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Topic: Circle segment

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Circle

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	Circular segment - Wikipedia, the free encyclopedia
		In geometry, a circular segment (also circle segment) is an area of a circle informally defined as an area which is "cut off" from the rest of the circle by a secant or a chord.
		Let R be the radius of the circle, c the chord length, s the arc length, h the height of the segment, and d the height of the triangular portion.
		The area of the circular segment is equal to the area of the circular sector minus the area of the triangular portion.
	en.wikipedia.org /wiki/Circular_segment (229 words)

	#1 Site For Learning Mathematics
		Pi is defined as the ratio of the circumference to the diameter of a circle.
		Hence seg AB is a chord of a circle.
		Secant of a circle : A line, which intersects the circumference of the circle in two distinct points, is known as the secant of a circle.
	home.att.net /~cat5a/circles.htm (720 words)

	Untitled Document (Site not responding. Last check: 2007-10-19)
		Having fixed the distance of the horizontal segment from the center of the circle through the above operation, construct a vesica pisces with points 3 and 6 as the centers of the large outer circles.
		If segment AK is arced to the point it crosses the vertical axis of point J in the diagram above, the ratio between the height and the half base of the resultant triangle is 1.272401.
		If segment AK is arced to the point it crosses the horizontal axis of point J in the diagram above, the ratio between the height and the half base of the resultant triangle is 1.273255.
	home.hiwaay.net /~jalison/hepta.html (597 words)

	Reading the Maps
		In this case the circle would be divided into 3 sections, the bottom half containing a device and filled by one color and the upper half empty and filled by two other colors.
		If no empty circle or circle segment of your color exists then look for a circle of the same color with a device attached, these are teleporters that will zap you back and forth between two points.
		Additionally, #704 (pink upper circle) is the destination for the button in room #707 (pink lower half of circle with the button) on the second floor.
	members.tripod.com /~RealmMaps/readmaps.htm (502 words)

	SparkNotes: Circles: Terms
		Chord - A segment whose endpoints are on a circle.
		Circle Segment - The region within a circle bounded by a chord of that circle and the minor arc whose endpoints are the same as those of the chord.
		Sectors - A region inside a circle bounded by a central angle and the minor arc whose endpoints intersect with the rays that compose the central angle.
	www.sparknotes.com /math/geometry1/circles/terms.html (318 words)

	Circle - Wikipedia, the free encyclopedia
		Circles are conic sections attained when a right circular cone is intersected with a plane perpendicular to the axis of the cone.
		All circles are similar; as a consequence, a circle's circumference and radius are proportional, as are its area and the square of its radius.
		The structure of the enneagram is based partly on the primary triangle of the circle at 0/360 degrees, 120 degrees and 240 degrees of the circle.
	en.wikipedia.org /wiki/Circle (1547 words)

	All Elementary Mathematics - Study Guide - Geometry - Geometrical locus. Circle and circumference...
		Segment of a circle is a part of a circle, bounded by the arc ACB and the corresponding chord AB (Fig.42).
		Sector of a circle is a part of a circle, bounded by the arc AmB and two radii OA and OB, drawn to the ends of the arc (Fig.43).
		A length of arc of a circle is proportional to its radius r and the corresponding central angle
	www.bymath.com /studyguide/geo/sec/geo10.htm (1116 words)

	Segment of a Circle - Math Open Reference (Site not responding. Last check: 2007-10-19)
		Definition: The region between a chord of a circle and its associated arc.
		A segment is defined by the arc and chord that form its outer boundary.
		The angle subtended by the segment to the center of the circle of which it is a part.
	www.mathopenref.com /segment.html (292 words)

	Chapter 5: Circles and Loci
		A circle is the set of all points in a plane that are a given distance from a fixed point in that plane.
		Talking about the radius, when set of all points whose distance from center of the circle is less than the radius, it is called the interior of the circle; when set of all points whose distance from the center of the circle is greater than the radius, it is called the exterior of the circle.
		In the same circle or in congruent circles, chords that are equidistant from the centers are congruent.
	library.advanced.org /16284/g_circle_1.htm (295 words)

	Developing an Equal Area Global Grid by Small Circle Subdivision
		A circle on a sphere is an intersection of a sphere and a plane.
		If the pole of the small circle is moved to a position on the sphere such that the area of the outer sub-triangle is just one-fourth of the area of its parent triangle, the small circle segment is determined.
		ZSC values for 4-fold small circle subdivision at recursion levels 1-6 were computed, with the values for recursion levels 2,4 and 6 plotted on the equilateral triangle diagrams (not the actual sub-triangle shapes) in Figure 19, along with corresponding ZSC values for the ISEA method.
	www.ncgia.ucsb.edu /globalgrids-book/song-kimmerling-sahr (6683 words)

	section7
		A circle is the set of all points in a plane at a fixed distance from a fixed point in the plane.
		A segment from a point of the circle to the center is also called a radius.
		From a given point A on a circle O a diameter AB and a chord AC, equal to the radius of O are constructed.
	www.math.psu.edu /geom/koltsova/section7.html (556 words)

