What are the uses of an ellipse?
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1. planetary orbits are ellipses\n2. the earth is an ellipsoid shape\n3. whispering galleries are ellipses\n4. machines use elliptical gears\n5. optical aberrations in telescopes and microscopes can be elliptical\n6. satellite orbits are ellipses\n7. the motion of particles in the ocean travel in  elliptical paths when a waves passes\n8. Rayleigh waves (from earthquakes) on the surface of the earth cause the particles on the surface to travel in retrograde elliptical paths. \n9. elliptical trainers use ellipses to make it easier to pedal\n10. focussing spherical acoustic waves by an elliptical reflector to break up kidney stones (see ref). \n11. ultrasonic motors for microsurgery (see ref.)\n12. confidence ellipse in statistics (see ref.)
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Tesselations are patterns of shapes that fill a surface.\n\nThe first poster is wrong.  They are not useless.\n\n3D computer games and 3D animation movies use tesselated surfaces of polygons to represent the shape of characters, objects, and surroundings.\n\nTesselated surfaces are also used in 3D modeling of surfaces of objects in CAD/CAM when designing products for manufacture.\n\nTesselations are also used to subdivide surfaces for mathematical analysis and simulations.\n\nThey are also used in Art.  M.C. Escher is famous for his tessellations.\nhttp://www.mcescher.com/\nhttp://www.mcescher.com/Gallery/gallery-symmetry.htm
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List is a bit long, so heres the link:\nhttp://en.wikipedia.org/wiki/List_of_geometric_shapes
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I asked that same question to my teacher last time. She told me that I have to Seperated the shape into different common shapes. (for example like lets say I wanted to seperate a "square" into some common shapes I could turn it into two seperate triangles or four different triangles. Well Just try to use the formulas you know for the areas of the different disected figures you get.
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Depending on your grade\n1- Determine the points of maximum and minimum values for your function ( using differential calculus)\n2- Determine the points of inflection \n3- Determine the  increasing and decreasing intervals\n4- Determine the  convex and concave intervals\n5- Get the points of intersection with x,y axis\n6- Get more points around the critical points you get\n7- Sketch the curve using all points you get
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You're referring to the use of ellipses (...) Just so you know, it's typically three periods at a time.\n\nI occasionally use them to highlight an incomplete or trailing thought.  I think they are an effective literary tool, but I wouldn't overuse them or people will think you don't have anything concrete to say.
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Area of rectangle = length x width \nArea of a circle = pi x R x R = pi R^2 where pi~3.14 and R - radius\nArea of an ellipse = pi x a x b see http://www.tpub.com/content/engineering/14069/css/14069_33.htm \n\nVolume = area of the base times hight\nVolume of a rectangular prism= area of rectangle x height = length x width x height\nVolume of a sphere = (4/3)pi x R x R x R = (4/3)pi x R^3\n \nCheck math tables or the web for equation of other geometric figures \n\nPercentage = 100 x (partial amount) / (total amount)\n\nHave fun
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Well, there are two kinds.\nOne is for orienteering.  It has a needle that points north.\nThe other is for drawing circles.  It is like an inverted "V".  One end has a point that is the center of the circle and the other end has a pencil attached to draw the circle.
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If your curve is the upper half of an ellipse, then when you rotate it, you have half an ellipsoid.\n\nWikipedia has the formula for the surface are of an ellipsoid, which (surprize!) involve eliptic integrals.
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because they are mutually perpendicular and the ellipse is symmetrical about both
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if you are asking .. how to sketch an eclipse ... take two verticies (two spots some distance apart left to right on a page) ... and using a compass play with intersecting the radius' of different lengths ... you will find that if you pick the one of equal length as the distance from the vertices ... you will get an intersection of the two radius' from the original vertices ... then playing with the new found radius' ... you will be able to place arcs on the ajoining vertices to creat the other two arcs and blend them together creating an approximate elipse ... a french curve help too
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The Capitol in Washington D.C. has a ceiling that follows an elliptical curve.  It is over the original senate chamber.\nThe nature of an ellipse is that the sum of the distances from the two focal points remains constant.  Also, the angles between rays from the foci to the curve will be equal.\nThe guys who built the senate chamber used those principles to create 2 focal points on the senate floor.  If you are sitting at one focal point, you can hear another person at the other focal point as clearly as if he/she is whispering in your ear.\nbtw. race tracks are ovals, not ellipses.
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There is no simple formula for the perimeter of an ellipse. The exact value is given by an ELLIPTIC INTEGRAL OF THE SECOND TYPE -- in the past people used extensive tables to find approximate answers, but today one gets greater accuracy using a calculator to approximate the integral. When the ellipse has semi-axes of length a and b (so that its equation is x^2/a^2 + y^2/b^2 = 1\nA simple approximate formula for perimetre is\n2pi*sqrt[(a^2+b^2)/2]
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One of the best approximation( range -0.04%) is obtained from the following formula,\nP = pi* (a+b) [ 1 + 3h / ( 10+ (4-3h)^(1/2) ) ]\nWhere h= (a-b)^2/(a + b)^2\nThis was Ramanujan's second formula \n\nLindler's formula has an error range of - 0.598%\nit states,\nP = pi* (a+b) [ 1 + h/8 ]^ 2\n\nHudson's formula gives an error range of -0.19%\naccording to this,\n\nP= pi* (a+b) (64 - 3 h^2)/(64 - 16 h)\nA more precise Padé approximant consists of the optimized ratio of two quadratic polynomials of h and leads to the following formula, credited to Jacobsen and Waadeland (1985). This expression gives a relative error for the perimeter of a round ellipse (low e) roughly equal to -33 e^20/2^38 and a relative error of about -0.0888 % for a flat ellipse. This is directly comparable with the accuracy of Ramanujan's second formula , which is 5.5 times better for the circumference of a round ellipse [and about 2.2 times better for a flat ellipse\n P =pi (a+b)(256 - 48 h - 21 h^2)/(256 - 112 h + 3 h^2)\n   \nThere are many other such formulae. Try these links
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Use it as a serving tray,\nUse it as an exercising item,\nUse is for Candid Camera type situations,\nUse it for hiding credit cards,\nUse it for computing, internet, email, TV, DVD player, MP3 Player -if its working.
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Hi,\n\nThe circle is also called envelope or enclosure. It has the functions defined here: http://www.kodkodkod.com/files/symbolenvelope.htm\n\nFor a BJT transistor, the envelope can serve the purposes mentioned in 1) 2) and 4). However, it is not really necessary to have the "circle" if 1),2) and 4) are not required. Indeed in many college textbooks and research publications in IEEE, people just omit the circle.\n\nPlease bear in mind that circuit symbol is the mean to represent the circuit in a readable way. Therefore, if the circle helps you to present the circuit, then use it (e.g. if you have bad hand drawing). If the circle makes your diagram more confusing (e.g. you have many transistors), then omit it.\n\nKodKodKod Learning Consulting -Here you get the answers!\nhttp://www.kodkodkod.com\nTo submit questions: http://www.kodkodkod.com/index_files/submitquestion.htm
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What you are referring to is probably one of the low, flat plastic trays used in the process of developing film and prints.  They are inexpensive, and can be handy for performing experiments where you need a large surface, but low volume of water -- such as the experiment where you calculate Avogadro's Number by determining the area covered by a droplet of a dilute solution of oleic acid.\n\nThey can also be useful for containing/controlling small parts that might roll away on a hard lab bench surface.\n\nJust a few ideas.