Image Apollonius theorem.svg thumb right 350px Area of Green Area of Purple Area of Red In geometry , Apollonius theorem is a theorem relating the length of a Median geometry median of a triangle to the lengths of its side. Specifically, in any triangle ABC , if AD is a median, then math AB 2 AC 2 2 AD 2 BD 2 , math It is a special case of Stewart s theorem . For an isosceles triangle the theorem reduces to the Pythagorean theorem . From the fact that diagonals of a parallelogram bisect each other, the theorem is equivalent to the parallelogram law . The theorem is named for Apollonius of Perga . Proof image ApolloniusTheoremProof.svg left thumb Proof of Apollonius theorem The theorem can be proved as a special case of Stewart s theorem, or can be proved using vectors see parallelogram law . The following is an independent proof using the law of cosines. ref Following Godfrey & Siddons ref Let the triangle have sides a , b , c with a median d drawn to side a . Let m be the length of the segments of a formed by the median, so m is half of a . Let the angles formed between a and d be and where includes b and includes c . Then is the supplement of and cos cos . The law of cosines for and states math begin align b 2 & m 2 d 2 2dm cos theta c 2 & m 2 d 2 2dm cos theta & m 2 d 2 2dm cos theta. , end align math Add these equations to obtain math b 2 c 2 2m 2 2d 2 , math as required. See also Stewart s Theorem References reflist cite book title Modern Geometry first1 Charles last1 Godfrey first2 Arthur Warry last2 Siddons publisher University Press year 1908 url http books.google.com books?id LGsLAAAAYAAJ&pg PA20 v onepage page 20 PlanetMath title Apollonius Theorem urlname ApolloniusTheorem DEFAULTSORT Apollonius Theorem Category Euclidean geometry Category Triangle geometry Category Articles containing proofs Category Theorems in plane geometry ar es Teorema de Apolonio fa fr Th or me de la m diane ko hy ... more details
, it has a point of instability in which it can be converted into a parallelogram and vice versa. For both the parallelogram and antiparallelogram linkages, if one of the long edges of the linkage is fixed as a base, the free joints move on equal circles, but in a parallelogram they move in the same ... Parallelogram pages 54 56 url http books.google.com books?id iIN 2WjBH1cC&pg PA54 . ref A pair ... more details
Image ArealVelocity.svg frame Figure 1 Areal velocity is the area shown in green swept out per unit time by a particle moving along a curve shown in blue . Areal velocity sector velocity , sectorial velocity is the rate at which area is swept out by a particle as it moves along a curve . In many applications, the curve lies in a plane, but in others, it is a space curve. The adjoining figure shows a continuously differentiable curve in blue. At time t , a moving particle is located at point B , and at time t t the particle has moved to point C . The area swept out during time period t by the particle is approximately equal to the area of triangle ABC . As t approaches zero this near equality becomes exact as a limit of a function limit . The vectors AB and AC add up by the parallelogram rule to vector AD , so that point D is the fourth corner of parallelogram ABDC shown in the figure. The area of triangle ABC in green is half the area of parallelogram ABDC , and the area of ABDC is equal to the magnitude of the cross product of vectors AB and AC . One may form a vector whose magnitude is the area ABCD , and which is perpendicular to the parallelogram ABCD . Then, math operatorname vector ,area ABDC vec r t times vec r t Delta t . math Hence, math operatorname vector ,area ABC vec r t times vec r t Delta t over 2 Delta vec A . math The areal velocity vector is math frac d vec A d t lim Delta t rightarrow 0 Delta vec A over Delta t lim Delta t rightarrow 0 vec r t times vec r t Delta t over 2 Delta t math math lim Delta t rightarrow 0 vec r t times vec r t vec r , t Delta t over 2 Delta t math math lim Delta t rightarrow 0 vec r t times vec r , t over 2 left Delta t over Delta t right math math vec r t times vec r , t over 2 . math But, math vec r , t math is the velocity vector math vec v t math of the moving particle, so that math frac d vec A d t vec r times vec v over 2 . math Image kepler second law.gif right thumb Figure 3 Illustration of Kepler s second law. ... more details
