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Topic: Tangent line

	PlanetMath: tangent plane (elementary) (Site not responding. Last check: 2007-10-08)
		The notion of tangent plane is a generalization of the notion of tangent vector to surfaces.
		Just as the tangent line is a special line which is associated to a point of a smooth curve, so too a tangent plane is a special plane which is associated to a point on a smooth surface.
		Just as the tangent to a line may be understood as the limit of a line connecting two nearby points in the limit where the points coalesce, so too the tangent plane can be regarded as a limit.
	planetmath.org /encyclopedia/TangentPlane.html (1872 words)

	Tangent
		In plane geometry, a straight line is tangent to a curve, at a some point, if both line and curve pass through said point with the same direction; such a line is the best straight-line approximation to the curve at that point.
		It is a mistake to think of tangents as lines which intersect a curve at only one single point.
		Above, it was noted that a secant can be used to approximate a tangent; it could be said that the slope of a secant approaches the slope (or direction) of the tangent, as the secants' points of intersection approach each other.
	www.ebroadcast.com.au /lookup/encyclopedia/ta/Tangent_line.html (544 words)

	PlanetMath: tangent line (Site not responding. Last check: 2007-10-08)
		Because the tangency is a local property on the curve, the tangent with the tangency point
		tangent, tangent of the curve, tangent to the curve
		This is version 8 of tangent line, born on 2004-11-22, modified 2006-04-28.
	planetmath.org /encyclopedia/TangencyPoint.html (163 words)

	tangent. The Columbia Encyclopedia, Sixth Edition. 2001-05
		For other curves and surfaces the tangent line at a given point P is defined as the limiting position, if such a limit exists, of a secant line through P and another point P´ on the curve or surface as P´ is allowed to approach P.
		The tangent plane to a surface at a point is the plane in which every line in the plane that passes through the point is a tangent line to the surface at that point.
		The study of tangent lines and planes usually requires the concepts of the calculus and is included within the scope of differential geometry.
	www.bartleby.com /65/ta/tangent.html (183 words)

	Tangents and slopes
		In terms of the unit circle diagram, the tangent is the length of the vertical line ED tangent to the circle from the point of tangency E to the point D where that tangent line cuts the ray AD forming the angle.
		Therefore, the slope is the tangent of the angle of slope.
		It may be better to say that the tangent of 90° is undefined since, using the circle definition, the ray out from the origin at 90° never meets the tangent line.
	www.clarku.edu /~djoyce/trig/tangents.html (1160 words)

	Tangent - Wikipedia, the free encyclopedia
		In plane geometry, a straight line is tangent to a curve, at some point, if both line and curve pass through the point with the same direction.
		Tangent was introduced by the Danish mathematician Thomas Fincke in his book Geometria rotundi (1583).
		The trigonometric tangent function arises as a generating function in combinatorics; see alternating permutation.
	en.wikipedia.org /wiki/Tangent (709 words)

	Mathwords: Tangent Line
		A line that touches a curve at a point without crossing over.
		Formally, it is a line which intersects a differentiable curve at a point where the slope of the curve equals the slope of the line.
		Note: A line tangent to a circle is perpendicular to the radius to the point of tangency.
	www.mathwords.com /t/tangent_line.htm (63 words)

	Tangent Line Applet (Site not responding. Last check: 2007-10-08)
		The red line in the following applet is the tangent line to the graph.
		The tangent line is the limit of secant lines that pass through two points of the function's graph.
		Notice that the secant line approaches the tangent line as you move the points closer together.
	www.unc.edu /~upshaw/Java/TanSec.html (241 words)

	The Tangent Line (Site not responding. Last check: 2007-10-08)
		In the event there is an interfering ball along the altered tangent line, you have the option of reaching the same position point with different tangent paths.
		Although the natural tangent line is to the short rail clear of the corner pocket, many beginners end up scratching in the corner (broken line).
		Hitting the shot thin creates a tangent line to the long rail between the side and corner pockets, and bottom english can actually bend the tangent to, and not away from the corner.
	coe.west.asu.edu /394/DaveF/tangent.html (515 words)

