What is a Paragon - Definition or alternatives?
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par·a·gon    ( P )  Pronunciation Key  (pr-gn, -gn)\nn. \n1. A model of excellence or perfection of a kind; a peerless example: a paragon of virtue. \n\n2. An unflawed diamond weighing at least 100 carats. \nA very large spherical pearl. \n\n3. Printing. A type size of 20 points.
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It's the formula for the area of a regular polygon\n\nArea = 1/2 times apothem times perimeter\n\n(apothem = perpendicular distance from center to midpoint of a side)
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Go to Google and search for\n\n define:paracompact\n\n(no spaces on either side of the ':')\n\nIt will show you the following excerpt from\n\n http://en.wikipedia.org/wiki/Paracompact\n\n> In mathematics, a paracompact space is a\n> topological space in which every open cover\n> admits an open locally finite refinement.\n> (Paracompact spaces are often required to\n> be Hausdorff, but we will not make that\n> assumption in this article.)\n\nRead the wikipedia article for definitions of the relevant terms.
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paraphrase is a re-wording\n\ncommentary adds extra materials and expounds
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cone: shape of an ice cream cone (without the ice cream)\nsphere: shape of a basketball\ncylinder: shape of a piece of pipe\npyramid: shape of ...well...a pyramid
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decagon - 2 d figure\nor \ndecahedron - 3 d figure
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polyhedron (pŏl'ēhē'drən) , closed solid bounded by plane faces; each face of a polyhedron is a polygon. A cube is a polyhedron bounded by six polygons (in this case squares) meeting at right angles. Although regular polygons are possible for any number of sides, there are only five possible regular polyhedrons, having congruent faces, each a regular polygon and meeting at equal angles. The five regular polyhedrons are also known as the Platonic solids, although they were known to the Greeks before the time of Plato. They are the tetrahedron, bounded by four equilateral triangles; the hexahedron, or cube, bounded by six squares; the octahedron, bounded by eight equilateral triangles; the dodecahedron, bounded by twelve regular pentagons; and the icosahedron, bounded by twenty equilateral triangles. The 18th-century Swiss mathematician Leonhard Euler showed that for any simple polyhedron, i.e., a polyhedron containing no holes, the sum of the number of vertices V and the number of faces F is equal to the number of edges E plus 2, or V+F=E+2
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parastatal\n\nADJECTIVE: \n\nOwned or controlled wholly or partly by the government: a parastatal mining corporation.\n \nNOUN: \n\nA company or agency owned or controlled wholly or partly by the government.
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Pythagorean triples are integer length sides of right triangles.\n\nIts in the form of (t^2 - s^2, 2st, t^2 + s^2)\n\nusing that can create another right triangle.\n\nSorry, but thats about all i could dig up. I'm not really all that familiar with P.T.
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I think the St. Louis Arch is a partial parabola. Or how about a satellite dish?\n\nHere's another interesting phenomenon. Some museums set up devices that look like satellite dishes so you can try out a similar effect:\n\nWhispering Gallery in NYC\nTalk into one corner of this room and your friend in the other corner will hear it.\nSounds do interesting things in round shapes, parabolas will bounce sound from a large area into one spot, or from that one spot to a large area and are used extensively in theaters. Another interesting phonomenon is a Whisper Gallery where you can stand along one wall and sound bounces along the sphere, travelling straight and then bouncing off the wall until it hits the wall again, continuing around the inner surface of the circle.\n\nWell, I just learned that there's one in Grand Central Station.\n\nIn the arched hallway outside the entrance, check out the engineering magic of the "whispering corners." When you and a companion stand in opposite corners and whisper, you can hear each other as well as if you were standing a foot apart.\n - http://www.newyorkmetro.com/pages/details/4218.htm
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The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of one of the sides.  It is used to calculate the area of the regular polygon:\n\nA = 1/2 a p  \n\nA = area\na = length of apothem\np = perimeter
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Cube, pyramid, sphere, cone, cylinder.  There are others.
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the answer you require is Paraguy
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uuuuuhhhhhh, no. a polygon is a MULTI-SIDED figure. hence the POLY prefix, meaning many.
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You can build all (or most of) the platonic and archimedaic solids using Origami.\n\nYou can also buid conic sections (hyperboles, parabola, ellypse and circle) by repeatedly folding a piece of paper along the tangents, point by point, using fundamental properties of each one. (= you get them as the envelope of their tangents).
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A parabola is a shape formed by all the points that are an equal distance from a line, called the directrix, and a point, called the focus. The interesting thing about parabolas is if you have a three-dimensional figure formed by rotating a parabola on its vertex, if you place a light source at the focus, the light that shines back and hits the parabolic surface will be reflected outward in parallel lines, creating a strong beam. This is how flashlights work. Also, if you use a parabolic shape for an antenna, signals coming in from space or whatever will hit the surface of the parabola and all be reflected onto the focus. If you put a receptor there, you will receive a very strong signal. That's a couple real life uses of parabolas.
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It's a parabola. I believe the astronomer Roger Angell proposed a parabolic reflector using mercury in a spinning container. The paraboloid is the natural equilibrium shape of minimum potential energy. The liquid assumes a level consistent with the local acceleration, which is the sum of gravity and radial acceleration given by w^2*r, where w is the rotational rate in rad/sec and r is the radius. The resulting paraboloid surface is perpendicular to the acceleration at all points.