File BerlinMusPap11529v.jpg thumb 200px Fragment of a 2nd century Greek mathematical text Berlin, Staatliche Museen, pap. 11529 is a fragment of 2nd century papyrus manuscript containing an unidentified Greek language Greek mathematics mathematical text and is one of the oldest extant illustrated Greek papyrus roll fragments. One side of the fragment contains a property deed dated 138. The other side contains two columns of text which consists of a series of Geometry geometrical and Stereometry stereometrical Proposition mathematics proposition s. Each proposition is illustrated with a crudely drawn diagram. Several lines of text in each proposition were left shorter than the remainder of the text lines in order to leave space in the right of the column for the illustrations. The left column has a parallelogram , and two right angled triangle s, while the right has an equilateral triangle, a stone, and two concentric circle s. References Kurt Wetizmann, Illustrations in Roll and Codex A study in the method of text illustration Princeton Princeton University Press, 1970 , pg. 48 Further reading W. Schubart, Mathematische Aufgaben auf Papyrus , Amtl. Berichte der Berliner Museen , XXXVII, 1915 1916. sci hist stub AncientGreece stub Category Papyri of the Staatliche Museen zu Berlin ... more details
Image with unknown copyright status removed Image 1sbc1.jpg thumb 250px right SBC Publishing Building The SBC Publishing Building is a tall office building in Troy, Michigan . It is located at 100 E. Big Beaver Road, The high rise was built in 1981 and finished in 1983. It stands at 16 stories in total height, with 15 above ground floors, and 1 basement floor. Official measurements state that the building stands 207ft 63m in total height. The building is used as offices for SBC Communications SBC , and was designed in the modern architecture modern architectural style . Description Owner Management Redico Real Estate Development REDICO This building is shaped like a parallelogram . External links http maps.google.com maps?f q&hl en&q 100 E Big Beaver Road Troy MI&ie UTF8&z 17&ll 42.562199, 83.146146&spn 0.004481,0.013497&t k&om 1 Google Maps location of the SBC Publishing Building http www.emporis.com en wm bu ?id 128946 SBC Publishing Building details at Emporis.com http www.skyscraperpage.com cities ?buildingID 40587 SkyscraperPage.com s Profile on SBC Publishing Building coord 42.5622 83.1461 type landmark source enwiki googlemaplink display title Category Skyscrapers in Troy, Michigan Category Buildings and structures completed in 1983 Michigan struct stub ... more details
orphan date January 2010 Unreferenced date September 2007 Image with unknown copyright status removed Image Mappp.gif thumb right speedy image c 2007 05 29 Targeting towers use a special device to ensure an Antenna radio antenna s stability when strong wind blows. This system is based on the geometrical properties of the parallelogram . Three vertical rods are used to maintain the top platform horizontal when the tower bends under the structural load wind effect . The top platform is pin connected to the mast, thanks to a special mechanical link based on universal joint system. The system allows to reduce the size and the weight of the towers, because contrary to standard poles, stiffness is not needed. In standard tower s, the antenna beam s rotation must not exceed a certain angle currently between 0.5 and 2 , otherwise the communication is cut. This design criterion is more severe than the resistance criteria and leads to use twice the steel quantity. Targeting towers have been used for the first time in 2004 in Italy for high radar supporting poles . Specific tests have been led on a tower test platform in Livorno Italy . The test used 2 cameras filming simultaneously a target meanwhile the pole was submitted to dynamic oscillations. One being fixed on the pole and the other on the top platform. The results of this test are shown on an external website http map3.net mappp english video.html . DEFAULTSORT Targeting Tower Category Radio frequency antenna types fr M t pendulaire pointage parall le ... more details
