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Topic: Taxicab geometry

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	Taxicab Angles and Trigonometry (Site not responding. Last check: 2007-10-08)
		Taxicab geometry, as its name might imply, is essentially the study of an ideal city with all roads running horizontal or vertical.
		The taxicab measure of a taxicab angle is the number of t-radians subtended by the angle on the unit taxicab circle about the vertex.
		This corollary implies the taxicab measure of a Euclidean angle in non-standard position is not necessarily equal to the taxicab measure of the same Euclidean angle in standard position.
	www.alpacacriations.com /Nivek/taxicab (2566 words)

	What Is Geometry? (Site not responding. Last check: 2007-10-08)
		The power of geometry, in the sense of accuracy and utility of these deductions, is impressive, and has been a powerful motivation for the study of logic in geometry.
		Although the word geometry derives from the Greek geo (earth) and metron (measure) [Words], which points to its practical roots, Plato already knew to differentiate between the art of mensuration which is used in building and philosophical geometry [Philebus (57)].
		However, depending on intuition may be misleading, as, for example, in projective geometry, according to the Duality Principle, all occurrences of the two terms in the axioms and theorems are interchangeable.
	www.cut-the-knot.org /WhatIs/WhatIsGeometry.shtml (1348 words)

	Amazon.de: Taxicab Geometry: An Adventure in Non-Euclidean Geometry: English Books: Eugene Krause (Site not responding. Last check: 2007-10-08)
		This form of travel is similar to the taxicab geometry in that movement is restricted to lines.
		Yet, the geometry is generally easier to understand because it is almost always how we move from place to place.
		Geometry is the godfather of abstract mathematics, being first used to codify the parceling of land and the construction of cities.
	www.amazon.de /Taxicab-Geometry-Adventure-Non-Euclidean/dp/0486252027 (621 words)

	Taxicab Geometry (Site not responding. Last check: 2007-10-08)
		Taxicab Geometry - an alternative geometry based on a distance function different from the usual Eucidean distance.
		Taxicabs in a city often must travel along a grid of squares (city streets), making distances between points different from the Euclidean "straight line" distance.
		Geometry and the ability to generalize geometric notions to arbitary distance functions.
	www.uml.edu /Dept/Math/m419/proj/taxicab/taxicab.html (205 words)

	[No title]
		In taxicab geometry, the distance between two points is found using only the grid lines that a taxi would follow as on city streets.
		A second difference between Euclidean and taxicab geometry is the formation of a circle.
		In Euclidean geometry, there exists a rule that says that if any two triangles have two equal sides and one equal angle, then the two triangles are congruent.
	www-math.cudenver.edu /~wcherowi/courses/history2/sum06/ab73.doc (400 words)

	Taxicab Geometry#
		To find the distance between two points in Taxicab geometry, we need to add the distance of the legs of the right triangle of which our two points make the hypoteneuse.
		As we can see, the rules for Taxicab geometry are different from the things most of us learned in high school.
		In Euclidean geometry, circles are defined as the set of points equidistant from the center.
	jwilson.coe.uga.edu /EMT668/EMAT6680.F99/DDavis/Taxicab/taxicab.html (410 words)

	Wikinfo \| Taxicab
		A taxicab (sometimes called taxi, cab, or hack) is a vehicle for hire which conveys passengers between locations of their choice.
		Although battery-powered vehicles enjoyed a brief success in Paris, London, and New York in the 1890s, the 1891 invention by German Wilhelm Bruhn of the taximeter (the familiar mechanical and now often electronic device that calculates the fare in most taxis) ushered in the modern taxi.
		In 1636, the number of carriages was set at 50--an early example of taxicab regulation.
	www.wikinfo.org /wiki.php?title=Taxicab (1582 words)

	taxicab1.htm
		They want to find an apartment such that the sum of the distances, using Taxicab geometry, each has to walk will be a minimum.
		In Taxicab geometry, it is the set of points of the rectangle with P and Q as opposite vertices.
		This means that distances in both Euclidean Geometry and Taxicab Geometry are preserved under linear transformations.
	newark.osu.edu /thays/taxicab1/taxicab1.htm (519 words)

	Taxicab geometry (Site not responding. Last check: 2007-10-08)
		In taxicab geometry the distance between place A & B is worked out by adding together the horizontal and vertical distances.
		A taxix cab firm is based at A. the posistion B is 7 units away from A. investigate all the posistions of B at 7 units.
		The taxicab distance between two points is the sum of the East-West distance and the North-South distance.
	mathcentral.uregina.ca /qq/database/QQ.09.99/jack1.html (353 words)

