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Topic: Heptagon

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	Heptagon - Wikipedia, the free encyclopedia
		In geometry, a heptagon is a polygon with seven sides and seven angles.
		In a regular heptagon, in which all sides and all angles are equal, the sides meet at an angle of 5π/7 radians, approximately 128.571 degrees.
		The heptagon is also sometimes referred to as the septagon, using "sept-" (an elision of septua-, a Latin-derived numerical prefix, rather than hepta-, a Greek-derived numerical prefix).
	en.wikipedia.org /wiki/Heptagon (269 words)

	Cherokee war: White and Red organizations
		The procession of priests bearing the candidate walked silently around the heptagon four times and then lowered the platform to within three feet of the ground, whereupon the candidate climbed onto the back of an appointed person and was carried into the heptagon.
		In case of a sudden attack, the standard was raised in front of the national heptagon, and the national council would, after assembling for divination with tobacco smoke to learn the nature and extent of the emergency.
		On arriving at the heptagon, which was already filled with the leaders of the Cherokee Nation, the group circled it once and then entered to lead the candidate to his seat, which faced east and was situated directly in front of the seats of the Uku and the retiring Great War Chief.
	www.cherokeebyblood.com /cherwar.htm (4222 words)

	euroLED 2006: The premier European event in Solid State Lighting
		Heptagon's highly skilled engineers support the customer from the initial concept through the design implementation to full-scale production, thus ensuring that new applications are developed in an integrated process.
		Heptagon's components are currently used in a variety of global market segments, including lighting, telecommunications, mobile datacomms and consumer electronics.
		Heptagons' customers are large multinational companies as well as medium and small -size high-tech and start-up companies.
	www.euroled.org /heptagon.html (242 words)

	heptagon (Site not responding. Last check: 2007-09-07)
		Conway's construction of a regular heptagon, given angle trisection.
		Inscribe a star of David in a regular hexagon in a circle, as shown.
		Note the eyeball indistinguishability between the length of the heptagon side (fl, leftmost vertical) = 4 sin pi/7 ~ 1.7355, and the separation of the horizontal sides of the star of David (green and brown) = sqrt 3 = 1.7321
	www.tweedledum.com /rwg/heptagon.htm (133 words)

	Figures and polygons
		The sum of the angles of a hexagon is 720 degrees.
		The sum of the angles of a heptagon is 900 degrees.
		The sum of the angles of an octagon is 1080 degrees.
	www.mathleague.com /help/geometry/polygons.htm (620 words)

	MIG: Member News Article (Site not responding. Last check: 2007-09-07)
		Heptagon is one of the few companies worldwide that has successfully implemented a nanoimprint lithography production process and is working with relatively large substrate sizes of 5" and 6".
		Heptagon is a privately held Finnish-Swiss company offering advanced diffractive and refractive micro-optics products to OEM suppliers.
		Heptagon's components are used in many applications including, LED lensing, imaging, display, optical communications, and consumer electronics.
	www.memsindustrygroup.org /news_view.asp?nid=678&p=1 (462 words)

	The Heptagon Flat
		The sevenly flat is the heptagonal version of the Fibonacci series.
		The numbers a and b are the chords of a heptagon, of edge 1.
		Logrithmetic: When these values are used, the numbers given are direct powers of the axies, in much the same way as the series based on 1 and 1.61803398875 are strictly the powers of tau.
	www.geocities.com /os2fan2/p7flat.html (540 words)

	heptagon (Site not responding. Last check: 2007-09-07)
		The heptagon is the seven-sided polygon, also known as a septagon.
		The regular heptagon is the regular polygon with seven sides.
		The regular heptagon cannot be constructed using the classical Greek rules of geometric construction, but it can be done using a Neusis construction.
	www.2dcurves.com /line/linehe.html (91 words)

	Connecting carbon nanotubes with pentagon-heptagon pair defects
		When the pentagon and heptagon are positioned at two diametrically-opposed sides of the structure, the axis of the two connected nanotubes make an angle around 35°.
		The angle can be made smaller by putting the pentagon and heptagon closer to each other [4], and it is even possible to connect two different nanotubes without bending the structure by aligning the pentagon and heptagon along the same side [5].
		The (9,0)-(12,0) connection illustrated on the left was constructed with a pair of pentagon and heptagon (by courtesy of Riichiro Saito).
	www.fundp.ac.be /~phlambin/Nanotube/knee.html (677 words)

