EscapementAn escapement is a mechanical linkage in mechanical watches and clocks that gives impulses to the timekeeping element and periodically releases the gear train to move forward, advancing the clock's hands. The impulse action transfers energy to the clock's timekeeping element (usually a pendulum or balance wheel) to replace the energy lost to friction during its cycle and keep the timekeeper oscillating. The escapement is driven by force from a coiled spring or a suspended weight, transmitted through the timepiece's gear train.
ClockA clock or chronometer is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month, and the year. Devices operating on several physical processes have been used over the millennia. Some predecessors to the modern clock may be considered "clocks" that are based on movement in nature: A sundial shows the time by displaying the position of a shadow on a flat surface.
Water wheelA water wheel is a machine for converting the energy of flowing or falling water into useful forms of power, often in a watermill. A water wheel consists of a wheel (usually constructed from wood or metal), with a number of blades or buckets arranged on the outside rim forming the driving car. Water wheels were still in commercial use well into the 20th century but they are no longer in common use. Uses included milling flour in gristmills, grinding wood into pulp for papermaking, hammering wrought iron, machining, ore crushing and pounding fibre for use in the manufacture of cloth.
ToothA tooth (: teeth) is a hard, calcified structure found in the jaws (or mouths) of many vertebrates and used to break down food. Some animals, particularly carnivores and omnivores, also use teeth to help with capturing or wounding prey, tearing food, for defensive purposes, to intimidate other animals often including their own, or to carry prey or their young. The roots of teeth are covered by gums. Teeth are not made of bone, but rather of multiple tissues of varying density and hardness that originate from the outermost embryonic germ layer, the ectoderm.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
WatchA watch is a portable timepiece intended to be carried or worn by a person. It is designed to keep a consistent movement despite the motions caused by the person's activities. A wristwatch is designed to be worn around the wrist, attached by a watch strap or other type of bracelet, including metal bands, leather straps, or any other kind of bracelet. A pocket watch is designed for a person to carry in a pocket, often attached to a chain. Watches were developed in the 17th century from spring-powered clocks, which appeared as early as the 14th century.
Mechanical watchA mechanical watch is a watch that uses a clockwork mechanism to measure the passage of time, as opposed to quartz watches which function using the vibration modes of a piezoelectric quartz tuning fork, or radio watches, which are quartz watches synchronized to an atomic clock via radio waves. A mechanical watch is driven by a mainspring which must be wound either periodically by hand or via a self-winding mechanism. Its force is transmitted through a series of gears to power the balance wheel, a weighted wheel which oscillates back and forth at a constant rate.
Simply connected spaceIn topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question. The fundamental group of a topological space is an indicator of the failure for the space to be simply connected: a path-connected topological space is simply connected if and only if its fundamental group is trivial.
GearA gear is a rotating circular machine part having cut teeth or, in the case of a cogwheel or gearwheel, inserted teeth (called cogs), which mesh with another (compatible) toothed part to transmit (convert) torque and speed. The basic principle behind the operation of gears is analogous to the basic principle of levers. A gear may also be known informally as a cog. Geared devices can change the speed, torque, and direction of a power source.
Worm driveA worm drive is a gear arrangement in which a worm (which is a gear in the form of a screw) meshes with a worm wheel (which is similar in appearance to a spur gear). The two elements are also called the worm screw and worm gear. The terminology is often confused by imprecise use of the term worm gear to refer to the worm, the worm wheel, or the worm drive as a unit. The worm drive or "endless screw" was invented by either Archytas of Tarentum, Apollonius of Perga, or Archimedes, the last one being the most probable author.
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
Field (mathematics)In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers.
Human tooth developmentTooth development or odontogenesis is the complex process by which teeth form from embryonic cells, grow, and erupt into the mouth. For human teeth to have a healthy oral environment, all parts of the tooth must develop during appropriate stages of fetal development. Primary (baby) teeth start to form between the sixth and eighth week of prenatal development, and permanent teeth begin to form in the twentieth week. If teeth do not start to develop at or near these times, they will not develop at all, resulting in hypodontia or anodontia.
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
Tooth enamelTooth enamel is one of the four major tissues that make up the tooth in humans and many animals, including some species of fish. It makes up the normally visible part of the tooth, covering the crown. The other major tissues are dentin, cementum, and dental pulp. It is a very hard, white to off-white, highly mineralised substance that acts as a barrier to protect the tooth but can become susceptible to degradation, especially by acids from food and drink. Calcium hardens the tooth enamel.
Pin-pallet escapementA Roskopf, pin-lever, or pin-pallet escapement is an inexpensive, less accurate version of the lever escapement, used in mechanical alarm clocks, kitchen timers, mantel clocks and, until the 1970s, cheap watches now known as pin lever watches. It was popularized by German watchmaker Georges Frederic Roskopf in its "proletarian watch" from 1867. It was invented by Louis Perron, of Besançon, suggested to Roskopf by Jules Grossmann.
Connected spaceIn topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties that are used to distinguish topological spaces. A subset of a topological space is a if it is a connected space when viewed as a subspace of . Some related but stronger conditions are path connected, simply connected, and -connected.
Direct sumThe direct sum is an operation between structures in abstract algebra, a branch of mathematics. It is defined differently, but analogously, for different kinds of structures. To see how the direct sum is used in abstract algebra, consider a more elementary kind of structure, the abelian group. The direct sum of two abelian groups and is another abelian group consisting of the ordered pairs where and . To add ordered pairs, we define the sum to be ; in other words addition is defined coordinate-wise.
Field (physics)In physics, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. For example, on a weather map, the surface temperature is described by assigning a number to each point on the map; the temperature can be considered at a certain point in time or over some interval of time, to study the dynamics of temperature change. A surface wind map, assigning an arrow to each point on a map that describes the wind speed and direction at that point, is an example of a vector field, i.
