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Topic: Equidistant

	Map Projections: Properties: Preserving Distances
		equidistant cylindrical map, all arrow lines have the same length; however, actual world distances (measured in km) between the ends of each arrow vary enormously.
		Sanson-Flamsteed equatorial map, all parallels are standard lines: if segment A is twice the length of B, corresponding lines on Earth follow the same proportion.
		Since all parallels are equally long in the map, horizontal scale increases quickly towards the top and bottom, reaching infinity at the poles.
	www.progonos.com /furuti/MapProj/Normal/CartProp/DistPres/distPres.html (494 words)

	Cycloidal equidistant curved gear transmission mechanism and its device - Patent 4922781
		The equidistant curves generally could not be carried out on a section of cycloids where the radius of curvature is smaller than the equidistant value, however arcs with equidistant values equal to the radii and the initial points of cycloids as center of curvature are permissible.
		The remaining portion of the cycloidal equidistant curve is the arc, the center point of which is at the cycloidal initial point and the value r of the equidistance as its radius.
		Double cycloid equidistant gear pumps and oil motors represent specific embodiments of the cycloidal equidistant gear mechanism which is constituted on the basis of arc-pancycloidal rotor pump and by modifying the arc tooth profile therein with the incorporation of gears having conjugated and mutually envelopable cycloidal equidistant tooth forms.
	www.freepatentsonline.com /4922781.html (3520 words)

	CM: NetLogo ProbLab: Equidistant Probability
		Equidistant Probability is authored in the NetLogo modeling-and-simulation environment.
		Equidistant Probability is perhaps an unusual model -- it bridges two domains of mathematics that are seldom found on the same page: geometrical analysis and probability.
		If all three turtles land on the same spot, then that spot is equidistant from their respective points of departure.
	ccl.northwestern.edu /ProbLab/EquidistantProbability.html (591 words)

	Adam Coffman --- equidistant surfaces (Site not responding. Last check: 2007-10-19)
		The locus of points in space which are equidistant from the line and the sphere is a "surface of Gerhard Miehlich." For a point P, let b denote the (non-negative) distance from P to L.
		Although points which are equidistant from L and S must satisfy the implicit equation, some of the following cases will show that there may be solutions of the implicit equation which are not equidistant points.
		Points on the negative x-axis (where the surface crosses itself) are equidistant from L and S, as are points on the line segment connecting the origin (0,0,0) to the center C = (1,0,0).
	www.ipfw.edu /math/Coffman/pov/miehlich.html (728 words)

	Math Forum - Geometry Problem of the Week (Site not responding. Last check: 2007-10-19)
		Since the center of a circle is equidistant from all point on a circle it must also be on the perpendicular bisector of the chord.
		Because the center of the circle is equidistant from the two endpoints of the chord, it is on the perpendicular bisector of the chord.
		By the definition of a circle the center is equidistant from all points on the circle and since the endpoints of a chord are on the circle the center is equidistant from them.
	mathforum.org /geopow/fullsolutions/053097.fullsolution.html (3061 words)

	Calculation of equidistant plant spacing (Site not responding. Last check: 2007-10-19)
		Theoretically, the best utilization of light, water, nutrients, and space by individual plants in a crop stand occurs when plants are equal distance from each other in all directions.
		This distance, known as the equidistant plant spacing, can be easily calculated using the stand density for the crop and the following equation:
		Since we want equal distance between all plants in the stand, our row spacing will be the same as the spacing between adjacent plants in the row.
	www.agron.iastate.edu /courses/Agron212/Calculations/Equidistant_spacing.htm (148 words)

	ekeqmid.html
		Show that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle.
		You only need to show that the midpoint is equidistant to the vertex at the right angle and one of the two other vertices.
		The midpoint of RS is (by definition) equidistant to both R and S.
	edc.org /mathproblems/problems/htmlProblems/ekEqMid/ekEqMid.asp?... (303 words)

