the entire wiki with video and photo galleries

find something interesting to watch in seconds

find something interesting to watch in seconds

YouTube Videos – Concentric objects and Related Articles

In geometry, two or more objects are said to be concentric, coaxal, or coaxial when they share the same center or axis. …

Kepler's cosmological model formed by concentric spheres and regular polyhedra

An archery target, featuring evenly spaced concentric circles that surround a "bullseye".

RELATED RESEARCH TOPICS

1. Concentric objects – In geometry, two or more objects are said to be concentric, coaxal, or coaxial when they share the same center or axis. Circles, regular polygons and regular polyhedra, and spheres may be concentric to one another, in the Euclidean plane, two circles that are concentric necessarily have different radii from each other. However, circles in three-dimensional space may be concentric, and have the radius as each other. For example, two different meridians of a terrestrial globe are concentric with each other and with the globe of the earth, more generally, every two great circles on a sphere are concentric with each other and with the sphere. The circumcircle and the incircle of a regular n-gon, and the regular n-gon itself, are concentric, for the circumradius-to-inradius ratio for various n, see Bicentric polygon#Regular polygons. The region of the plane between two circles is an annulus, and analogously the region of space between two concentric spheres is a spherical shell. For a given point c in the plane, the set of all circles having c as their forms a pencil of circles. Each two circles in the pencil are concentric, and have different radii, every point in the plane, except for the shared center, belongs to exactly one of the circles in the pencil. Every two disjoint circles, and every hyperbolic pencil of circles, may be transformed into a set of circles by a Möbius transformation. The ripples formed by dropping an object into still water naturally form an expanding system of concentric circles. Evenly spaced circles on the used in target archery or similar sports provide another familiar example of concentric circles. Coaxial cable is a type of cable in which the combined neutral. Johannes Keplers Mysterium Cosmographicum envisioned a system formed by concentric regular polyhedra. Concentric circles are found in diopter sights, a type of mechanic sights commonly found on target rifles. They usually feature a disk with a small-diametre hole near the shooters eye. When these sights are aligned, the point of impact will be in the middle of the front sight circle. Centered cube number Homoeoid Focaloid Circular symmetry Magic circle Geometry, Concentric circles demonstration With interactive animation

2. Muscle contraction – Muscle contraction is the activation of tension-generating sites within muscle fibers. The termination of muscle contraction is followed by muscle relaxation, which is a return of the fibers to their low tension-generating state. Muscle contractions can be described based on two variables, length and tension, a muscle contraction is described as isometric if the muscle tension changes but the muscle length remains the same. In contrast, a muscle contraction is isotonic if muscle length changes, if the muscle length shortens, the contraction is concentric, if the muscle length lengthens, the contraction is eccentric. In natural movements that underlie locomotor activity, muscle contractions are multifaceted as they are able to produce changes in length, therefore, neither length nor tension is likely to remain the same in muscles that contract during locomotor activity. In vertebrates, skeletal muscle contractions are neurogenic as they require synaptic input from neurons to produce muscle contractions. A single motor neuron is able to innervate multiple muscle fibers, once innervated, the protein filaments within each skeletal muscle fiber slide past each other to produce a contraction, which is explained by the sliding filament theory. The contraction produced can be described as a twitch, summation, or tetanus, in skeletal muscles, muscle tension is at its greatest when the muscle is stretched to an intermediate length as described by the length-tension relationship. Unlike skeletal muscle, the contractions of smooth and cardiac muscles are myogenic, the mechanisms of contraction in these muscle tissues are similar to those in skeletal muscle tissues. Muscle contractions can be described based on two variables, force and length, force itself can be differentiated as either tension or load. Muscle tension is the force exerted by the muscle on an object whereas a load is the force exerted by an object on the muscle, when muscle tension changes without any corresponding changes in muscle length, the muscle contraction is described as isometric. If the muscle length changes while muscle tension remains the same, in an isotonic contraction, the muscle length can either shorten to produce a concentric contraction or lengthen to produce an eccentric contraction. Furthermore, if the muscle length shortens, the contraction is concentric, but if the muscle length lengthens, then the contraction is eccentric. In natural movements that underlie locomotor activity, muscle contractions are multifaceted as they are able to produce changes in length, therefore, neither length nor tension is likely to remain constant when the muscle is active during locomotor activity. An isometric contraction of a muscle generates tension without changing length, an example can be found when the muscles of the hand and forearm grip an object, the joints of the hand do not move, but muscles generate sufficient force to prevent the object from being dropped. In isotonic contraction, the tension in the muscle remains constant despite a change in muscle length and this occurs when a muscles force of contraction matches the total load on the muscle. In concentric contraction, muscle tension is sufficient to overcome the load, and this occurs when the force generated by the muscle exceeds the load opposing its contraction. During a concentric contraction, a muscle is stimulated to contract according to the sliding filament theory and this occurs throughout the length of the muscle, generating a force at the origin and insertion, causing the muscle to shorten and changing the angle of the joint