	Constructing A Heptagon
		This circle intersects the original circle at two points of the heptagon.
		G,P, and P2 are points of the heptagon.
		Make one of the points of the heptagon the point where the circle intersects the y-axis.
	www.geocities.com /robinhuiscool/heptagon.html (254 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-09-07)
		Date: 04/06/2001 at 13:12:34 From: Todd McCready Subject: Properties of a Regular Heptagon I am stuck on a problem I was given for a math contest.
		It seems that perhaps using the law of sines we should be able to show that in a triangle whose angles are in the ratio A:B:C = 1:2:4, the sides a, b and c satisfy the relation 1/a = (1/b)+(1/c)...
		So here is the proof of the proposition: I'm going to let a, b and c represent the lengths, respectively, of the side of the regular heptagon, the short diagonal of the regular heptagon, and the long diagonal of the regular heptagon.
	mathforum.org /library/drmath/view/51702.html (1122 words)

	Heptagon -- from Wolfram MathWorld (via CobWeb/3.1 planet03.csc.ncsu.edu) (Site not responding. Last check: 2007-09-07)
		According to Bankoff and Garfunkel (1973), "since the earliest days of recorded mathematics, the regular heptagon has been virtually relegated to limbo." Nevertheless, Thébault (1913) discovered many beautiful properties of the heptagon, some of which are discussed by Bankoff and Garfunkel (1973).
		Although the regular heptagon is not a constructible polygon using the classical rules of Greek
		Although the regular heptagon is not constructible using classical techniques, Dixon (1991) gives constructions for several angles very close to
	mathworld.wolfram.com.cob-web.org:8888 /Heptagon.html (370 words)

	The Heptagon: About Us (via CobWeb/3.1 planet03.csc.ncsu.edu) (Site not responding. Last check: 2007-09-07)
		These are seven college-aged students bringing varying experiences together in one site as a foundation for what they hope will become a meeting place for young aspiring sports writers throughout the country as well as a number of athletes, coaches, fans and numerous others.
		One way The Heptagon hopes to do this is by frequently providing weekly columns and monthly links that shed a humorous light on the sports world, in addition to other provided links.
		Though the creators of The Heptagon have high ambitions for the site, we concede that this is a tedious process housed within the confines of busy class schedules, internships and jobs.
	www.theheptagon.com.cob-web.org:8888 /about.html (931 words)

	From Pentagon to Heptagon by Marcus the Marinite for the Nexus Network Journal vol.3 no.3 Summer 2001 (Site not responding. Last check: 2007-09-07)
		Geometer Marcus the Marinite presents a construction for the heptagon that is within an incredibly small percent deviation from the ideal.
		With four of the seven sides of the heptagon completed by the two bisections, and using the lengths of each of the four completed sides of the heptagon to obtain the final three sides by measuring them with the compasses or dividers, cut the rest of the circle of the heptagon.
		Now the radius for the heptagon, OH (r4), is established by doubling the spacing a out from the excircle of the pentagon (this new spacing is labeled "b").
	www.nexusjournal.com /GA-3.3.html (2317 words)

	Heptagon Oy \| Nanovip.com
		Heptagon has special computer programs for analyzing and designing binary, multilevel, and continuous micro and nanosctuctures.
		Heptagon is a privately held Swiss-Finnish manufacturer of diffractive and refractive micro-optical products.
		Heptagon's components are used in optical communication equipment, miniature displays, and a number of optical sensors, to single out only the most important customer segments.
	www.nanovip.com /node/840 (195 words)

	Search ScienceWorld
		It is the locus of points a fixed distance away from a line as measured along a line from the focus point (MacTutor Archive).
		A heptagon, sometimes also known as a septagon, is a seven-sided polygon.The regular heptagon, illustrated above, has Schläfli symbol {7}.
		Using a Neusis construction, cube duplication, angle trisection, and construction of the regular heptagon are soluble.
	scienceworld.wolfram.com /search/index.cgi?as_q=Nicomedes+I (460 words)

	"Heptagon" - one of the sample fractals.
		The "Heptagon" fractal is one of the Mandelbrot type or Type M example fractals.
		The Heptagon fractal is a portion of the Mandelbrot fractal shown at a magnification of 10,000,000,000X.
		The Heptagon fractal uses seven key colors for the exterior (the maximum), spanning the full color spectrum (rainbow).
	www.creativitysoftware.com /fractals-images/pages-hs/heptagon.htm (234 words)