	Locus equidistant from two points.
		The locus of points equidistant from two points, P and Q, is the perpendicular bisector of the line segment determined by the two points.
		Notice the formation of the isosceles triangles, where the congruent (equal) sides represent the distances to each friend.
		The different positions where you might stand form the locus of points equidistant from your two friends.
	regentsprep.org /Regents/math/locusTpt/LocusPTS.htm (169 words)

	Retract-like structures for SE(3) \| Projects \| Sensorbased Planning Laboratory (Site not responding. Last check: 2007-10-19)
		As in the planar case, the accessibility is defined using the gradient ascent, denote H3(q,t).
		The junction region J_{ijkl} is defined as the pre-image of a four-way equidistant configuration surface CF_{ijkl}.
		Then it can be shown that the union of the four-way equidistant configuration surfaces and the 1-tangent-edges forms a connected set.
	voronoi.sbp.ri.cmu.edu /retract/rsch_rodHGVG3.html (951 words)

	Azimuthal equidistant projection - Wikipedia, the free encyclopedia
		The azimuthal equidistant projection is a particular map projection.
		An example of an azimuthal equidistant projection can be seen on the United Nations flag.
		Some types of wide-angle camera lenses, known as "fisheye lenses" produce an azimuthal equidistant projection of the photographed scene onto the photographic medium.
	en.wikipedia.org /wiki/Azimuthal_equidistant_projection (239 words)

	Parallel (geometry) - Wikipedia, the free encyclopedia
		In general, equidistant lines are not geodesics so the equidistant definition cannot be used.
		Equidistant lines on the sphere are called parallels of latitude in analog to latitude lines on a globe.
		An object traveling along such a line has to accelerate away from the geodesic it is equidistant to avoid intersecting with it.
	en.wikipedia.org /wiki/Parallel_(geometry) (1037 words)

	Square root of 2 is irrational
		No two integers are equidistant from the square root of 2.
		No two rational numbers are equidistant from the square root of 2.
		Second, if a real number is equidistant from two distinct rational points, the number is necessarily the average of the two points, and is, therefore, rational.
	www.cut-the-knot.org /do_you_know/diffDist.shtml (828 words)

	Equidistant line - MapProjections
		A line of a map projection along which the principal scale is conserved.
		This is the case of the meridians in normal cylindric and conic equidistant projections, the great circles that irradiate from the centre in azimuthal equidistant projections and also all parallels in Bonne and normal ortographic projections.
		Note that an equidistant line is always a line of constant scale but not necessarily a conformal line.
	www.csiss.org /map-projections/wiki/index.php/Equidistant_line (76 words)

	Map Projections Poster
		For example, the basic Mercator projection is unique; it yields the only map on which a straight line drawn anywhere within its bounds shows a particular type of direction, but distances and areas are grossly distorted near the map's polar regions.
		On an equidistant map, distances are true only along particular lines such as those radiating from a single point selected as the center of the projection.
		For example, an Azimuthal Equidistant map centered at Washington shows the correct distance between Washington and any other point on the projection.
	erg.usgs.gov /isb/pubs/MapProjections/projections.html (3465 words)

	Untitled Document
		Now that we've found the point equidistant from A and the specific point P on our circle, what is the location of 'E' for all of the points of the circle.
		So, in order to prove that the locus of point equidistant from a fixed point and a circle is an ellipse, we need to find our two foci and the make sure the sum of r1 and r2 is, indeed, a constant.
		Let's move point A outside of the circle and use the same construction as before to find the point E which is equidistant from the circle and A. Click on 'Animate' in this GSP file to see how E moves as P goes around the circle.
	jwilson.coe.uga.edu /EMAT6680Fa05/Alford/Assign6/Assign610.html (1120 words)

