Properties of Geometric Shapes????? PLEASE?
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HEPTAGON - a seven-sided polygon.\n\nTRIANGULAR PYRAMID - a pyramid with a triangular base and 3 triangular faces.\n\nSCALENE TRIANGLE - a triangle none of whose sides have equal length. The angles don't have the same measures, too.\n\nISOSCELES TRIANGLE - a triangle 2 of whose sides have equal measures. Therefore, the angles opposite the congruent sides have equal measures also.\n\nEQUILATERAL TRIANGLE - a triangle all of whose sides have equal measures. The angles have equal measures, too.\n\nRIGHT TRIANGLE - a triangle 1 of whose angles has a measure of 90 degrees. The other 2 angles have measures that are less than 90 degrees. The side opposite the 90-degree angle is the longest side and is called the hypotenuse. The other sides are called legs.\n\nSPHERE - is shaped like a ball (round).\n\nCONE - it is a pyramid with a circular base.\n\nDECAGON - a polygon with 10 sides.\n\nDODECAGON - a polygon with 12 sides.
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It depends what you mean by "different" shapes.  For example, is a long chain, 3 lengths on the bottom, 2 lengths on the top different from the same shape upside-down?  Assuming that the usual set of transformations ensuring congruence (translation, reflection and rotation) are allowed as not making different shapes, and also assuming you're looking for closed shapes (rather than, say, 5 triangles arranged so that no sides are touching, only meeting at vertices), then there are only 4 different arrangements.\n\nI'll do my best to try to describe them:\n\n- All 5 triangles in a straight line, 3 facing up, 2 facing down.\n- A hexagon with 1/6 missing (like a pie with 1 piece eaten).\n- A larger equilateral triangle (4 pieces) with one extra triangle on one of the sides (doesn't matter where, due to reflections and rotations)\n- A chain of 4 triangles, making a parallelogram, with one extra triangle in one of the locations that will make a different shape than the one above.
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I know exactly what you mean by raising up this question, I have asked myself 10,000 times...but I have found out that without Geometry, this world would not be what it is by now... put it as simple as this, not even your keyboard of your computer would exist... everything in terms of architecture and design (every single fashion) is based on GEOMETRY... Is tough I now...but it is necessary!!!...
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There are different formulas for different shapes. This page has a list of them: http://www.math.com/tables/geometry/volumes.htm
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Spiral, lenticular, elliptical and irregular\n\nSee the link
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http://local.wasp.uwa.edu.au/~pbourke/geometry/2circle/\n\nit tells you how
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symetric designs, ratios from diagram to real material
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i think the 2 characteristics of a vector are-\n\nit has a definite direction and it follows the vector addition. i hope thats correct!!
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The elements of design are :\nLINE\nLine can be considered in two ways. The linear marks made with a pen or brush or the edge created when two shapes meet.\nSHAPE \nA shape is a self contained defined area of geometric or organic form. A positive shape in a painting automatically creates a negative shape.\nDIRECTION \nAll lines have direction - Horizontal, Vertical or Oblique. Horizontal suggests calmness, stability and tranquillity. Vertical gives a feeling of balance, formality and alertness. Oblique suggests movement and action\nsee notes on direction\nSIZE \nSize is simply the relationship of the area occupied by one shape to that of another.\nTEXTURE \nTexture is the surface quality of a shape - rough, smooth, soft hard glossy etc. Texture can be physical (tactile) or visual.\nsee notes on texture\nCOLOUR\nAlso called Hue\nsee notes on colour\nVALUE\nValue is the lightness or darkness of a colour. Value is also called Tone\nsee notes on tonal contrast\nThe principles of design are:\nBALANCE\nBalance in design is similar to balance in physics\nA large shape close to the center can be balanced \nby a small shape close to the edge. A large light \ntoned shape will be balanced by a small dark toned \nshape (the darker the shape the heavier it appears to be)\nGRADATION\nGradation of size and direction produce linear perspective. Gradation of of colour from warm to cool and tone from dark to light produce aerial perspective. Gradation can add interest and movement to a shape. A gradation from dark to light will cause the eye to move along a shape.\nREPETITION\nRepetiton with variation is interesting, without variation repetition can become monotonous\nsee notes on repetition\nCONTRAST\nContrast is the juxtaposition of opposing elements eg. opposite colours on the colour wheel - red / green, blue / orange etc. Contrast in tone or value - light / dark. Contrast in direction - horizontal / vertical. \nThe major contrast in a painting should be located at the center of interest. Too much contrast scattered throughout a painting can destroy unity and make a work difficult to look at. Unless a feeling of chaos and confusion are what you are seeking, it is a good idea to carefully consider where to place your areas of maximum contrast.\nHARMONY\nHarmony in painting is the visually satisfying effect of combining similar, related elements. eg.adjacent colours on the colour wheel, similar shapes etc.\nDOMINANCE\nDominance gives a painting interest, counteracting confusion and monotony. Dominance can be applied to one or more of the elements to give emphasis\nUNITY\nRelating the design elements to the the idea being expressed in a painting reinforces the principal of unity.eg. a painting with an active aggressive subject would work better with a dominant oblique direction, course, rough texture, angular lines etc. whereas a quiet passive subject would benefit from horizontal lines, soft texture and less tonal contrast.\nUnity in a painting also refers to the visual linking of various elements of the work.
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Differential geometry/manifolds, Optimization word problems in 3D, topology proofs.
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Its been a long time since I took Geometry but maybe I can give you a small pointer.\n\nTry dividing the rectangle into 3 segments lengthwise and 3 segments widthwise\n\nA--B--C--D\nE--F--G--H\nJ---K--L--M\nN--O--P--Q\n\nDraw the diagonal through NKGD\n\nProve that the segments NK, KG, and DG are equal (prove that the triangles are the same)\n\nNow draw the segments from the vertex Q to the mid point of AD and AN.  Prove that the mid point of AD is the same as the mid point of BC and the same for AN and EJ.\n\nNow we have to prove that the line segment we drew in the last step instersect points K and G. You can probably do this with similar triangles (the triangle NQ and mid point of EJ is similar to JK and mid point of EJ therefore the point K is in the triangle)\n\nSo if you prove that the lines drawn from Q to the midpoints intersect K and G and we proved that NK KG and GD are congruent we have proved the original hypothesis.\n\nYou can turn this gabably gook into a real mathematical proof.\n\nGood Luck
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Floral and geometric design
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r=radius\nd=diameter\n\n1 C=2r(pi)\n2 C=d(pi)\n\n(Same thing because 2r=d)
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lines, polylines, blocks, circles etc... look in the help files if you have the software\n\nhttp://www.we-r-here.com/cad/tutorials/index.htm
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two circles, in parallel planes with the line connecting their centers forming right-angles with each plane in all directions. ... and the walls comprising the set of line segments one of whose end points is on one circel and the other end point on the other circle withe the property that the segments at each point on circle(A) is the minimum distance to circle(B).\n\n.. or, since you use the word "cylinder" in the question:\n\na cylinder, each of whose end-faces is a circle.
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The simplest way to do this would be to use the Paint program that comes with Windows.\n\nYou can draw simple geometric shapes.  Then you can select one, paste a copy, then rotate/reflect the copied shape with Image->Flip/Rotate menu selection.\n\nThat ought to do it.
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Check Out This Website!! \n\nGives You Examples And Everything!! \n\nhttp://www.mathleague.com/help/geometry/geometry.htm