Use dmy dates date April 2012 unreferenced date February 2008 Image Zijlpoort2010JuneEarly.jpg thumb right 250px Zijlpoort Image Zijlpoort en brug Leiden.jpg thumb right 250px Zijlpoort Zijlpoort is a city gate in Leiden , The Netherlands. The gate was built in 1667 in the classical style according to a design by the Leiden architect Willem van der Helm and with sculpture by Rombout Verhulst . Because the gates have to connect with the city wall as well as with a bridge, the building is in the form of a parallelogram . Together with the Morspoort, the Zijlpoort is the only one of the original eight gates that survive. The name refers to the nearby river, the Zijl . The predecessor of the Zijlpoort stood at the end of the Haarlemmerstraat that is now called the Havenplein. In the course of time, the Zijlpoort has, together with the hall above the passage, fulfilled different purposes over time for example, at the beginning of the 18th century, a shipping company was based there, and from 1736 there was a school for poor children. In the last quarter of the 20th century, the Zijlpoort was renovated twice on a large scale. During the last renovation, in the 1990s, supporting constructions were put up on both sides of the gate. Since 1999, a catering shop has been established in one of them. coord 52 09 42 N 4 30 15 E display title region NL type landmark source nlwiki Category Gates Category Buildings and structures in Leiden Category Buildings and structures completed in 1667 nl Zijlpoort Leiden ... more details
File Stadttor Duesseldorf.jpg thumb D sseldorf Stadttor in 2004 Stadttor meaning City gate in German is a convert 72.55 m ft tall building in D sseldorf Unterbilk , and a prominent landmark in D sseldorf . The building was designed by D sseldorf based architecture firm Petzinka, Overdiek und Partner and completed in 1998. It marks the Southern entrance of Rheinufertunnel , which is also reason for its parallelogram shaped floor plan. The building features a 15 story tall atrium and a double facades, allowing natural ventilation even at high altitude floors. The total gross floor area is some 30.000 m . ref http www.duesseldorf.de planung hafen einzelprojekte 03 stadttor.shtml Stadttor duesseldorf.de ref Since 1999, the Stadttor is seat of the state chancellery of the Prime ministers of North Rhine Westphalia . See also List of tallest buildings in Germany References references External links commonscat Stadttor D sseldorf structurae s0002513 coord 51 12 55 N 6 45 40 E region DE type landmark display title Category Buildings and structures completed in 1998 Category Buildings and structures in D sseldorf Category Skyscrapers in Germany Category Skyscrapers between 50 and 99 meters Category High tech architecture NorthRhineWestphalia struct stub de Stadttor D sseldorf ru ... more details
orphan date December 2011 Geometric shapes This is a short list of some common mathematical shapes and figures and the formulas that describe them. Two dimensional shapes class wikitable Shape Area Perimeter Circumference Rectangle A l w P 2l 2w Circle A math r 2 math C 2 r Ellipse where a is the semimajor axis and b is the semiminor axis A a b Triangle A b h P a b c Parallelogram b base, h height, a side A b h P 2a 2b Trapezoid where a and b are the bases A a b h ref http www.austincc.edu tutor students resources Geometry.pdf ref ref http www.math.com tables geometry areas.htm ref Three dimensional shapes class wikitable Shape Volume Surface area Cube math V s 3 math math 6s 2 math Rectangular Prism l length, h height, w width V l w h S 2lw 2l h 2 wh Sphere V math 4 3 math math r 3 math 4 math r 2 math Right Circular Cylinder V math r 2 math h S 2 rh 2 math r 2 math ref http www.math.com tables geometry volumes.htm ref References references geometry stub Category Elementary geometry ... more details
italic title Taxobox name Argyresthia pedmontella image Argyresthia pedmontella.JPG image caption Wing image2 regnum Animal ia phylum Arthropod a classis Insect a ordo Lepidoptera familia Yponomeutidae subfamalia Argyresthiinae genus Argyresthia species A. pedmontella binomial Argyresthia pedmontella binomial authority Chambers, 1877 ref http mothphotographersgroup.msstate.edu species.php?hodges 2469 mothphotographersgroup ref synonyms Argyresthia pedmontella is a moth of the Yponomeutidae family. It is found in North America , including Colorado . The wingspan is about 13 mm. The forewings are white, strongly suffused with dark brown on the costal and apical parts. The dorsal part below the fold is only slightly sprinkled with dark scales. There is an irregular series of darker brown spots intervened by pure white dashes on the costal edge from the basal third to the apex. Around the apex and along the base of the dorsal cilia, a thin blackish brown line is found. Furthermore, there is large, oblique, dark brown spot shaped like a parallelogram on the middle of the dorsal edge, reaching across the light dorsal area to the more densely dusted costal part. The hindwings are light fuscous. ref http si pddr.si.edu dspace bitstream 10088 13945 1 USNMP 32 1506 1907.pdf Revision Of The American Moths Of The Genus Argyresthia ref References Reflist Category Animals described in 1877 Category Argyresthia Yponomeutidae stub ... more details
