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Topic: Golden angle

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	Kurt Angle: WWF's Golden Boy
		Angle's muscles ripple out of his tight red trunks as he viciously kicks his opponent, Wolfie D, a good ole boy hillbilly who wears baggy shorts and carries a rusted hubcap.
		Angle is scheduled to make his first televised WWFappearance tonight in a pay-per-view show in Detroit:a slammin', gruntin', trash-talkin' coming-out party, if you will, in front of millions of fans.
		Angle is endorsing a WWF meat snack called Ostrim, a sort of low-fat version of a Slim Jim.
	www.post-gazette.com /magazine/19991114angle2.asp (2650 words)

	Golden angle - Wikipedia, the free encyclopedia
		In geometry, the golden angle is the angle created by dividing the circumference c of a circle into a section a and a smaller section b such that
		Let f be the fraction of the circumference subtended by the golden angle, or equivalently, the golden angle divided by the angular measurement of the circle.
		Perhaps most notably, the golden angle is the angle separating the florets on a sunflower.
	en.wikipedia.org /wiki/Golden_angle (241 words)

	Golden ratio - Wikipedia, the free encyclopedia
		Shapes proportioned according to the golden ratio have long been considered aesthetically pleasing in Western cultures, and the golden ratio is still used frequently in art and design, suggesting a natural balance between symmetry and asymmetry.
		Equivalently, they are in the golden ratio if the ratio of the larger one to the smaller one equals the ratio of the smaller one to their difference, i.e.
		Hellenistic mathematician Euclid spoke of the "golden mean" this way, "a straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser".
	en.wikipedia.org /wiki/Golden_ratio (2449 words)

	Patterns in nature (1)
		For instance, the golden spiral is a logarithmic or equiangular spiral – a type of spiral found in unicellular foraminifera, sunflowers, seashells, animal horns and tusks, beaks and claws, whirlpools, hurricanes, and spiral galaxies.
		The golden ratio appears in pentagonal forms of symmetry, notably in the five-pointed star (or pentagram), which was the emblem of the Pythagorean brotherhood.
		The sum of the angles of the platonic solids is 3600 degrees for the icosahedron, 6480 for the dodecahedron, 1440 for the octahedron, 2160 for the cube, and 720 for the tetrahedron.
	ourworld.compuserve.com /homepages/dp5/pattern1.htm (3992 words)

	Nutritional Sounds Sound - Music
		Nature: Phi Golden Means ratio (1.618034) The sunflower, as in many of nature's creations, displays a predictable angle between successive primordia (growth from small lumps of plant tissue), which is very close to 137.5 degrees.
		If we multiplied the G# 26.697561 by the golden means angle we would end up at the note of C 16.50 (our starting point).
		The golden means angle is also a counterclockwise rotation, a yang energy.
	www.nutritionalsounds.com /holder.asp?content=sound (741 words)

	SIMPLE (Site not responding. Last check: 2007-10-20)
		Less ancient is the related "golden angle" of 36° occurring in the pentagon and in Penrose tessellations.
		However, to counter these eurocentrists who proclaim the frequent occurrence of the golden ratio is a proof of Western superiority, some committed multiculturalists, with an eventual political agenda, "discovered" it on their turn in African statues or Arab mosques.
		The "golden mean gauge" commercial announcement checks a moth's wing for presence of the Golden Proportion while the golden section dental set verifies the beauty of teeth.
	www.mi.sanu.ac.yu /vismath/visbook/huylebrouck (954 words)

	Golden Ratio
		A tall golden triangle is any isosceles triangle with two long sides and one short side, where the ratio of long to short is the golden ratio.
		A short golden triangle is any isosceles triangle with two short sides and one long side, where the ratio of long to short is the golden ratio.
		Prove that ACD is a short golden triangle: that it has two equal short sides, and the ratio of long to short is the golden ratio.
	www.math.csusb.edu /courses/m129/golden/golden_ratio.html (1363 words)

	[No title]
		This angle is known as the golden angle.
		At angles just less than (below left) or just greater than (below right) the golden angle, a fairly tight packing is achieved; however, the tightest packing (below center) occurs when the angle of divergence is the golden angle.
		Another theory is that the golden angle was not always present in the generative spiral, but that over time plants have been fine-tuned by natural selection to favor the tightest packing of primordia.
	www.yellowpigs.net /thesis/extramath.tex.txt (5199 words)

	the golden ratio
		The vertices of three golden rectangles two by two orthogonal are the vertices of a regular icosahedron; more generally two opposite edges of a regular icosahedron define a golden rectangle (thus there are 15).
		A rhombus whose diagonal's ratio is the golden ratio is a golden rhombus (its vertices are the midpoints of the sides of a golden rectangle).
		An ellipse inscribed in a golden rectangle is a golden ellipse (ratio of the axis equal to φ).
	www.ac-noumea.nc /maths/amc/polyhedr/gold_.htm (653 words)