	Equidistant Conic Projection -- 3DSoftware.com (Site not responding. Last check: 2007-10-19)
		The Equidistant Conic projection is commonly used in the spherical form in atlases for maps of small countries.
		Once the standard parallels are selected, all these projections are constructed by using formulas used for the Equidistant Conic with two standard parallels.
		John Bartholomew combined the Equidistant Conic projection with the Bonne projection.
	www.3dsoftware.com /Cartography/USGS/MapProjections/Conic/Equidistant (422 words)

	Azimuthal Equidistant Projection -- 3DSoftware.com (Site not responding. Last check: 2007-10-19)
		The Azimuthal Equidistant projection is an Azimuthal map projection.
		Two-Point Equidistant shows correct distances (but not azimuths) from either of two points to any other point.
		The three points are placed near the edges of the region being mapped to reduce overall distortion.
	www.3dsoftware.com /Cartography/USGS/MapProjections/Azimuthal/AzimuthalEquidistant (465 words)

	The Equatorial Cylindrical Equidistant Projections and Grids
		The Equatorial Cylindrical Equidistant (ECE) projection is perhaps the most popular projection for researchers working with global scale data.
		The cylindrical equidistant map is defined as true at at the equator
		The values of C, r0, and s0 are determined by the grid that is chosen to overlay the projection.
	nsidc.org /data/psq/grids/ece_grids.html (871 words)

	Equidistant Converter \| PCNC Laboratory - CNC, Computer Numerical Control systems (Site not responding. Last check: 2007-10-19)
		The Equidistant Converter is intended to make the equidistant correction in the flow program file.
		It means, that the flow program block will be put into the buffer and additionally processed (the analysis of intersection with other flow program blocks; correction of the geometric movement in the block).
		In order to analyze the equidistant contour, it is additionally necessary to save information about previous contour elements.
	www.ncsystems.ru /en/products/converter (507 words)

	StatSci-Equidistant Letter Sequences in the Book of Genesis
		It has been noted that when the Book of Genesis is written as two-dimensional arrays, equidistant letter sequences spelling words with related meanings often appear in close proximity.
		He found some interesting patterns in the Hebrew Pentateuch (the Five Books of Moses), consisting of words or phrases expressed in the form of equidistant letter sequences (ELS's)--that is, by selecting sequences of equally spaced letters in the text.
		Define an equidistant letter sequence (ELS) as a sequence of letters in the text whose positions, not counting spaces, form an arithmetic progression; that is, the letters are found at the positions
	www.torahcodes.co.il /wrr1/wrr1.htm (5148 words)

	Definition of equidistant - Merriam-Webster Online Dictionary
		Etymology: Middle French or Late Latin; Middle French, from Late Latin aequidistant-, aequidistans, from Latin aequi- + distant-, distans, present participle of distare to stand apart -- more at
		Learn more about "equidistant" and related topics at Britannica.com
		Find more about "equidistant" instantly with Live Search
	www.m-w.com /cgi-bin/dictionary?book=Dictionary&va=equidistant (68 words)

	Commentary on “Equidistant Letter Sequences in the Book of Genesis”
		His research was revived by American mathematician Daniel Michaelson, and later the trio of Israeli scientists Witztum, Rips and Rosenberg.
		The Israelis' preferred decoding method involves “equidistant letter sequences,” words encoded in the Bible text by skipping a fixed number of intervening letters.
		A list of Church Fathers could be hidden in the Pentateuch beside the rabbis the Israelis chose to seek, and indeed some enthusiasts have published books about Jesus-in-code.
	home.earthlink.net /~mcdemarco/portfolio/els_math.html (2959 words)

	Map Projections: Azimuthal Projections
		However, for lesser overall distortion the latter may be presented in a separate map centered on the antipodal point.
		In the north polar aspect, the azimuthal equidistant is familiar as part of both flag and emblem of the United Nations Organization, with olive branches replacing Antarctica.
		Like the superficially similar azimuthal equidistant, the azimuthal projection published by Johann H. Lambert in 1772 strongly distorts shapes in the boundary of a worldwide map.
	www.progonos.com /furuti/MapProj/Normal/ProjAz/projAz.html (836 words)