n parallelotope. Thus a parallelogram is a 2 parallelotope and a parallelepiped is a 3 parallelotope ... ed. New York Dover, p. 122, 1973. He define parallelotope as a generalization of a parallelogram ... more details
This is a list of two dimensional geometric shape s. For objects in three or more dimensions, see list of polygons, polyhedra and polytopes and list of mathematical shapes . Generally composed of straight line segments main Polygon concave polygon constructible polygon convex polygon cyclic polygon equiangular polygon equilateral polygon regular polygon Penrose tile Polyform balbis Polygons with specific numbers of sides henagon 1 sided digon 2 sided triangle acute triangle equilateral triangle isosceles triangle obtuse triangle rational triangle right triangle 30 60 90 triangle isosceles right triangle Kepler triangle scalene triangle quadrilateral cyclic quadrilateral Square geometry square kite geometry kite parallelogram rhombus equilateral parallelogram Lozenge rhomboid rectangle square geometry square regular quadrilateral tangential quadrilateral trapezoid or trapezium isosceles trapezoid pentagon regular pentagon hexagon Lemoine hexagon heptagon octagon regular octagon nonagon decagon regular decagon hendecagon dodecagon hexadecagon icosagon swastika Star polygon star without crossing lines star polygon hexagram star of David heptagram octagram star of Lakshmi Decagram geometry decagram pentagram Curved annulus mathematics annulus arbelos circle disk mathematics disc Archimedes twin circles Bankoff circle circumcircle excircle incircle nine point circle circular sector circular segment crescent ellipse various Lemniscate disambiguation lemniscate s Lune mathematics lune Oval geometry oval Reuleaux polygon Reuleaux triangle lens geometry lens , vesica piscis fish bladder salinon semicircle sphere tomoe , magatama triquetra Yin Yang Not composed of circular arcs Archimedean spiral astroid deltoid curve deltoid ellipse super ellipse tomahawk geometric shape tomahawk See also Glossary of shapes with metaphorical names List of curves List of triangle topics List of circle topics List of surfaces List of geometric surfaces Cuisenaire rods Unicode Geometric Shapes ... more details
In geometry , the Japanese theorem states that no matter how one polygon triangulation triangulates a Circumscribed circle cyclic polygon , the sum of inradius inradii of triangle s is Constant mathematics constant . class wikitable style width 320px valign top Image Japanese theorem 1.jpg 310px style width 320px valign top Image Japanese theorem 2.jpg 310px colspan 2 align center sum of the radii of the green circles sum of the radii of the red circles Conversely, if the sum of inradii independent from the triangulation, then the polygon is cyclic. The Japanese theorem follows from the Carnot s theorem it is a Sangaku problem . This theorem also follows from a simple extension of the Japanese theorem for cyclic quadrilaterals . That theorem shows that a rectangle is formed by the two pairs of incenters corresponding to the two possible triangulations of the quadrilateral. The steps of this theorem require nothing beyond basic constructive Euclidean geometry. With the additional construction of a parallelogram having sides parallel to the diagonals, and tangent to the corners of the rectangle of incenters, the quadrilateral case of the concyclic polygon theorem can be proved in a few steps. The equality of the sums of the radii of the two pairs is equivalent to the condition that the constructed parallelogram be a rhombus, and this is easily shown in the construction. Also, it s readily shown that the quadrilateral case suffices to prove the general case of the concyclic polygon theorem. The quadrilateral rule can be applied to quadrilateral components of a general partition of a cyclic polygon, and repeated application of the rule, which flips one diagonal, will generate all the possible partitions from any given partition, with each flip preserving the sum of the inradii. Hence the concyclic polygon theorem considered here can be regarded as a corollary of the extended cyclic quadrilateral theorem. See also Carnot s theorem , which is used in a proof of the theore ... more details