	Untitled Document
		The perpendicular from the centre of a circle to a chord bisects the chord.
		Chords of a circle (or of congruent circles) that are equidistant from the centres are equal.
		The degree measure of an arc of a circle is twice the angle subtended by it at any point of the alternate segment of circle with respect to the arc.
	www.classteacher.com /student/arena/syllabus/syllabusmaths.html (1038 words)

	Nicolaus of Cusa: Quadrature of the Circle
		A segment that is cut off from a circle by a straight line cannot, in respect to its incidental angles, which are parts of its surface, be transformed into a rectilinearly enclosed figure; therefore also not in respect to its totality.
		If therefore this length is extended, in the proportion of the segment lying between the endpoint on eb and the point e to the length ab, or in the proportion of the segment lying between the endpoint on eb and b to the length ab, it remains always proportional.
		Proceeding still farther, we observe the diversity of circles, and that only one can be the largest, the circle in perfected reality, the self-subsisting, eternal and infinite, to which one cannot ascend through ever so many circles, since, in things that admit of larger and smaller, one cannot come to the simply maximum.
	www.schillerinstitute.org /fid_91-96/941_quad_circle.html (4597 words)

	All Elementary Mathematics - Study Guide - Geometry - Ball (sphere)...
		The largest circle is in a section, going through a center of a ball and is called a large circle.
		The segment MN of a perpendicular, drawn from a center N of the circle ABC till intersection with a spherical surface, is called a height of a spherical segment.
		A part of a ball, bounded by a curved surface of a spherical segment (AMCB, Fig.93) and the conic surface OABC, a base of which is a base of a segment (ABC), and a vertex – a center of a ball O, is called a spherical sector.
	www.bymath.com /studyguide/geo/sec/geo18.htm (440 words)

	[No title]
		The radius of a circle is a segment determined by the center and a point on the circle.
		A diameter of a circle is a segment that contains the center and has its endpoints on the circle.
		A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point.
	www.mnstate.edu /peil/M416/Student/joglp2.doc (845 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		Move the endpoint of the segment that lies on the circle around the circle.
		Construct your different circles by locating both the point where you click and hold (the center) and the point where you let go (point on the circumference) in different places, e.g.
		Your final sketch should have a circle, the center point and defining point on the circumference, the diameter and the endpoints of the diameter.
	www.math.sunysb.edu /~dowker/517/worksheetaddendum.doc (781 words)

	Rectangle inside circular segment - GameDev.Net Discussion Forums (Site not responding. Last check: 2007-10-19)
		Then, for each line segment of the rectangle, if a line segment perpendicular to the segment, with a length of the circle's diameter whose midpoint is the circle's center intersects with the original segment, the circle and rect collide.
		For the box vs. circle inclusion test, the fastest way might be (as previously suggested) to test the squared distance between each box corner and the circle center.
		For each line segment from the verts of the rect to the arc's center, the vert is within the arc if the angle is greater than angle 1, and less than angle 2 of the arc.
	www.gamedev.net /community/forums/viewreply.asp?ID=2548203 (821 words)

	Circle Formulas (Site not responding. Last check: 2007-10-19)
		Here are the procedures by which the Circle Calculator determines all of a circle's data from just 2 variables.
		Yes, it turns out that "chord" CD is also the circle's diameter and the 2 chords meet at right angles but neither is required for the theorem to hold true.
		Segment Height ED = Radius AO - Apothem OE 2) Radius AO & Chord AB From the Pythagorean Theorem OE² = AO² - AE²
	www.1728.com /circpart.htm (373 words)

	The Aztec Calendar:The Spatial Divisions
		The remaining seven segments appear to be enclosed, except possibly for the entrance point marked off by the heads of the serpents.
		The remaining 7 segments of the circle may then be considered a whole, as in the following illustration.
		By subtracting one segment from the circle's 360 degrees, a configuration of 7 segments is created that encloses 315 degrees.
	www.earthmatrix.com /aztec/spatial/division.htm (397 words)

	Nazca
		The azimuth of the great circle segment from the axis point to Giza is 9° and the azimuth of the great circle segment from the axis point to Nazca is 120°, showing that the angle at the axis point is also 111°.
		Since the great circle segments from the axis point are perpendicular to the great circle itself, the angles at Giza and Nazca are also 90°.
		Alternatively, the two great circle segments from the axis point to Nazca and from the axis point to Giza are each 25% of the circumference of the earth while the great circle segment from Nazca to Giza is 30.9% of the circumference of the earth.
	home.hiwaay.net /~jalison/nazca.html (638 words)