	Developing map projections with Java, the equidistant cylindrical projection
		In the second article of a multi-part series, one of the simplest map projections, the equidistant cylindrical projection, is developed.
		The equidistant cylindrical projection is the simplest of the projections to implement.
		Equidistant cylindrical map projection of Earth from NASA's Blue Marble web site.
	www.raben.com /articles/MapProjections/part_2_1.html (585 words)

	NASA RP 1369: Equidistant Conic Projection Map of the Eclipse Path (Site not responding. Last check: 2007-10-19)
		Equidistant Conic Projection Map of the Eclipse Path
		Figures 3 and 4 are equidistant conic projection maps selected to minimize distortion, and which isolate specific regions of the umbral path.
		The size of each city is logarithmically proportional to its population using 1990 census data (Rand McNally, 1991).
	umbra.nascom.nasa.gov /eclipse/970309/text/eqconic-projection.html (162 words)

	Equidistant Letter Sequences in the Book of Genesis
		Key words and phrases: Genesis, equidistant letter sequences, cylindrical representations, statistical analysis.
		Then we check whether ELS's representing conceptually related words tend to appear in "close proximity." Suppose we are given a text, such as Genesis (G).
		Define an equidistant letter sequence (ELS) as a sequence of letters in the text whose positions, not counting spaces, form an arithmetic progression; that is, the letters are found at the positions n, n+d, n+2d,...
	www.answering-islam.org /Religions/Numerics/genesis.html (2414 words)

	NetLogo Models Library: Equidistant Probability
		Because there are exactly as many creatures as there are selected squares, and because they all step forward at the same moment, if all the creatures arrive at the same square at the same moment, then that square is "equidistant" (equally far away) from all the selected squares.
		In that case, the square where they all landed becomes green and keeps a count of how often, out of all their "attempts," the creatures met there.
		When you are through with selecting, un-press the button so as not to make further selections by mistake while the model is running.
	ccl.northwestern.edu /netlogo/models/EquidistantProbability (1770 words)

	Equidistant Letter Sequences in the Book of Genesis
		They published their study, Equidistant Letter Sequences in the Book of Genesis, in the scholarly journal Statistical Science, (Statistical Science 9:429-438), about what they called ELS (Equidistant Letter Sequences) in Genesis.
		Their summary said: “When the Book of Genesis is written as two-dimensional arrays, equidistant letter sequences spelling words with related meanings often appear in close proximity, with analysis showing that the (statistical) effect is significant at the level of 0.00002”, (i.e.
		The dead were judged according to what they had done as recorded in the books.
	digilander.libero.it /asali/equidistant.htm (910 words)

	NASA RP 1318: General Maps of the Eclipse Path: Equidistant Conic Projection
		NASA RP 1318: General Maps of the Eclipse Path: Equidistant Conic Projection
		Figures 3, 4, and 5 are equidistant conic projection maps which isolate specific regions of the eclipse path.
		The last two figures also include the center line of the umbral path.
	umbra.nascom.nasa.gov /eclipse/941103/text/eqconic-projection.html (172 words)

	Equidistant Letter Sequences in the Book of Genesis
		It has been noted that when the Book of Genesis is written as two-dimensional arrays, equidistant letter sequences spelling words often appear in close proximity with portions of the text which have related meaning.
		Genesis, Equidistant letter sequences, Strings of letters, Cylindrical representations, Statistical analysis.
		Since this tradition was passed orally, only few expressions that belong to the "hidden text" were preserved in writing (Rabbenu Bahya, 1492 and Cordovero, 1592); actually almost all the words and the syntax are unknown.
	cs.anu.edu.au /~bdm/dilugim/Nations/WRR2/index.html (5580 words)

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