	[No title]
		Taxicab Geometry Assignment Part I. Consider the two points (0,0) and (2,3) on the Cartesian plane.
		If you can travel only horizontally or vertically (like a taxicab in a city where all the streets run North-South and East-West), the distance you have to travel to get from the origin to the point (2,3) is 5.
		In Euclidean geometry, for three points A, B, and C we always have EMBED Equation.3 This is called the triangle inequality.
	www.kctm.org /taxicab.doc (749 words)

	Geometry -- Taxicab Treasure Hunt
		Taxicab geometry is a special kind of geometry that works on city streets.
		The computer tells you the distance using taxicab geometry.
		In taxicab geometry the shortest distance between two points is not a straight line, but rather the number of blocks a taxi has to travel along the streets.
	www.learner.org /teacherslab/math/geometry/shape/taxicab/index.html (123 words)

	Interested in Taxicab geometry? (via CobWeb/3.1 planetlab2.cs.umd.edu) (Site not responding. Last check: 2007-10-08)
		When operating they that the in a called fare only is to a taxi a as town because their the outside of good pick medallion area, car, issued taxicab geometry are livery is up it.
		Take Fleet taxicab geometry your Ford advantage of account.The next is taxicab geometry more passenger forthcoming.Gil Verrazano Narrows and Memorial, Hodges Bridges.Take Fleet your Ford advantage of account.You prior should your your luggage have to making reservations.
		Wheelchair are of in fleet wheelchair use the reserved the most for so not taxicab geometry are regular taxis part cases, exclusively of and users.
	conveyedgy.501megs.com.cob-web.org:8888 /taxicab/geometry.html (833 words)

	[No title]
		On the surface, this activity is a simple game that gives students practice with coordinates, but it is also an introduction to taxicab geometry, a gateway to non-Euclidean geometry.
		Here's the difference: In regular (Euclidean) geometry, the shortest distance between two points is a straight line, but in driving a taxicab, a straight line is not usually possible.
		Use coordinate geometry to represent and examine the properties of geometric figures.
	www.ohiorc.org /ohiorc_resource_display.aspx?recId=15 (515 words)

	Course Descriptions
		We will discuss what it means to specify a geometry in terms of a set of axioms, and we will illustrate this concept with simple finite geometries.
		We will also study the beautiful model of geometry called taxicab geometry, which is based on the notion that the "taxicab" distance between two points is not in a straight line "as a crow flies" but rather along streets "as a taxicab drives".
		The prerequisite for MTH 338 is MTH 252 or consent of the instructor.
	oregonstate.edu /~drayt/Courses/courses.html (812 words)

	Taxicab geometry - Wikipedia, the free encyclopedia
		Any route from a corner to another one that is 3 blocks East and 6 blocks North, will cover at least 9 blocks.
		A circle in taxicab geometry consists of those points that are a fixed Manhattan distance from the center.
		These circles are squares whose sides make a 45° angle with the coordinate axes.
	en.wikipedia.org /wiki/Taxicab_geometry (478 words)

	Taxicab Geometry (Site not responding. Last check: 2007-10-08)
		Explain the difference between geometries that are Euclidean and those which are not.
		Introduce Taxicab geometry and give examples that compare/contrast the two geometries.
		Taxicab Geometry An Adventure in non-Euclidean Geometry, by Eugene F. Krause.
	share3.esd105.wednet.edu /lbohl/lbohl2.htm (297 words)

	Non-Euclidean Geometry
		This lesson is designed to improve students understanding of geometry and measurement concepts.
		Identify the similarities and diferences between geometry on a plane and geometry on a sphere.
		Be sure they record any properties they notice about this geometry on a sheet of paper.
	www.shodor.org /succeed/mathcon/nonEuclid.html (679 words)

	Elementary Mathematics
		Geometry of the Ancients: An exploration of area, perimeter, and volume.
		Polygons..."Demonstrate an understanding of the use of the properties and relationships in geometry and use manipulatives to identify properties of a polygon.
		Taxicab Geometry: In taxicab geometry the shortest distance between two points is not a straight line, but rather the number of blocks a taxi has to travel to find the treasure.
	www.bcps.org /offices/lis/curric/elem/elemgeo.html (1557 words)

	Geometry (Site not responding. Last check: 2007-10-08)
		Geometry is one of the oldest forms of mathematics, used in every ancient culture from Egyptians and Greeks to Mayas and Azteks.
		Although in the time of Euclid, geometry was modelled on a flat plane, in the past century mathematicians have turned to the study of curved spaces like the surface of the earth and more exotic spaces like the grid of streets navigated by a taxi driver.
		Although such a space can be explained to a high school student, the study of metric spaces is one of the most advanced fields of mathematics.
	comet.lehman.cuny.edu /sormani/explore/geometry.html (275 words)