	Heavenly Harmonies
		The interior of this golden tent is brightly illuminated by glass lanterns hung from polished brass chains, dangling a mere hand's breath above the height of a Gor'Tog.
		On the pine table you see a large white ironwood angle harp inlaid with glittering brass suns, a large oak angle harp inlaid with tiny ivory fae, a large redwood angle harp carved with men stalking a dragon and a large rosewood angle harp delicately engraved with chains of interwoven roses.
		On the pine table you see a child's ironwood angle harp, a child's cedar angle harp, a large ebonwood angle harp, a large golden oak angle harp, a large ironwood angle harp, a large cedar angle harp, a child's ebonwood angle harp and a child's golden oak angle harp.
	members.aol.com /hrshellkw/dr/simufest/hva.htm (1845 words)

	fibonacci
		This angle is called the golden angle, and it divides the complete 360 degree circle in the golden section, 0.618033989.
		The plant uses the golden angle, not because it is a philosopher, a mathematician or an aesthete, but because it packs the most into the smallest area.
		Apart from the numbers needed to specify the width of the trunk and the spacing of the rings, the only parameters used were the golden angle and the direction of winding.
	www.brantacan.org.uk /fibonacci.htm (3332 words)

	Christian Lange
		The golden egg has a lenght of 0,423584 units and a width of 0,261789 units, the volume is 0,009408 volume-units.
		If you draw a line between pyramids top to the mid of one of the 4 borders, the lenght of this line is 1,618034 times longer than the line from the center of the quadratic base to the mid of a side borderline.
		For this reason, the angle of 51,84° is the golden angle.
	www.sectioaurea.com /sectioaurea/the_golden_angle.htm (833 words)

	Joseph Campbell Foundation Forums - View Topic (Site not responding. Last check: 2007-10-20)
		The sum of the angles of all the triangles formed by the sides of the polygon and the radii taken together are the number sides, n, of the polygon times two right angles, or 180 degrees.
		The sum of the angles of the polygon are that of the triangles minus the angles at its center, or A, the sum of the angles of the polygon equals n(180 degrees)-360 degrees, or
		Now it is entirely possible that ancient cultures might have noticed times when the moon set at an angle of rotation clockwise around the horizon from north that is the same angle of rotation around the stem of a plant by consecutive leaves, and identified this as approximately 2/3, an approximation to the golden angle.
	www.jcf.org /forum/viewtopic.php?topic=1295&forum=34&1 (2531 words)

	World Mysteries - Science Mysteries, Fibonacci Numbers and Nature
		The spiral inside a nautilus shell is remarkably close to the golden section, and the ratio of the lengths of the thorax and abdomen in most bees is nearly the golden ratio.
		Golden Ratio: 1, 1, 2, 3, 5, 8, 13, 21, 34 etc. Each succeeding number after 1 is equal to the sum of the two preceding numbers.
		The golden ratio and its application are similar although the golden ratio is not as well known and its' points of intersection are closer together.
	www.world-mysteries.com /sci_17.htm (4159 words)

	FiboGolden
		The Golden Angle is related to the Golden Mean, itself a limit of quotients of Fibonacci numbers.
		The angle between leaves 2 and 3 and the angle between leaves 5 and 6 are both very close to 137.5
		The Golden Section is the only way to divide a segment so that the ratio of the large segment (Red here) over the small (Gold) is the same as the ratio of the whole segment (Whole) over the large (Red).
	maven.smith.edu /~phyllo/About/fibogolden.html (529 words)

	Intelligent design, the golden angel and Fibonacci sequence - Forums powered by UBBThreads™ (Site not responding. Last check: 2007-10-20)
		I had never heard of either the golden angle (approximately 137.5 degrees) or the Fibonacci sequence (each number after one is the sum of the previous two numbers) which is: 1,1,2,3,5,8,13,21,34,55,89....
		Straying from the golden angle by even one tenth of a degree causes the effect to be lost.
		Now creation by intelligent design of the golden angle and Fibonacci sequence into the various genes involved in various flowers is a logical explanation for this.
	uplink.space.com /showflat.php?Board=phenomena&Number=575200 (2112 words)

