Base (geometry) - Factbites

Base (geometry) - Factbites
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Topic: Base (geometry)

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	Right circular cone - Wikipedia, the free encyclopedia
		In geometry, a right circular cone is a cone whose base is a circle and whose apex is on a line perpendicular to the plane containing the base.
		â” the area of the side of the cone â” equals the circumference of the base circle multiplied by the slant height of the cone (the distance from the apex to any point on the outside of the base).
		equals the area of the base circle multiplied by the height of the cone (the distance from the apex to the center of the base).
	en.wikipedia.org /wiki/Right_circular_cone

	Prism (geometry) - Wikipedia, the free encyclopedia
		In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides.
		A parallelepiped is a prism of which the base is a parallelogram, or equivalently a polyhedron with 6 faces which are all parallelograms.
		The volume of a prism is the product of the area of the base and the distance between the two base faces (in the case of a non-right prism, note that this means the perpendicular distance).
	www.wikipedia.org /wiki/Prism%2B(geometry)

	Triangle - Wikipedia, the free encyclopedia
		The area S of a triangle is S = ½bh, where b is the length of any side of the triangle (the base) and h (the altitude) is the perpendicular distance between the base and the vertex not on the base.
		A median of a triangle is a straight line through a vertex and the midpoint of the opposite side, and divides the triangle into two equal areas.
		A triangle is one of the basic shapes of geometry: a two-dimensional figure with three vertices and three sides which are straight line segments.
	en.wikipedia.org /wiki/Triangle_(geometry)

	CONE - LoveToKnow Article on CONE
		The axis of the cone is the side about which the triangle revolves; the circle traced by the other side containing the right angle is the base; the hypotenuse in any one of its positions is a generator or generating line ; and the intersection of the axis and a generator is termed the vertex.
		The subcontrary section of an oblique cone is made by a plane not parallel to the base, but perpendicular to the principal section, and inclined to the generating lines in that section at the same angles as the base; this section is a circle.
		References should be made to the articles GEOMETRY and SURFACE for further discussion; and to the bibliographies of these articles for sources where the subject can be further studied.
	www.1911encyclopedia.org /C/CO/CONE.htm

	MSN Encarta - Search Results - Cone (geometry)
		Cone (geometry), in geometry, surface generated by a straight line that moves along a closed curve while always passing through a fixed point.
		A cone is a pyramid with a circular base.
		A cone is a right cone if a line joining the center of its base to its apex is perpendicular to its base....
	encarta.msn-ppe.com /Cone_(geometry).html

	Geometry: Triangles 165 Shop Essentials
		In a triangle, a line drawn perpendicular to the base, from the base to the opposite vertex, that represents the height of the triangle.
		In an isosceles triangle, one of the two angles formed by the base and a leg.
		In an isosceles triangle, one of the two sides that are equal in length.
	www.toolingu.com /tu/Shop_Essentials/Geometry_Triangles/Geometry_Triangles.html

	Re: GEOMETRY HELP -- Plane Sections
		You have to imagine slicing this figure with a plane that's parallel to its base.
		sketch the plane section and name its shape: parallel to the base of a square pyramid?" : You have to imagine slicing this figure with a plane that's parallel to its base.
		Much like slicing a loaf of bread, you must cut the figure but only using your mind's eye.
	www.mathguide.com /bbs/Messages2001/625.html (259 words)

	gencyl2, gencyl3
		creates a solid straight homogenous generalized cylinder geometry object with base surface
		, with a solid circle base surface, cylinder axis of length 1 along the z-axis, and size of top surface equal to base surface.
		creates a solid straight homogenous generalized cylinder geometry object
	www-math.cudenver.edu /~jmandel/doc/refman/ref116.htm (166 words)

	ninemsn Encarta - Pyramid (geometry)
		The volume of a pyramid is thus one-third of the volume of a prism that has the same base and altitude.
		Pyramid (geometry), solid figure formed by connecting every point on or interior to a plane polygon to a single point not in the plane.
		The volume of any pyramid is hK/3, in which h is the altitude of the pyramid and K is the area of the base.
	au.encarta.msn.com /encyclopedia_761552486/Pyramid_(geometry).html (166 words)

	How Probe Tip Geometry Affects Contact Reliability
		A chisel contacting the rim of an open via is a special case (a chisel is essentially a pyramid with a triangular base).
		This attack angle principle is the same for the various blade point styles (a blade is essentially a pyramid with a diamond-shaped base), but the pressures are higher since there are two points of contact on the rim of the hole instead of three.
		The area of contact is easy to envision - it is spread over three regions which are the points of contact between the rim of the hole and the three ridges formed by the intersections of the chisel faces.
	www.qatech.com /tech/applications_notes/AN02.htm (166 words)