	MCS 275: REVIEW FOR EXAM 2
		Declare a variable of type Circle and initialize it at the same time with coordinates (1.0, 0.0) for its center and value 3.0 for its radius.
		Write the source code for a function that is passed pointers to two circles and returns 1 if the regions (including boundaries) they enclose have a point in common.
		Write the source code for a function that is passed a segment as a parameter and a returns the circle that contains that segment as a diameter.
	www.math.uic.edu /~srinirm/review2.htm (527 words)

	NonEuclid: The Pseudosphere
		Noticed that the closer a segment is to the Boundary Circle, the "shorter" it appears.
		This set of segments can be thought of as radii of a circle (since they are congruent, and have a common endpoint).
		The set of segments in Figure-3b, have a common endpoint at the center of the Boundary Circle.
	cs.unm.edu /~joel/NonEuclid/pseudosphere.html (624 words)

	Math Forum: Ask Dr. Math FAQ: Segments of Circles
		Suppose you have a segment of a circle, bounded by an arc of the circle and the chord subtending it.
		), the distance from the midpoint of the chord to the center of the circle (the apothem) be d, and the area be K.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /dr.math/faq/faq.circle.segment.html (1009 words)

	Lab 2 – Ap. Circles and Inversion Images
		Now, construct a circle with center A and radius PR and another circle with center B and radius QR. Then when you drag Q, the intersection points S and T of the two circles will trace out the locus for a fixed k.
		Check by measuring the appropriate angle that the red circle and the blue circle are always orthogonal.
		Be able to construct the elliptic pencil of circles and the orthogonal hyperbolic pencil of circles from two points A and B. Explain how to invert the two pencils above to get the set of lines through a point and the circles centered at the same point.
	www.math.washington.edu /~king/coursedir/m445w04/lab/lab02.html (940 words)

	Area of a circle segment - Math Open Reference (Site not responding. Last check: 2007-10-19)
		It can also be found by calculating the area of the whole pie-shaped sector and subtracting the area of the isosceles triangle △ACB.
		The formula for the area of a segment of a circle is:
		R is the radius of the circle of which the segment is a part.
	www.mathopenref.com /segmentarea.html (167 words)

	[No title]
		The function is zero at the points where the circle intersects the extended line along the segment.
		In the remaining case, the segment is neither inside or outside the circle.
		To avoid this, we consider a point on the circle if its distance to the center is "almost" the radius.
	www.math.utah.edu /~treiberg/M2160s6.txt (794 words)

	Dynamic Geometry Workshop: Sketchpad Basics
		Move onto the window and highlight a circle by moving the arrow close to a circle until the arrow becomes horizontal.
		Highlight the circle and hide it using either the menu or the keyboard shortcut.
		Construct a circle, then a triangle ABC, with each of the vertices A, B, and C on the circle.
	www.ux1.eiu.edu /~cfpga/DynamicGeometry/lesson1.html (3103 words)

	Finding out if two areas on the globe intersect
		We present a one-line algorithm that tests for the intersection of two segments of a circle.
		Therefore, in the body of this article, we concentrate on a one-dimensional problem of checking two segments of a circle for intersection.
		Note: since we assumed that segments A and B intersect, one segment must contain an internal point of the other.
	okmij.org /ftp/circle-segments-intersect-p.html (873 words)

	How to script a circle segment between twopoints on a circle line and an angle? - GroupBrowser
		I know the value of the angle, the x/y coordinates of two path points which are elements of the imagined circle, the midpoint coordinates of the circle and its diameter.
		First attempt was to to influence the anchors of the two path points by their handlers to the left and the right by script, but all I get is far away from a nice symmetric curve or better, a segment of a circle.
		If you draw a circle in Illustrator, you will notice that for each 90-degree segment the direction points lie on lines (drawn from the centre of the circle) that make an angle of 28.93 degrees from the vertical or horizontal...
	adobe.groupbrowser.com /t128496.html (1253 words)

	Circle Inscribed in a Circular Segment
		Extend AB beyond A and let it intersect the perpendicular OM to ST at point N. The two triangles AO'B and NOB are similar.
		The two circles are homothetic with center B. The lowest point A of the circle C' is mapped by that homothety onto the lowest point of the circle C, which is M. But any two points that correspond by a homothety lie on a line through the center of the homothety.
		Radical Axis of Circles Inscribed in a Circular Segment
	www.cut-the-knot.org /Curriculum/Geometry/IncircleInSegment.shtml (182 words)

	Geometry (Site not responding. Last check: 2007-10-19)
		To ensure realistic behavior, shapes should be constructed from a combination of line segments with zero-radius circles at the end points.
		For example: A ball is located at (0,0) and is moving in the (1,1) direction towards two line segments; one segments spans the points (1,1),(1,2) and the other spans (1,1),(2,1).
		However, if a circle with zero radius is placed at (1,1) then the ball will bounce off the circle in the expected manner.
	www.mit.edu /~6.170/api/gizmoball/physics/Geometry.html (2896 words)

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