cantons of Switzerland, canton of Aargau. The List of towns in Switzerland, town is also the capital of the district of Aarau (district), Aarau. It is German-speaking and predominantly Protestant. Aarau is situated on the Swiss plateau, in the valley of the Aare, on the river's right bank, and at the southern foot of the Jura Mountains, and is west of Zürich, south of Basel and northeast of Bern. The municipality borders directly on the canton of Solothurn to the west. It is the largest town in Aargau. At the beginning of 2010 Rohr, Aargau, Rohr became a district of Aarau. The official language of Aarau is (the Swiss variety of Standard) Swiss Standard German, German, but the main spoken language is the local variant of the Alemannic German, Alemannic Swiss German (linguistics), Swiss German dialect. Geography and geology The old city of Aarau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Teacher
A teacher, also called a schoolteacher or formally an educator, is a person who helps students to acquire knowledge, competence, or virtue, via the practice of teaching. ''Informally'' the role of teacher may be taken on by anyone (e.g. when showing a colleague how to perform a specific task). In some countries, teaching young people of school age may be carried out in an informal setting, such as within the family (homeschooling), rather than in a formal setting such as a school or college. Some other professions may involve a significant amount of teaching (e.g. youth worker, pastor). In most countries, ''formal'' teaching of students is usually carried out by paid professional teachers. This article focuses on those who are ''employed'', as their main role, to teach others in a ''formal'' education context, such as at a school or other place of ''initial'' formal education or training. Duties and functions A teacher's role may vary among cultures. Teachers may provide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Priest
A priest is a religious leader authorized to perform the sacred rituals of a religion, especially as a mediatory agent between humans and one or more deities. They also have the authority or power to administer religious rites; in particular, rites of sacrifice to, and propitiation of, a deity or deities. Their office or position is the 'priesthood', a term which also may apply to such persons collectively. A priest may have the duty to hear confessions periodically, give marriage counseling, provide prenuptial counseling, give spiritual direction, teach catechism, or visit those confined indoors, such as the sick in hospitals and nursing homes. Description According to the trifunctional hypothesis of prehistoric Proto-Indo-European society, priests have existed since the earliest of times and in the simplest societies, most likely as a result of agricultural surplus and consequent social stratification. The necessity to read sacred texts and keep temple or church rec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Göttingen
Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, the population was 118,911. General information The origins of Göttingen lay in a village called ''Gutingi, ''first mentioned in a document in 953 AD. The city was founded northwest of this village, between 1150 and 1200 AD, and adopted its name. In Middle Ages, medieval times the city was a member of the Hanseatic League and hence a wealthy town. Today, Göttingen is famous for its old university (''Georgia Augusta'', or University of Göttingen, "Georg-August-Universität"), which was founded in 1734 (first classes in 1737) and became the most visited university of Europe. In 1837, seven professors protested against the absolute sovereignty of the House of Hanover, kings of Kingdom of Hanover, Hanover; they lost their positions, but be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leipzig
Leipzig ( , ; Upper Saxon: ) is the most populous city in the German state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's eighth most populous, as well as the second most populous city in the area of the former East Germany after (East) Berlin. Together with Halle (Saale), the city forms the polycentric Leipzig-Halle Conurbation. Between the two cities (in Schkeuditz) lies Leipzig/Halle Airport. Leipzig is located about southwest of Berlin, in the southernmost part of the North German Plain (known as Leipzig Bay), at the confluence of the White Elster River (progression: ) and two of its tributaries: the Pleiße and the Parthe. The name of the city and those of many of its boroughs are of Slavic origin. Leipzig has been a trade city since at least the time of the Holy Roman Empire. The city sits at the intersection of the Via Regia and the Via Imperii, two important medieval trad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rytz's Construction
The Rytz’s axis construction is a basic method of descriptive geometry to find the axes, the semi-major axis and semi-minor axis and the vertices of an ellipse, starting from two conjugated half-diameters. If the center and the semi axis of an ellipse are determined the ellipse can be drawn using an ellipsograph or by hand (see ellipse). Rytz’s construction is a classical construction of Euclidean geometry, in which only compass and ruler A ruler, sometimes called a rule, line gauge, or scale, is a device used in geometry and technical drawing, as well as the engineering and construction industries, to measure distances or draw straight lines. Variants Rulers have long ... are allowed as aids. The design is named after its inventor David Rytz of Brugg (1801–1868). Conjugate diameters appear always if a circle or an ellipse is projected parallelly (the rays are parallel) as images of orthogonal diameters of a circle (see second diagram) or as images of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ellipse
In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity (mathematics), eccentricity e, a number ranging from e = 0 (the Limiting case (mathematics), limiting case of a circle) to e = 1 (the limiting case of infinite elongation, no longer an ellipse but a parabola). An ellipse has a simple algebraic solution for its area, but only approximations for its perimeter (also known as circumference), for which integration is required to obtain an exact solution. Analytic geometry, Analytically, the equation of a standard ellipse centered at the origin with width 2a and height 2b is: : \frac+\frac = 1 . Assuming a \ge b, the foci are (\pm c, 0) for c = \sqrt. The standard parametric e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjugate Diameters
In geometry, two diameters of a conic section are said to be conjugate if each chord parallel to one diameter is bisected by the other diameter. For example, two diameters of a circle are conjugate if and only if they are perpendicular. Of ellipse For an ellipse, two diameters are conjugate if and only if the tangent line to the ellipse at an endpoint of one diameter is parallel to the other diameter. Each pair of conjugate diameters of an ellipse has a corresponding tangent parallelogram, sometimes called a bounding parallelogram (skewed compared to a bounding rectangle). In his manuscript De motu corporum in gyrum, and in the ' Principia', Isaac Newton cites as a lemma proved by previous authors that all (bounding) parallelograms for a given ellipse have the same area. It is possible to reconstruct an ellipse from any pair of conjugate diameters, or from any bounding parallelogram. For example, in proposition 14 of Book VIII of his ''Collection'', Pappus of Alexandria g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Verlag Harri Deutsch
The (VHD, HD) with headquarters in Frankfurt am Main, Germany, as well as in Zürich and Thun, Switzerland, was a German publishing house founded in 1961 and closed in 2013. Overview The ' with headquarters in Frankfurt am Main, Germany, was a German publishing house founded by Harri Deutsch in 1961 as a spin-off of the scientific bookstore Fachbuchhandlung Harri Deutsch (FHD), which had existed for about a decade earlier. Both were situated near Goethe-Universität Frankfurt am Main. Between 1963 and about 1979 the publisher also had an office in Zürich. Around 1974 another branch was opened in Thun. The company's activities focussed mostly on textbooks and encyclopedic works in the areas of mathematics, physics, chemistry and other sciences and technologies, in the first three decades in particular titles licensed from publishers of the former Eastern Bloc including the East-German publishers Edition Leipzig, , Akademie Verlag, VEB Bibliographisches Institut, VEB Verlag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