	Encyclopedia: Cone (geometry)
		The term cone is sometimes extended to more general shapes, such as the image of a common cone by an affine map — which may turn the basis into an ellipse (producing an elliptical cone) and/or tilt the axis relative to the base (an oblique cone).
		The volume V of a cone of height h and base radius r is 1/3 of the volume of the cylinder with the same dimensions, i.e.
		In common usage and elementary geometry, a cone ( Greek : κώνος) is a solid object obtained by rotating a right triangle around one of its two short sides, the cone's axis.
	www.nationmaster.com /encyclopedia/Cone-(geometry) (166 words)

	cone (geometry)
		In geometry, a pyramid with a circular base.
		The distance from the edge of the base of a cone to the vertex is called the slant height.
		A right circular cone is generated by rotating an isosceles triangle about its line of symmetry.
	www.tiscali.co.uk /reference/encyclopaedia/hutchinson/m0006655.html (166 words)

	Geometry and Topology - Numericana
		Geometry from the Land of the Incas by Antonio Gutierez.
		Rr, if r is the radius of its base and R is the distance from the circumference of the base to the apex.
		/50, the parameter is 25 and the focal distance is 12.5.
	home.att.net /~numericana/answer/geometry.htm (7724 words)

	Siriusly - Supplement [Sacred Geometry]
		This squaring of the circle works with a right triangle that represents the apothem(ZY) (a line drawn from the base of the center of one of the sides to top of the pyramid), down to the center of the base (ZE), and out to the point where the apothem touches the Earth (EY).
		All of the Sacred Geometry ratios we will be working with, the square roots of two (1.414), three (1.732) and five (2.238), phi (1.618) and pi (3.1416), are all irrational numbers.
		The claim is that the smaller circle (in square abcd) is to the larger circle (in square ABCD) as the Moon is to the Earth.
	www.dudeman.net /siriusly/0/sup/sacgeom.shtml (2378 words)

	PinkMonkey.com Geometry Study Guide - 8.2 Prism
		The two congruent polygons are called the two bases of the prism.
		If the lateral edges are not perpendicular to the base the prism is called an oblique prism.
		If the lateral edges are perpendicular to the base the prism is called a right prism.
	www.pinkmonkey.com /studyguides/subjects/geometry/chap8/g0808201.asp (2378 words)

	Glencoe Mathematics - Online Study Tools
		Find the area of a parallelogram with a base of 5 meters and a height of 3 meters.
		Find the length of the base of a parallelogram with height 8 units and area 88 units.
		Find the area of the rectangle with length 13 units and width 3 units.
	www.glencoe.com /sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-833051-X&chapter=1&lesson=7 (49 words)

	Cupolas
		You can bypass all of this geometry and cut right to the chase using a level, a pencil and a square piece of cardboard that is 12 inches longer than the base of the cupola.
		If you decide to cut a hole in the roof so that the cupola works as a ventilator, then make sure the roof hole is about 6 inches less in width and length than the outer base of the cupola.
		You can simply rest the cupola on the roof without cutting a hole in the roof or you can cut a hole so that the cupola actually acts as a decorative ventilation device.
	www.askthebuilder.com /printer_330_Cupolas_-_Those_Funny_Hats_on_Garages.shtml (759 words)

	Cube/Rectangular Prism Activity
		Discuss with the students the formulas to calculate the area and volume of a cube and rectangular prism given the length of the side or the length, height and width of the prism.
		Students manipulate cubes and rectangular prisms, drawing geometric shapes using grid paper and also manipulating geometric shapes using the ESCOT Runner software to observe geometric relations.
		What is the relation between the area of the base of the pink rectangular prism and the area of the base of the blue rectangular prism?
	mathforum.org /alejandre/escot/cube.prism.html (759 words)

	Protonation Studies and Multivariate Curve Resolution on Oligodeoxynucleotides Carrying the Mutagenic Base 2-Aminopurine -- Gargallo et al. 81 (5): 2886 -- Biophysical Journal
		the P·C base pair and a Watson-Crick geometry for the P·T base
		for the wobble geometry for the P·C base pair.
		Base pairing and mutagenesis: observation of a protonated base pair between 2-aminopurine and cytosine in an oligonucleotide by proton NMR.
	www.biophysj.org /cgi/content/full/81/5/2886 (5111 words)

	The Gregorian Calendar and The Life of Christ
		Enter the Chaldeans with a base 60 geometry at about 4000 BC.
		An hour, like a degree of arc, is founded upon a numbering scheme called " a decimal base 60 system " (60 seconds of time makes a minute, 60 minutes make an hour- 6 increments of 10).
		This method is just like geometry where 60-seconds-of-arc make a minute-of-arc and 60 minutes-of-arc make a degree-of-arc.
	www.templeofsolomon.org /chrono.htg/chrono.htm (5111 words)

	Solids III - Sphere, Ellipsoid, Cylinder, Cone, Truncated Cone - Analytical Geometry with POV-Ray
		Cone with base center M1, base radius R1 and top point M2:
		Solids III - Sphere, Ellipsoid, Cylinder, Cone, Truncated Cone - Analytical Geometry with POV-Ray
		Truncated cone, centers of the ends M1, M2, radii R1, R2:
	www.f-lohmueller.de /pov_tut/a_geo/a_geo65e.htm (5111 words)

