|
Zindler Curve
A Zindler curve is a simple closed plane curve with the defining property that: :(L) All chords, which cut the curve length into halves, have the same length. The most simple examples are circles. The Austrian mathematician Konrad Zindler discovered further examples, and gave a method to construct them. Herman Auerbach was the first, who used (in 1938) the now established name ''Zindler curve''. Auerbach proved that a figure bounded by a Zindler curve and with half the density of water will float in water in any position. This gives a negative answer to the bidimensional version of Stanislaw Ulam's problem on floating bodies (Problem 19 of the Scottish Book), which asks if the disk is the only figure of uniform density which will float in water in any position (the original problem asks if the sphere is the only solid having this property in three dimension). Zindler curves are also connected to the problem of establishing if it is possible to determine the direction of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanislaw Ulam
Stanisław Marcin Ulam (; 13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics. He participated in the Manhattan Project, originated the Teller–Ulam design of thermonuclear weapons, discovered the concept of the cellular automaton, invented the Monte Carlo method of computation, and suggested nuclear pulse propulsion. In pure and applied mathematics, he proved some theorems and proposed several conjectures. Born into a wealthy Polish Jewish family, Ulam studied mathematics at the Lwów Polytechnic Institute, where he earned his PhD in 1933 under the supervision of Kazimierz Kuratowski and Włodzimierz Stożek. In 1935, John von Neumann, whom Ulam had met in Warsaw, invited him to come to the Institute for Advanced Study in Princeton, New Jersey, for a few months. From 1936 to 1939, he spent summers in Poland and academic years at Harvard University in Cambridge, Massachusetts, where he worked to establish import ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reuleaux Polygon
In geometry, a Reuleaux polygon is a curve of constant width made up of circular arcs of constant radius. These shapes are named after their prototypical example, the Reuleaux triangle, which in turn, is named after 19th-century German engineer Franz Reuleaux. The Reuleaux triangle can be constructed from an equilateral triangle by connecting each two vertices by a circular arc centered on the third vertex, and Reuleaux polygons can be formed by a similar construction from any regular polygon with an odd number of sides, or from certain irregular polygons. Every curve of constant width can be accurately approximated by Reuleaux polygons. They have been applied in coinage shapes. Construction If P is a convex polygon with an odd number of sides, in which each vertex is equidistant to the two opposite vertices and closer to all other vertices, then replacing each side of P by an arc centered at its opposite vertex produces a Reuleaux polygon. As a special case, this construction i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curve Of Constant Width
In geometry, a curve of constant width is a simple closed curve in the plane whose width (the distance between parallel supporting lines) is the same in all directions. The shape bounded by a curve of constant width is a body of constant width or an orbiform, the name given to these shapes by Leonhard Euler. Standard examples are the circle and the Reuleaux triangle. These curves can also be constructed using circular arcs centered at crossings of an arrangement of lines, as the involutes of certain curves, or by intersecting circles centered on a partial curve. Every body of constant width is a convex set, its boundary crossed at most twice by any line, and if the line crosses perpendicularly it does so at both crossings, separated by the width. By Barbier's theorem, the body's perimeter is exactly times its width, but its area depends on its shape, with the Reuleaux triangle having the smallest possible area for its width and the circle the largest. Every superset of a body o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Function
A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which repeat at intervals of 2\pi radians, are periodic functions. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function that is not periodic is called aperiodic. Definition A function is said to be periodic if, for some nonzero constant , it is the case that :f(x+P) = f(x) for all values of in the domain. A nonzero constant for which this is the case is called a period of the function. If there exists a least positive constant with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) Often, "the" period of a function is used to mean its fundamental period. A function with period will repeat on intervals of length , and these intervals are sometimes also referred to as periods of the function. Geometrically, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curve Of Constant Width
In geometry, a curve of constant width is a simple closed curve in the plane whose width (the distance between parallel supporting lines) is the same in all directions. The shape bounded by a curve of constant width is a body of constant width or an orbiform, the name given to these shapes by Leonhard Euler. Standard examples are the circle and the Reuleaux triangle. These curves can also be constructed using circular arcs centered at crossings of an arrangement of lines, as the involutes of certain curves, or by intersecting circles centered on a partial curve. Every body of constant width is a convex set, its boundary crossed at most twice by any line, and if the line crosses perpendicularly it does so at both crossings, separated by the width. By Barbier's theorem, the body's perimeter is exactly times its width, but its area depends on its shape, with the Reuleaux triangle having the smallest possible area for its width and the circle the largest. Every superset of a body o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herman Auerbach
Herman Auerbach (October 26, 1901, Tarnopol – August 17, 1942) was a Polish mathematician and member of the Lwów School of Mathematics. Auerbach was professor at Lwów University. During the Second World War because of his Jewish descent he was imprisoned by the Germans in the Lwów ghetto. In 1942 he was murdered at Bełżec extermination camp. News on wartime fates of Polish mathematicians, pp. 868–869. See also *Jewish ghettos in German-occupied Poland *List of Nazi-German concentration camps *The Holocaust in Poland *World War II casualties of Poland References External links *Author profilein the database zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure mathematics, pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Informa ... 1901 births 1942 deaths People from Ternopil People from the Kingdom of Galicia and Lodomeria J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Konrad Zindler
Konrad is a German (with variants ''Kunz'' and ''Kunze'') given name and surname that means "bold counselor" and may refer to: People Given name Surname *Alexander Konrad (1890–1940), Russian explorer *Antoine Konrad (born 1975), birth name of DJ Antoine, Swiss DJ *Carina Konrad (born 1982), German politician * Christoph Werner Konrad (born 1957), German politician *Edmond Konrad (1909–1997), Rear Admiral, United States Navy *Franz Konrad (racing driver) (born 1951), Austrian racing driver *Franz Konrad (SS officer) (1906–1952), German SS officer executed for war crimes *Franz Conrad von Hötzendorf (1852–1925), Chief of the General Staff of the Austro-Hungarian Army at outbreak of World War I *Franz Konrad von Rodt (1706–1775), Bishop of Constance * György Konrád (1933–2019), Hungarian writer *Rudolf Konrad (1891–1964), German general during World War II *Michaela Konrad (born 1972), Austrian artist *Otto Konrad (born 1964), Austrian football player *Paul Konrad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius. Usually, the radius is required to be a positive number. A circle with r=0 (a single point) is a degenerate case. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. Specifically, a circle is a simple closed curve that divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a '' disc''. A circle may also be defined as a special ki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