	Envelope of lines meeting a fixed line and tangent to 2 spheres
		The common tangent lines are the lines in the tangent plane meeting the point of tangency.
		The common tangent lines are the ruling of the cone.
		The common tangents are the lines in that plane tangent to the circle.
	www.math.tamu.edu /~frank.sottile/stories/3Spheres (472 words)

	Solve Tangent Lines Problems in Calculus
		Tangent lines problems and their solutions are presented.
		The points at which the tangent lines are parallel to the x axis are: (-1,2) and (1,-2).
		- 3x where the tangent line is parallel to the line whose equation is given by y = 9x + 4.
	www.analyzemath.com /calculus/Problems/tangent_lines.html (534 words)

	Center for Technology and Teacher Education: Mathematics Activities
		To construct the tangent line to the curve at C', we need the coordinates of a point through which the tangent line passes and the slope of the tangent line.
		Is the slope of the tangent line to the the graph of f(x) through (-1, 0) the same as the slope to the tangent line to the graph of f(x) through (-2, 0)?
		A tangent line to a curve is a line meeting a curve or surface at a point and having at that point the same direction as the curve or surface.
	teacherlink.org /content/math/activities/skpv4-tangentlines/guide.htm (1551 words)

	Topics in trigonometry: Line values
		THE LINE VALUE of a trigonometric function is a straight line whose length represents the value of that function.
		As the central angle changes, the line becomes a kind of "graph" of the function during one revolution.
		The graph of a trigonometric function is basically its line value plotted as the y-coördinate, versus radian angle x.
	www.themathpage.com /aTrig/line.htm (750 words)

	Tangent Lines
		The line in question is the tangent line to the graph of f at the point (a,f(a)).
		When f is differentiable at a, an equation that describes the tangent line can be obtained as follows.
		An equation for the tangent line arises from the point-slope equation for a line.
	oregonstate.edu /instruct/mth251/cq/Stage5/Lesson/tangentLine.html (377 words)

	Delaware Geological Survey
		They are the east-west boundary, or Transpeninsular Line; the north-south boundary, or the Tangent Line, Arc, and North lines;; the Delaware-Pennsylvania boundary, including the Top of the Wedge Line and the 12-mile Circle; and the Delaware-New Jersey boundary including the 1934 Mean Low Water Line and the Delaware Bay Line.
		The Arc Line is a small portion of the 12-mile Circle that extends west of a line that would run due north of the Tangent Stone.
		This is the point where the Arc Line intersects the due north line extending from the Tangent Stone.
	www.udel.edu /dgs/Publications/pubsonline/info6.html (1177 words)

	Fanzing 1 - December 1997 - Tangent Reviews
		Tangent was a concept by Dan Jurgens, inspired by Julius Schwartz.
		These comics can't possibly be spun-off into ongoing series, given that their names are being used by the current characters; when Julie Schwartz intro'd The Flash and Green Lantern, the previous characters of those names had been out of usage for many years, and that's a substantial difference.
		Atom is the "Superman" of the Tangent Universe.
	www.fanzing.com /mag/fanzing01/feature.shtml (1060 words)

	Tangent Planes and Normal Lines (Site not responding. Last check: 2007-10-08)
		In particular the gradient vector is orthogonal to the tangent line of any curve on the surface.
		These two vectors will both be perpendicular to the tangent line to the curve at the point, hence their cross product will be parallel to this tangent line.
		Hence the equation of the tangent line is
	ltcconline.net /greenl/courses/107/PartDeriv/tanplane.htm (340 words)

	tangent_lines.html
		of the line tangent to the graph of
		Plot both the function and the tangent line in the same window.
		Use the solve command to find the x-coordinate of the point where the tangent line intersects the x-axis.
	www.math.uga.edu /calclab/calclab2200/tangent_lines1.html (602 words)