	Traingles with common base
		From news@mathforum.org Fri Jul 26 10:43:09 2002 From: Steve Gray Subject: Traingles with common base Date: Fri, 26 Jul 2002 13:11:56 +0000 (UTC) To: geometry-puzzles@moderators.isc.org To: geometry-puzzles@support1.mathforum.org Draw an equilateral triangle Z0,Z1,Z2 and put point Y somewhere inside it.
		This gives three triangles having Y as their "apex" angle.
		Type "r" to reset the diagram to its initial state
	www.math.umbc.edu /~rouben/Geometry/steve_gray.html (237 words)

	Geometry and Topology - Numericana
		Geometry from the Land of the Incas by Antonio Gutierez.
		Rr, if r is the radius of its base and R is the distance from the circumference of the base to the apex.
		/50, the parameter is 25 and the focal distance is 12.5.
	home.att.net /~numericana/answer/geometry.htm (237 words)

	Golden Mean
		The length of the extension will then exactly equal f [and the base�s total length being F.] From this same geometry, we can
		The Golden Mean can be determined via geometry by taking a square with all sides equal to 1, drawing an arc with the center of radius at the midpoint of one side and through the corner of an opposite side, and extending the original side to where it intersects the arc.
		The west facade of the Notre Dame Cathedral in Paris is also loaded with Golden Mean ratios, and more recently, the United Nations Building in New York City is designed as three golden rectangles (equivalent to three Parthenons stacked upon one another).
	www.halexandria.org /dward101.htm (237 words)

	Examples, Tables, and Proof Sketches: A Supplement to Bayes' Theorem
		But, when asking questions about total evidence one must attend closely to the base rate, which almost always provides evidentially relevant information about the hypothesis.
		Notice how incremental and total evidence make different uses of information about the base rate of heroin use in the population.
		People often commit the "base rate fallacy" (Kahneman and Tversky 1973, 237-251) by mistaking incremental evidence for total evidence.
	adt.library.usyd.edu.au /stanford/entries/bayes-theorem/supplement.html (237 words)

	Optometric Management
		This is the steepest region of any reverse geometry lens for ortho-K. Use this curve to connect the base curve to the alignment curve while maintaining the ideal relationship of these zones to the underlying cornea.
		These are the same changes that would be made to the base curve of a traditional (non-reverse geometry) lens design.
		The base curve radius is 0.50D to 0.75D flatter than the flattest corneal radius.
	www.optometric.com /article.aspx?article=70557 (1241 words)

	Optometric Management
		Reverse geometry lenses have a secondary curve that's steeper than the base curve radius (BCR).
		Rather, a reverse geometry lens is fitted to give an apical tear layer thickness of about 10 microns.
		The corneal shape is commonly described as a prolate ellipse because the radius of curvature flattens gradually from the apex of the cornea to the periphery.
	www.optometric.com /article.aspx?article=&loc=articles\2001\may\0501086.htm (1346 words)

	agmod-web.txt
		Therefore, algebraic geometry is a theory which is based on the two funda* *mental notions of affine scheme and Grothendieck topology.
		This has led to the theory of relative* * algebraic ge- ometry, which allows one to do algebraic geometry over well behaved symmetric m* onoidal base* categories (see [De1, De2, Ha ]); usual algebraic geometry corresponds th* en to the ä bsolute" case where the base* category is the category of Z-modules.
		Our motivations for starting such a program* * come from several questions in algebraic geometry and algebraic topology and will be* * clari- fied in the two entries Examples and applications and Relations with other work* *s of this introduction.
	hopf.math.purdue.edu /Toen-Vezzosi/agmod-web.txt (1346 words)

	Aqualens Toric
		Tori geometry 1: n mathematics and theoretical physics, '''toric geometry''' is a set of methods in algebraic ge 11: The approach of Taric geometry is to write 19: The triangle is the '''toric base''' of the complex projective plane.
		geometry 1: n mathematics and theoretical physics, '''toric geometry''' is a set of methods in algebraic ge 11: The approach of Tlric geometry is to write 19: The triangle is the '''toric base''' of the complex projective plane.
		List of algebraic geometry topics 86: * Toeic geometry
	www.bodawg.com /point/2826-aqualens-toric.html (311 words)

	GEOMETRY - LoveToKnow Article on GEOMETRY
		Pythagoras (q.v.), seeking the key of the universe in arithmetic and geometry, investigated logically the principles underlying the, known propositions; and this resulted in the formulation of definitions, axioms and postulates which, in addition to founding a science of geometry, permitted a crystallization, fractional, it is true, of the amorphous collection of material at hand.
		Pythagorean geometry was essentially a geometry of areas and solids; its goal was the regular solids the tetrahedron, cube, octahedron, dodecahedron and icosahedronwhich symbolized the five elements of Greek cosmology.
		The geometry of the circle,, previously studied in Egypt and much more seriously by Tbales, was somewhat neglected, although this curve was regarded as the most perfect of all plane figures and the sphere the most perfect of all solids.
	www.1911encyclopedia.org /G/GE/GEOMETRY.htm (21277 words)

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