	The Heptagon
		With college wound down for the summer, The Heptagon will shut down to re-tool while our editor and writers work on other projects, including a complete overhaul of the website with a brand new interface.
		In a Heptagon face-off, two New York baseball fans argue why their team is better to root for than the other
		(The Heptagon is a forum for writers, athletes, coaches, fans and all others to tell their story.
	theheptagon.com (146 words)

	The Heptagon
		The Heptagon (7 sided polygon) has been a shape of much mystery in geometry.
		It is impossible to construct a heptagon with compass and straightedge only.
		A and E are two points of the heptagon.
	hep.50g.com /_framed/50g/hep/heptagon.htm (384 words)

	François Viète
		However, I would like to describe here some of his work in geometry, which seems to be less well known: the trisection of the angle, the solution of the ``casus irreducibilis'' of the cubic equation, and the construction of the regular heptagon.
		Then I claim BE is the side of the regular heptagon inscribed in the circle.
		Campanus, in his commentary to Euclid, Book IV, mentions that you could construct a heptagon if you had an isosceles triangle whose base angles are three times the vertex angle.
	math.berkeley.edu /~robin/Viete/construction.html (1493 words)

	Heptagonal number - Wikipedia, the free encyclopedia
		A heptagonal number is a figurate number that represents a heptagon.
		The first few heptagonal numbers are: 1, 7, 18, 34, 55, 81, 112, 148, 189, 235, 286, 342, 403, 469, 540, 616, 697, 783, 874, 970
		Like square numbers, the digital root in base 10 of a heptagonal number can only be 1, 4, 7 or 9.
	en.wikipedia.org /wiki/Heptagonal_number (119 words)

	case study - Heptagon Oy
		Heptagon Oy’s key competence lies in the field of refractive and diffractive optics.
		Several exercises are of course customised to reflect the particular situation of Heptagon Oy.
		Specific results are achieved in telephone calls (securing appointments), determining the needs of potential clients and in presenting Heptagon in front of clients.
	www.krauthammer.com /com-en/who/casestudy-heptagon-oy.html (310 words)

	Nick's Mathematical Puzzles: Solution 91 (Heptagon diagonals)
		A regular heptagon is cyclic (as is as any regular polygon), and therefore any quadrilateral defined by four of its vertices is also cyclic.
		Ptolemy's Theorem states that in a cyclic quadrilateral the sum of the products of the two pairs of opposite sides equals the product of its two diagonals.
		The nonagon diagonals puzzle may be solved by applying Ptolemy's Theorem to cyclic quadrilateral ABDG.
	www.qbyte.org /puzzles/p091ss.html (136 words)

	The Fitful Flog » How to Make a Heptagon from a Circle (Site not responding. Last check: 2007-09-07)
		Here’s the sequenced crease pattern for making the heptagon and here’s an unimproved CP for making a seven pointed twist star.
		I saw there a small video on the famous drawing of the vitruvian man in which they said the distance between the feet was the edge of a heptagon.
		The heptagon fascinated people because it was so hard to construct, I think.
	origami.oschene.com /archives/2006/10/01/how-to-make-a-heptagon-from-a-circle (485 words)

	Heptagon Individual Fitness - Palo Alto, CA, 94301-1045 - Citysearch
		They do a digital body positioning analysis, determine what your posture problems are and take a detailed history.
		The thing I like about Heptagon is that they use whatever works: some pilates-style exercises, some weight lifting.
		And they really listen to you and how your body is reacting to the workout.
	www.citysearch.com /profile/37031880 (154 words)

	[No title] (Site not responding. Last check: 2007-09-07)
		Heptagon Capital, which is headquartered in Hamburg, is an independent, open-end equity investment company for all "free“ i.e.
		We invest venture capital in progressive enterprises with expanding and long-term equity requirements, in particular medium-sized, high-tech as well as innovative, young companies from all lines of business.
		With our many years‘ experience and our pool of professional competence, plus the comprehensive, nationwide network of private savings banks, we are poised and ready to help our partners whenever they need us.
	www.heptagon-capital.de /en/about (132 words)

	Crockett Johnson Homepage: Paintings by Crockett Johnson
		Johnson's construction for a regular heptagon using a compass and straightedge with one mark.
		Angle EDF measures 180/7 degrees, EOF measures 360/7 degrees, and line segment EF is one side of a regular heptagon.
		ABCDEFG is a regular heptagon, with each central angle measuring 360/7 degrees.
	www.k-state.edu /english/nelp/purple/art.html (595 words)

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