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Euler's Disk
Euler's Disk, invented between 1987 and 1990 by Joseph Bendik, is a trademarked scientific educational toy. It is used to illustrate and study the dynamic system of a spinning and rolling disk on a flat or curved surface. It has been the subject of several scientific papers. Bendik named the toy after mathematician Leonhard Euler. Discovery Joseph Bendik first noted the interesting motion of the spinning disk while working at Hughes Aircraft (Carlsbad Research Center) after spinning a heavy polishing chuck on his desk at lunch one day. The apparatus is a dramatic visualization of energy exchanges in three different, tightly coupled processes. As the disk gradually decreases its azimuthal rotation, there is also a decrease in amplitude and increase in the frequency of the disk's axial precession. The evolution of the disk's axial precession is easily visualized in a slow motion video by looking at the side of the disk following a single point marked on the disk. The evolutio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vacuum
A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often discuss ideal test results that would occur in a ''perfect'' vacuum, which they sometimes simply call "vacuum" or free space, and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space. In engineering and applied physics on the other hand, vacuum refers to any space in which the pressure is considerably lower than atmospheric pressure. The Latin term ''in vacuo'' is used to describe an object that is surrounded by a vacuum. The ''quality'' of a partial vacuum refers to how closely it approaches a perfect vacuum. Other things equal, lower gas pressure means higher-quality vacuum. For example, a typical vacuum cleaner produces enough suction to reduce air pressur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at the centre of a circle by an Circular arc, arc that is equal in length to the radius. The unit was formerly an SI supplementary unit and is currently a dimensionless unit, dimensionless SI derived unit,: "The CGPM decided to interpret the supplementary units in the SI, namely the radian and the steradian, as dimensionless derived units." defined in the SI as 1 rad = 1 and expressed in terms of the SI base unit metre (m) as . Angles without explicitly specified units are generally assumed to be measured in radians, especially in mathematical writing. Definition One radian is defined as the angle at the center of a circle in a plane that wikt:subtend, subtends an arc whose length equals the radius of the circle. More generally, the magnit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Viscosity
Viscosity is a measure of a fluid's rate-dependent resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for example, syrup has a higher viscosity than water. Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per metre squared, or pascal-seconds. Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's center line than near its walls. Experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion. For a tube with a constant rate of flow, the strengt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
G-force
The g-force or gravitational force equivalent is a Specific force, mass-specific force (force per unit mass), expressed in Unit of measurement, units of standard gravity (symbol ''g'' or ''g''0, not to be confused with "g", the symbol for grams). It is used for sustained accelerations that cause a perception of weight. For example, an object at rest on Earth's surface is subject to 1 ''g'', equaling the conventional value of gravitational acceleration on Earth, about . More transient acceleration, accompanied with significant jerk (physics), jerk, is called Shock (mechanics), ''shock''. When the g-force is produced by the surface of one object being pushed by the surface of another object, the reaction force to this push produces an equal and opposite force for every unit of each object's mass. The types of forces involved are transmitted through objects by interior Stress (mechanics), mechanical stresses. Gravitational acceleration is one cause of an object's accelera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Singularity
In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity. For example, the reciprocal function f(x) = 1/x has a singularity at x = 0, where the value of the function is not defined, as involving a division by zero. The absolute value function g(x) = , x, also has a singularity at x = 0, since it is not differentiable there. The algebraic curve In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane cu ... defined by \left\ in the (x, y) coordinate system has a singularity (called a cusp (singularity), cusp) at (0, 0). For singularities in algebraic geometry, see singular point of an algebraic variety. For singul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinity
Infinity is something which is boundless, endless, or larger than any natural number. It is denoted by \infty, called the infinity symbol. From the time of the Ancient Greek mathematics, ancient Greeks, the Infinity (philosophy), philosophical nature of infinity has been the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including Guillaume de l'Hôpital, l'Hôpital and Johann Bernoulli, Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or Magnitude (mathematics), magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. the other being Derivative, differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter. A definite integral computes the signed area of the region in the plane that is bounded by the Graph of a function, graph of a given Function (mathematics), function between two points in the real line. Conventionally, areas above the horizontal Coordinate axis, axis of the plane are positive while areas below are n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Keith Moffatt
Henry Keith Moffatt, FRS FRSE (born 12 April 1935) is a British mathematician with research interests in the field of fluid dynamics, particularly magnetohydrodynamics and the theory of turbulence. He was Professor of Mathematical Physics at the University of Cambridge from 1980 to 2002. Early life and education Moffatt was born on 12 April 1935 to Emmeline Marchant and Frederick Henry Moffatt''.'' He was schooled at George Watson's College, Edinburgh, going on to study Mathematical Sciences at the University of Edinburgh, graduating in 1957. He then went to Trinity College, Cambridge, where he studied mathematics and, 1959, he was a Wrangler. In 1960, he was awarded a Smith's Prize while preparing his PhD. He received his PhD in 1962; his dissertation, ''Magnetohydrodynamic Turbulence'', was supervised by George Batchelor. Career After completing his PhD, Moffatt joined the staff of the Mathematics Faculty at the University of Cambridge as an Assistant Lecturer and became ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nature (journal)
''Nature'' is a British weekly scientific journal founded and based in London, England. As a multidisciplinary publication, ''Nature'' features Peer review, peer-reviewed research from a variety of academic disciplines, mainly in science and technology. It has core editorial offices across the United States, continental Europe, and Asia under the international scientific publishing company Springer Nature. ''Nature'' was one of the world's most cited scientific journals by the Science Edition of the 2022 ''Journal Citation Reports'' (with an ascribed impact factor of 50.5), making it one of the world's most-read and most prestigious academic journals. , it claimed an online readership of about three million unique readers per month. Founded in the autumn of 1869, ''Nature'' was first circulated by Norman Lockyer and Alexander MacMillan (publisher), Alexander MacMillan as a public forum for scientific innovations. The mid-20th century facilitated an editorial expansion for the j ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heads Or Tails
Coin flipping, coin tossing, or heads or tails is using the thumb to make a coin go up while spinning in the air and checking which side is showing when it is down onto a surface, in order to randomly choose between two alternatives. It is a form of sortition which inherently has two possible outcomes. History Coin flipping was known to the Romans as ''navia aut caput'' ("ship or head"), as some coins had a ship on one side and the head of the emperor on the other. In England, this was referred to as ''cross and pile''. Process During a coin toss, the coin is thrown into the air such that it rotates edge-over-edge an unpredictable number of times. Either beforehand or when the coin is in the air, an interested party declares "heads" or "tails", indicating which side of the coin that party is choosing. The other party is assigned the opposite side. Depending on custom, the coin may be caught; caught and inverted; or allowed to land on the ground. When the coin comes to rest, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
US Quarter
The quarter, formally known as the quarter dollar, is a coin in the United States valued at 25 cents, representing one-quarter of a dollar. Adorning its obverse is the profile of George Washington, while its reverse design has undergone frequent changes since 1998. Since its initial production in 1796, the quarter dollar has held a significant place in American numismatics, with consistent production since 1831. It has a diameter of 0.955 inch (24.26 mm) and a thickness of 0.069 inch (1.75 mm). Its current version is composed of two layers of cupronickel (75% copper, 25% nickel) clad on a core of pure copper. With the cupronickel layers comprising 1/3 of total weight, the coin's overall composition is therefore 8.33% nickel, 91.67% copper. Its weight is 0.1823 troy oz. or 0.2000 avoirdupois oz. (5.670 grams). Designs before 1932 The choice of a quarter-dollar as a denomination, as opposed to the or the 20-cent piece that is more common elsewhere, originated with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