	VMTWiki: TaxicabGeometry (Site not responding. Last check: 2007-10-08)
		The problem is to explore geometry on a grid.
		The taxicab drivers in Gridville have their own version of geometry to help them find their way around efficiently.
		Draw a taxicab-circle of all points that are a distance 4 blocks from a center point.
	mathforum.org /wiki/VMT/VMT?TaxicabGeometry (279 words)

	FundingFactory Lesson Plans
		Knowledge and Skills: The student should be able to: • Analyze the differences in Euclidean and non-Euclidean geometry • Formulate the distance formula and midpoint formula in taxicab geometry • Apply taxicab geometry to a real-life problem
		Activity Two: The teacher will introduce taxicab geometry, a type of non-Euclidean geometry.
		After a discussion of the principles of taxicab geometry, the class will play a treasure hunt game in which the theory of taxicab geometry is stressed (http://www.learner.org/teacherslab/math/geometry/shape/taxicab/).
	lessonplans.fundingfactory.com /plan_details.aspx?id=357 (359 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Subject: Re: taxicab geometry Date: Wed, 20 Dec 2000 03:15:42 GMT Newsgroups: sci.math Summary: [missing] The taxicab distance is more usually called the l_1 (ell sub 1) distance, as part of a large class of distances l_p for 0
		> Is taxicab geometry typically used as a example in non-Euclidean geometry, > or is it considered more of popular curiosity?
		At least on the > popular side "pi" = 4 in taxicab space gets people to think about what > a "circle" is, what "circumference" is, essentially what distance is, > in a non-Euclidean space.
	www.math.niu.edu /~rusin/known-math/00_incoming/taxicab (136 words)

	Amazon.com: Taxicab Geometry: An Adventure in Non-Euclidean Geometry: Books: Eugene F. Krause (Site not responding. Last check: 2007-10-08)
		Students learn to think of the world as Euclidean through most of their instruction; Taxicab Geoemetry gives teachers a very straghtforward way to introduce non-Eucliean Geometry.
		Admittedly, this book is not thorough, and it is very open ended (which I consider to be positive).
		I thought that this book would be about geometry of exotic (but real) places in outer space (such as a fl hole, for example).
	www.amazon.com /Taxicab-Geometry-Adventure-Non-Euclidean/dp/0486252027 (1468 words)

	Taxicab Geometry by Eugene F. Krause, New, Used Books, Cheap Prices, ISBN 0486252027
		The Taxicab: An Urban Transportation Survivor (By Gorman Gilbert,Robert E. Samuels)
		The scale coordinate and its geometry: The quantiz...
		All such content is provided to you "as is." this content and your use of it are subject to change and/or removal at any time.
	www.bookfinder4u.com /detail/0486252027.html (319 words)

	The Geometry Junkyard: Rectilinear Geometry
		This includes geometric problems defined on squares and rectangles, higher dimensional boxes, cubes, and hypercubes, right triangles and other right-angled figures, and "taxicab geometry" in which distances are measured in terms of axis-parallel paths.
		See also Robert Harley's four-colored squared square, Mathworld's perfect square dissection page, a Geometry Forum problem of the week on squared squares, Keith Burnett's perfect square dissection page, and Bob Newman's squared square drawing.
		From the Geometry Junkyard, computational and recreational geometry pointers.
	www.ics.uci.edu /~eppstein/junkyard/rect.html (1398 words)

	Taxicab Geometry assignment
		In your paper, you should explain what Taxicab geometry is and what you have learned about it.
		Is taxicab distance always less or more than Euclidean distance?
		Are there any theorems of Euclidean geometry that aren’t true in taxicab geometry?
	hopper.unco.edu /course/math342/taxicab.html (190 words)

	Taxicab Geometry: An Adventure in Non-Euclidean Geometry
		A straightedge, compass and a little thought are all that’s needed to discover intellectual excitement of geometry.
		Harmonic division and Apollonian circles, inversive geometry, hexlet, Golden Section, more.
		With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry.
	store.doverpublications.com /0486252027.html (101 words)

	Price Compare ISBN 0486252027 Taxicab Geometry: An Adventure in Non-Euclidean Geometry by Eugene F. Krause - Direct ... (Site not responding. Last check: 2007-10-08)
		Some years ago, I was employed by a company that built mapping software.
		The problems cover topics such as finding the point(s) of minimum distance between two or more points and what the taxicab analogues of circles and ellipses are.
		Geometry is the godfather of abstract mathematics, being first used to codify the parceling of land and the construction of cities.
	www.directtextbook.com /prices/0486252027 (667 words)

	[No title]
		ð»¨In coordinate geometry a circle is defined as the set of points in a plane that are the same distance from a given point in the plane.
		ð¨Assumptions of Taxicab Geometry: The grid's horizontal and vertical lines represent streets.
		The numerical coordinates of points in taxicab geometry must therefore always be integers.
	members.aol.com /SKHmath1/act9.ppt (173 words)

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