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Circumference
In geometry, the circumference (from Latin circumferentia, meaning "carrying around") of a circle is the (linear) distance around it.[1] That is, the circumference would be the length of the circle if it were opened up and straightened out to a line segment. Since a circle is the edge (boundary) of a disk, circumference is a special case of perimeter.[2] The perimeter is the length around any closed figure and is the term used for most figures excepting the circle and some circular-like figures such as ellipses
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Inscribed Figure
In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid. To say that "figure F is inscribed in figure G" means precisely the same thing as "figure G is circumscribed about figure F". A circle or ellipse inscribed in a convex polygon (or a sphere or ellipsoid inscribed in a convex polyhedron) is tangent to every side or face of the outer figure (but see Inscribed sphere
Inscribed sphere
for semantic variants). A polygon inscribed in a circle, ellipse, or polygon (or a polyhedron inscribed in a sphere, ellipsoid, or polyhedron) has each vertex on the outer figure; if the outer figure is a polygon or polyhedron, there must be a vertex of the inscribed polygon or polyhedron on each side of the outer figure
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Chudnovsky Brothers
David Volfovich Chudnovsky (born 1947 in Kiev) and Gregory Volfovich Chudnovsky (born 1952 in Kiev) are American mathematicians and engineers known for their world-record mathematical calculations and developing the Chudnovsky algorithm used to calculate the digits of π with extreme precision. Careers in mathematics[edit] A 1992 article in The New Yorker
The New Yorker
quoted the opinion of several mathematicians that Gregory Chudnovsky is one of the world's best living mathematicians. David Chudnovsky works closely with and assists his brother Gregory, who has myasthenia gravis.[1] The Chudnovsky brothers have held records, at different times, for computing π to the largest number of places, including two billion digits in the early 1990s on a supercomputer they built (dubbed "m-zero") in their apartment in Manhattan
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Concentric Circle
In geometry, two or more objects are said to be concentric, coaxal, or coaxial when they share the same center or axis. Circles,[1] regular polygons[2] and regular polyhedra,[3] and spheres[4] may be concentric to one another (sharing the same center point), as may cylinders[5] (sharing the same central axis).Contents1 Geometric properties 2 Applications and examples 3 See also 4 References 5 External linksGeometric properties[edit] In the Euclidean plane, two circles that are concentric necessarily have different radii from each other.[6] However, circles in three-dimensional space may be concentric, and have the same radius as each other, but nevertheless be different circles. For example, two different meridians of a terrestrial globe are concentric with each other and with the globe of the earth (approximated as a sphere)
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Circumscribed Circle
In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. A polygon which has a circumscribed circle is called a cyclic polygon (sometimes a concyclic polygon, because the vertices are concyclic). All regular simple polygons, all isosceles trapezoids, all triangles and all rectangles are cyclic. A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it
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Semi-major And Semi-minor Axes
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the widest points of the perimeter. The semi-major axis is one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter
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Christoph Grienberger
Christoph (Christophorus) Grienberger (also variously spelled Gruemberger, Bamberga, Bamberger, Banbergiera, Gamberger, Ghambergier, Granberger, Panberger) (2 July 1561 – 11 March 1636) was an Austrian Jesuit astronomer, after whom the crater Gruemberger on the Moon
Moon
is named.Catalogus veteres affixarum longitudines, ac latitudines conferens cum novis, 1612Contents1 Biography 2 See also 3 References 4 Sources 5 External linksBiography[edit] Born in Hall in Tirol, in 1580 Christoph Grienberger
Christoph Grienberger
joined the Jesuits
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Archimedes
Archimedes
Archimedes
of Syracuse (/ˌɑːrkɪˈmiːdiːz/;[2] Greek: Ἀρχιμήδης; c. 287 – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer.[3] Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Generally considered the greatest mathematician of antiquity and one of the greatest of all time,[4][5] Archimedes
Archimedes
anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola.[6] Other mathematical achievements include deriving an accurate approximation of pi, defining and investigating the spiral bearing his name, and creating a system using exponentiation for expressing very large numbers
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Ratio
In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.[1] For example, if a bowl of fruit contains eight oranges and six lemons, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7). The numbers in a ratio may be quantities of any kind, such as quantities of persons, objects, lengths, weights, etc. A ratio may be either a whole number or a fraction. A ratio may be written as "a to b" or a:b, or it may be expressed as a quotient of "a and b".[2] When the two quantities are measured with the same unit, as is often the case, their ratio is a dimensionless number
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Greek Letter
The Greek alphabet
Greek alphabet
has been used to write the Greek language
Greek language
since the late 9th century BC or early 8th century BC.[3][4] It was derived from the earlier Phoenician alphabet,[5] and was the first alphabetic script to have distinct letters for vowels as well as consonants. It is the ancestor of the Latin and Cyrillic scripts.[6] Apart from its use in writing the Greek language, in both its ancient and its modern forms, the Greek alphabet
Greek alphabet
today also serves as a source of technical symbols and labels in many domains of mathematics, science and other fields. In its classical and modern forms, the alphabet has 24 letters, ordered from alpha to omega
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Constant (mathematics)
In mathematics, the adjective constant means non-varying. The noun constant may have two different meanings. It may refer to a fixed and well-defined number or other mathematical object. The term mathematical constant (and also physical constant) is sometimes used to distinguish this meaning from the other one. A constant may also refer to a constant function or its value (it is a common usage to identify them)
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Unit Circle
In mathematics, a unit circle is a circle with a radius of one. Frequently, especially in trigonometry, the unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. The unit circle is often denoted S1; the generalization to higher dimensions is the unit sphere. If (x, y) is a point on the unit circle's circumference, then x and y are the lengths of the legs of a right triangle whose hypotenuse has length 1. Thus, by the Pythagorean theorem, x and y satisfy the equation x 2 + y 2 = 1. displaystyle x^ 2 +y^ 2 =1
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Regular Polygon
Regular polygonsEdges and vertices nSchläfli symbol n Coxeter–Dynkin diagramSymmetry group Dn, order 2nDual polygon Self-dualArea (with side length, s) A = 1 4 n s 2 cot ⁡ ( π n ) displaystyle A= tfrac 1 4 ns^ 2 cot left( frac pi n right) Internal angle ( n − 2 ) × 180 ∘ n displaystyle (n-2)times frac 180^ circ n Internal angle
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Limit (mathematics)
In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value.[1] Limits are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. In formulas, a limit is usually written as lim n → c f ( n ) = L displaystyle lim _ nto c f(n)=L and is read as "the limit of f of n as n approaches c equals L". Here "lim" indicates limit. The fact that function f(n) approaches the limit L as n approaches c is represented by the right arrow (→), as in f ( n ) → L   . displaystyle f(n)to L
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Edge (geometry)
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.[1] In a polygon, an edge is a line segment on the boundary,[2] and is often called a side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces meet.[3] A segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal.Contents1 Relation to edges in graphs 2 Number of edges in a polyhedron 3 Incidences with other faces 4 Alternative terminology 5 See also 6 References 7 External linksRelation to edges in graphs[edit] In graph theory, an edge is an abstract object connecting two graph vertices, unlike polygon and polyhedron edges which have a concrete geometric representation as a line segment
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Line Segment
In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. Examples of line segments include the sides of a triangle or square. More generally, when both of the segment's end points are vertices of a polygon or polyhedron, the line segment is either an edge (of that polygon or polyhedron) if they are adjacent vertices, or otherwise a diagonal
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