	Tangent Computer: Press Releases
		Tangent Computer, Inc., manufacturer of computer systems engineered for education and government environments, today announced the introduction of the Shuttle 6700 notebook computer with integrated 802.11b wireless.
		Tangent Computer is the largest computer manufacturer selling directly and exclusively to educational institutions and state & local governments.
		Tangent, the Tangent logo, and Valera are registered trademarks and Pillar and Network Alert are trademarks of Tangent Computer, Inc. Pentium, Intel Inside, and Intel Inside logo are trademarks or registered trademarks of Intel Corporation or its subsidiaries in the United States and other countries.
	www.tangent.com /news/press38.htm (460 words)

	A Tangent Plane Applet
		It should be noted that the tangent plane, if it exists, is the plane that contains the two tangent lines for the slice curves.
		If you rotate the function graph so that you are looking at one of the tangent lines head on, the tangent plane seems to be a tangent line to the other slice curve.
		For the function we start with, the tangent plane is tangent to the surface in the sense of touching the surface at (x0, y0, f(x0, y0)), and at no other point in the neighborhood.
	www.slu.edu /classes/maymk/banchoff/TangentPlane.html (360 words)

	Tangent Line Approximation - HMC Calculus Tutorial
		)) and moving along the tangent line to approximate the value of the function at x.
		Zoom in on the point to see geometrically how close together the curve and the tangent line are at x = 1.04.
		The equation of the tangent line is given by
	www.math.hmc.edu /calculus/tutorials/tangent_line (326 words)

	[No title]
		For illustration, we draw the tangent line to the function y = -.2x 3 — (x — 1)2 + 4 at x = 1.
		Enter the x-value at which you want the tangent line.
		The indicated point is marked, the tangent line is drawn, and its equation is displayed.
	www.humboldt.edu /~cmb2/technology/ti86index/tangentline.doc (181 words)

	SULIS Implementation - Landscape Design Principles: How Line Forms Dictate Space and Style
		Line forms emphasize real and imaginary lines and play an important role in the creation of large and small spaces within a landscape.
		Line forms dictate traffic patterns within the landscape and help visitors guide visitors through the various spaces.
		Each type of line form -- rectilinear, arc and tangent, curvilinear, etc. -- will create spaces differently and the designer should be aware that the line form they choose to define a space will depend on the design style they are trying to achieve and the desired experience.
	www.sustland.umn.edu /design/lineforms.html (849 words)

	Secant line - Wikipedia, the free encyclopedia
		A secant line of a curve is a line that intersects two or more points on the curve.
		A chord is a segment of a secant line whose both ends lie on the curve.
		Draw a secant line to the unit circle (centered at the origin) that passes through the origin and through (cos θ, sin θ), the point on the unit circle at an angle of θ.
	en.wikipedia.org /wiki/Secant_line (391 words)

	Tangent Line (Site not responding. Last check: 2007-10-08)
		The derivative is a slope-predictor of a tangent line to a particular function.
		To show the graph of the tangent line at any point, in graphing calculator we can type in the equation y+x^2 and for the equation of the tangent line y=(2a)(x-a)+a^2.
		The equation for the tangent lines would be f(x)=(cos a)(x)-a(a-(cos a)).
	jwilson.coe.uga.edu /EMT668/EMAT4680.folders/Swain/tangentline.html (284 words)

	Spin and the Tangent Line - Easy Pool Tutor (Site not responding. Last check: 2007-10-08)
		In this diagram, Line A is the line to the pocket, Line B is the tangent line.
		Line B is perpendicular (makes a right angle) with Line A. If we use a medium pace stroke with a center ball hit on the CB, the CB will travel more or less along this line.
		Re: Spin and the Tangent Line by doomcue on Thu, Jun 3, 2004 @ 13:00:52 CDT
	www.easypooltutor.com /article62.html (671 words)

	Differentiation: gradient of the tangent (Site not responding. Last check: 2007-10-08)
		The gradient of a curve is the gradient of its tangent
		The straight line that's as steep as the curve is called the tangent to the curve at that point.
		It is possible to draw tangents "by eye", but this is notoriously inaccurate.
	metric.ma.ic.ac.uk /differentiation/principles/tangents (240 words)

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