About history and other uses gnomon Unreferenced date December 2009 File gnomon.svg thumb right 200px A gnomon In geometry , a gnomon is a plane figure formed by removing a similarity geometry similar parallelogram from a corner of a larger parallelogram. More generically, the term gnomon denotes the form that is to be added to a figure to produce a larger figure of the same shape. Building figurative numbers Figurate numbers were a concern of Pythagoras Pythagorean geometry , since Pythagoras is credited with initiating them, and the notion that these numbers are generated from a gnomon or basic unit. The gnomon is the piece which needs to be added to a figurate number to transform it to the next bigger one. For example, the gnomon of the square number is the odd number , of the general form 2 n 1, n 1, 2, 3, ... . The square of size 8 composed of gnomons looks like this br cellpadding 2 align center 8 8 8 8 8 8 8 8 8 7 7 7 7 7 7 7 8 7 6 6 6 6 6 6 8 7 6 5 5 5 5 5 8 7 6 5 4 4 4 4 8 7 6 5 4 3 3 3 8 7 6 5 4 3 2 2 8 7 6 5 4 3 2 1 To transform from the n square the square of size n to the n 1 square, one adjoins 2 n 1 elements one to the end of each row n elements , one to the end of each column n elements , and a single one to the corner. For example, when transforming the 7 square to the 8 square, we add 15 elements these adjunctions are the 8s in the above figure. Note that this gnomonic technique also provides a mathematical proof proof that the sum of the first n odd numbers is n sup 2 sup the figure illustrates nowrap 1 3 5 7 9 11 13 15 64 8 sup 2 sup . See also Golden triangle mathematics Golden gnomon Golden gnomon Pythagorean Pythagorean triple Figurate number DEFAULTSORT Gnomon Figure Category Figurate numbers geometry stub ... more details
motion of one pen to the other. The pantograph consists of two complete variable parallelogram s. Base parallelogram The base parallelogram is attached to two fixed pivot points at the far side ... and this part remains in a plane parallel to the base. Extension parallelogram The extension parallelogram is attached to the base parallelogram by pivots that allow the pen side edge to be lifted away from the base. Decending pantograph A second pair of parallelogram links maintains vertical correspondence between the two pens. These consist of two variable parallelogram frames attached at a common ... more details
fretboard s with double parallelogram inlays, crown peghead inlay on headstock s, gold tuners ... to double parallelogram in 1984. Modern Classic model The Hummingbird Modern Classic model is an electric ... from mahogany, as well as rosewood fretboard with double parallelogram inlays, crown peghead ... parallelogram ones. It also has adjustable saddle and an original 60 s style hummingbird pickguard ... more details
scale identified by the feature detector, and the green parallelogram is constructed from the coordinates ... gradient direction of the ellipse, converts the ellipse into a parallelogram, and takes a Scale invariant feature transform SIFT descriptor on the resulting parallelogram. Color information is used also ... system of the feature parallelogram also correspond, as do the points 0, 1 in the parallelogram ... more details
Infobox Polygon name Rectangle image Rectangle example.svg caption type quadrilateral , parallelogram , orthotope edges 4 symmetry D sub 2 sub , 2 , 22 schl fli wythoff coxeter CDD node 1 2 node 1 area dual rhombus properties convex , isogonal figure isogonal , Cyclic polygon cyclic In Euclidean geometry Euclidean plane geometry , a rectangle is any quadrilateral with four right angle s. Another name is equiangular quadrilateral , since equiangular means that all of its angles are equal 360 4 90 . It can also be defined as a parallelogram containing a right angle. The term wikt oblong oblong is occasionally used to refer to a non square rectangle. ref http www.mathsisfun.com definitions oblong.html Definition of Oblong . Mathsisfun.com. Retrieved 2011 11 13. ref ref http www.icoachmath.com SiteMap Oblong.html Oblong Geometry Math Dictionary . Icoachmath.com. Retrieved 2011 11 13. ref A rectangle with Vertex geometry vertices ABCD would be denoted as rectanglenotation ABCD . The word rectangle comes from the Latin rectangulus , which is a combination of rectus right and angulus angle . A so called crossed rectangle is a crossed self intersecting quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals. ref Cite journal doi 10.1098 rsta.1954.0003 last1 Coxeter first1 Harold Scott MacDonald author1 link Harold Scott MacDonald Coxeter last2 Longuet ... 