3. Geometry – Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer, Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes. Geometry began to see elements of mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into a form by Euclid, whose treatment, Euclids Elements. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC, islamic scientists preserved Greek ideas and expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid footing by mathematicians such as René Descartes. Since then, and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, while geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, contemporary geometry has many subfields, Euclidean geometry is geometry in its classical sense. The mandatory educational curriculum of the majority of nations includes the study of points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, Euclidean geometry also has applications in computer science, crystallography, and various branches of modern mathematics. Differential geometry uses techniques of calculus and linear algebra to problems in geometry. It has applications in physics, including in general relativity, topology is the field concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, this often means dealing with large-scale properties of spaces, convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues, often using techniques of real analysis. It has close connections to convex analysis, optimization and functional analysis, algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques. It has applications in areas, including cryptography and string theory. Discrete geometry is concerned mainly with questions of relative position of simple objects, such as points. It shares many methods and principles with combinatorics, Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics. The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia, the earliest known texts on geometry are the Egyptian Rhind Papyrus and Moscow Papyrus, the Babylonian clay tablets such as Plimpton 322. For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, later clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiters position and motion within time-velocity space

4. Circle – A circle is a simple closed shape in Euclidean geometry. The distance between any of the points and the centre is called the radius, a circle is a simple closed curve which divides the plane into two regions, an interior and an exterior. Annulus, the object, the region bounded by two concentric circles. Arc, any connected part of the circle, centre, the point equidistant from the points on the circle. Chord, a segment whose endpoints lie on the circle. Circumference, the length of one circuit along the circle, or the distance around the circle and it is a special case of a chord, namely the longest chord, and it is twice the radius. Disc, the region of the bounded by a circle. Lens, the intersection of two discs, passant, a coplanar straight line that does not touch the circle. Radius, a line segment joining the centre of the circle to any point on the circle itself, or the length of such a segment, sector, a region bounded by two radii and an arc lying between the radii. Segment, a region, not containing the centre, bounded by a chord, secant, an extended chord, a coplanar straight line cutting the circle at two points. Semicircle, an arc that extends from one of a diameters endpoints to the other, in non-technical common usage it may mean the diameter, arc, and its interior, a two dimensional region, that is technically called a half-disc. A half-disc is a case of a segment, namely the largest one. Tangent, a straight line that touches the circle at a single point. The word circle derives from the Greek κίρκος/κύκλος, itself a metathesis of the Homeric Greek κρίκος, the origins of the words circus and circuit are closely related. The circle has been known since before the beginning of recorded history, natural circles would have been observed, such as the Moon, Sun, and a short plant stalk blowing in the wind on sand, which forms a circle shape in the sand. The circle is the basis for the wheel, which, with related inventions such as gears, in mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. Some highlights in the history of the circle are,1700 BCE – The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 256/81 as a value of π.300 BCE – Book 3 of Euclids Elements deals with the properties of circles