763 2 pages 53 ref a parallelogram with at least one right angle an equiangular parallelogram a parallelogram with diagonals of equal length a parallelogram ABCD where triangles ABD and DCA are congruent ... hierarchy A rectangle is a special case of a parallelogram in which each pair of adjacent sides is perpendicular. A parallelogram is a special case of a trapezium known as a trapezoid in North America ... diagonals form a rectangle. A parallelogram with equal diagonals is a rectangle. The Japanese ... can be a parallelogram or a trapezoid trapezoid trapezium . these 2D figures ARE planar, not non ... more details
and using the odd plastic part he jumped in up to his neck and made the entire parallelogram both knuckles and both parallelogram plates out of polyoxymethylene which Du Pont branded as Delrin ... more details
types of quadrilaterals. UK denotes British English and US denotes American English. A parallelogram ... over square including a square . Rhomboid a parallelogram in which adjacent sides are of unequal lengths ... a square is a parallelogram , that the diagonals perpendicularly bisect each other, and are of equal ... quadrilaterals are the antiparallelogram s, crossed quadrilaterals in which like a parallelogram ... quadrilateral, the latter formula becomes math K tfrac 1 2 ad bc sin A . math In a parallelogram ... a 2 c 2 b 2 d 2 right . math In the case of a parallelogram, the latter formula becomes math K tfrac ... s quadrilateral theorem and is a generalization of the parallelogram law . Leonhard Euler Euler also ... 2011 . ref Bimedians Image Varignon theorem convex.png 300px thumb The Varignon parallelogram EFGH The midpoint s of the sides of a quadrilateral are the vertices of a parallelogram called the Varignon s theorem Varignon parallelogram . The sides in this parallelogram are half the lengths of the diagonals of the original quadrilateral, the area of the Varignon parallelogram equals half the area of the original quadrilateral, and the perimeter of the Varignon parallelogram equals the sum of the diagonals of the original quadrilateral. The diagonals of the Varignon parallelogram are the Quadrilateral ... p.126 math displaystyle p 2 q 2 2 m 2 n 2 . math This is also a corollary to the parallelogram law applied in the Varignon parallelogram. The length of the bimedians can also be expressed in terms of two ... nb10 Isosceles trapezoid Kite geometry Kite Orthodiagonal quadrilateral col break Parallelogram ... more details
Image Supplementary angles2.svg right 250px thumb A pair of supplementary angles wiktionarypar supplementary Merge Complementary angles Vertical angles Adjacent angles Transversal geometry target Special angle relationships discuss Talk Vertical angles Merge? date December 2011 Supplementary angles are pairs of angle s that add up to 180 Degree angle degrees . Thus the supplement of an angle of x degrees is an angle of 180 x degrees. If the two supplementary angles are adjacent angles adjacent i.e. have a common vertex geometry vertex and share just one side , their non shared sides form a line geometry straight line . However, supplementary angles do not have to be on the same line, and can be separated in space. For example, adjacent angles of a parallelogram are supplementary, and opposite angles of a cyclic quadrilateral one whose vertices all fall on a single circle are supplementary. If a point P is exterior to a circle with center O, and if the tangent lines to circles tangent lines from P touch the circle at points T and Q, then TPQ and TOQ are supplementary. Trigonometric ratios The sine s of supplementary angles are equal. Their cosine s and tangent s unless undefined are equal in magnitude but have opposite signs. See also Complementary angles External links http www.mathopenref.com anglesupplementary.html Animated demonstration Interactive applet and explanation of the characteristics of supplementary angles. http www.mathopenref.com tocs anglestoc.html Angle definition pages with interactive applets that are also useful in a classroom setting. Math Open Reference Category Angle Category Elementary geometry Elementary geometry stub ar ast ngulos suplementarios bg ca Angles suplementaris et K rvunurgad eo Suplementaj anguloj es ngulos suplementarios fa fi Suplementtikulmat fr Angles suppl mentaires he it Angolo supplementare mk no Supplementvinkler pl K ty przyleg ... more details
This is a list of mathematical topics in classical mechanics , by Wikipedia page. See also list of variational topics , correspondence principle . Newtonian physics Newton s laws of motion Inertia , point mass Kinematics , rigid body Momentum , kinetic energy Parallelogram of force Circular motion Rotational speed Angular speed Angular momentum torque angular acceleration moment of inertia parallel axes rule perpendicular axes rule stretch rule centripetal force , centrifugal force fictitious centrifugal force , Reactive centrifugal force Laplace Runge Lenz vector Euler s disk elastic potential energy Mechanical equilibrium D Alembert s principle Degrees of freedom physics and chemistry Frame of reference Inertial frame of reference Galilean transformation Principle of relativity Conservation law s Conservation of momentum Conservation of linear momentum Conservation of angular momentum Conservation of energy Potential energy Conservative force Conservation of mass Law of universal gravitation Projectile motion Kepler s laws of planetary motion Escape velocity Potential well Weightlessness Lagrangian point N body problem Kolmogorov Arnold Moser theorem Virial theorem Gravitational binding energy Speed of gravity Newtonian limit Hill sphere Roche lobe Roche limit Hamiltonian mechanics Phase space Symplectic manifold Liouville s theorem Hamiltonian Poisson bracket Poisson algebra Poisson manifold Antibracket algebra Hamiltonian constraint Moment map Contact geometry Analysis of flows Nambu mechanics Lagrangian mechanics Action physics Lagrangian Euler Lagrange equations Noether s theorem Category Mathematics related lists Classical mechanics ... more details
pair. Each pair a , b defines a parallelogram, all with the same area, the magnitude of the cross product . One parallelogram fully defines the whole object. Without further symmetry, this parallelogram ... domain or set of two of them than a parallelogram consisting of part of a tile and part ... more details
Merge from List of geometry topics date September 2011 The following outline is provided as an overview of and topical guide to geometry Geometry &ndash branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Essence of geometry Main Geometry History of geometry Main History of geometry General geometry concepts General concepts Geometric progression Geometric shape Geometry Pi angular velocity velocity linear velocity De Moivre s theorem parallelogram rule Pythagorean theorem similar triangles trigonometric identity unit circle Trapezoid Triangle Theorem point geometry point line mathematics Ray ray plane mathematics plane line mathematics line line segment Measurements bearing navigation Bearing Angle degree angle Degree minute of arc Minute Radian Circumference Diameter Trigonometric functions Trigonometric function Asymptotes Circular functions Periodic functions Law of cosines Law of sines Vectors Main vector geometric Amplitude Dot product Norm mathematics also known as magnitude Position vector Scalar multiplication Vector addition Zero vector Vector spaces and complex dimensions Complex plane Imaginary axis Linear interpolation One to one Orthogonal Polar coordinate system Pole complex analysis Pole Real axis Secant CIrcular sector or sector Semiperimeter Lists List of mathematical shapes List of differential geometry topics List of geometers list of curves list of curve topics See also Portal Geometry List of basic mathematics topics List of mathematics articles Table of mathematical symbols Further reading cite book last Rich first Barnett title Schaum s Outline of Geometry edition 4th publisher McGraw Hill location New York year 2009 isbn 9780071544122 External links outline footer Sister project links Geometry Category Outlines Geometry Category Geometry Category Mathematics related lists Geometry ... more details
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