	Flowers and Fibonacci
		In fact, if the angle between the appearance of each seed is a portion of a turn which corresponds to a simple fraction, 1/3, 1/4, 3/4, 2/5, 3/7, etc (that is a simple rational number), one always obtains a series of straight lines.
		The corresponding angle, the golden angle, is 137.5 degrees.
		With this angle, one obtains the optimal filling, that is, the same spacing between all the seeds (figure 3).
	www.popmath.org.uk /rpamaths/rpampages/sunflower.html (740 words)

	Fibonacci spirals seen in the arrangement of florets in CYCAS REVOLUTA flower
		Extensive observations in botany show that in more than 90% of the plants studied worldwide primordia emerge as protuberances at locations such that the angle phi subtended at the apical center by two successive primordia is equal to the golden angle {2pie(1-(1/tau))) where tau is the golden* mean and is approximately equal to 137.5 degrees.
		etc., underlying the golden angle are exhibited by the parastichy pairs e.g., 5 spirals in the clock-wise (anti clock-wise) direction are always accompanied by 8 spirals in the counterclock-wise (clock wise) direction.
		For example, the ratio of the length of the diagonal to the side in a regular pentagon is equal to the golden ratio.
	members.tripod.com /~amselvam/cycas/cycas.html (847 words)

	Introduction to the Theory of Design (Site not responding. Last check: 2007-10-20)
		The radius increase in proportion to the angle.
		If the angle increases with the same quantity, the radii at these angles satisfy the following proportionalities.
		In nature we have a lot of plants with a phyllotaxis of five-fold rotational symmetry or that with golden ratio.
	www.kobe-du.ac.jp /gsdr/gsdr/kiso04/03-e.html (698 words)

	Fibonacci
		The plant uses the golden angle, not because it is a philosopher, a mathematician or an aesthete, but because it packs the most into the smallest area.
		Apart from the numbers needed to specify the width of the trunk and the spacing of the rings, the only parameters used were the golden angle and the direction of winding.
		Then it uses the golden angle so that you can see how no obvious pattern emerges, and how the space is filled without apparent bias.
	www.branta.connectfree.co.uk /fibonacci.htm (5852 words)

	Irrational Number 5
		The angle between one stem and the next is always the same.
		This would explain why the "golden mean" angle, and angles related to it, appear so often in nature.
		Using the "golden mean" spacing g, as the seed size varies, the different convergents manifest themselves: different combinations of Fibonacci numbers appear as the number of left and right-hand "spirals":
	e-math.ams.org /featurecolumn/archive/irrational5.html (228 words)

	The Golden Angle
		Well I felt that perhaps the angle 18 was represented by Isis instead so I did a little reading and studying and found that the sine of 18 degrees is.30901699437494 So what you might ask.
		the angle that generates a sine of the golden mean or as I call it now the "GOLDEN ANGLE" is 38 degrees 10 minutes 21.75 seconds.
		Now I contend that with all the erosion and damage it is not hard to imagine that the angle of the GP is indeed the GOLDEN ANGLE which I have stated above and that this is indeed what the Ancient Egyptians were trying to tell us or at least show us.
	www.fortunecity.com /meltingpot/gipsy/670/TheGoldenAngle.html (725 words)

	Diminishing angle: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-20)
		(the golden angle is the angle created by dividing the circumference c of a circle into a section a and a smaller section b such...
		A central angle is an angle whose vertex is the center of a circle, EHandler: no quick summary.
		The angular diameter of an object as seen from a given position is the diameter measured as an angle....
	www.absoluteastronomy.com /encyclopedia/d/di/diminishing_angle.htm (576 words)

	Phyllotaxy (Site not responding. Last check: 2007-10-20)
		In many cases, such as the celebrated case of the sunflower head, phyllotactic patterns involve the golden angle.
		Leaf placement is more favorable for certain angles than for other angles, and the ''optimal'' leaf placement is achieved when the angle is 360/φ.
		If you picked an angle like 90 degrees, you would be making a mistake, because then when the time came to put out leaf #5, you would have gone all the way around your stalk and leaf #5 would point in the same direction as leaf #1 and keep the sun from reaching it.
	www.wwwtln.com /finance/144/phyllotaxy.html (662 words)

	1.618 is the magic number \| Technology \| Guardian Unlimited Technology
		The golden ratio is the only number whose square can be produced simply by adding 1 and whose reciprocal by subtracting 1.
		The golden ratio is also difficult to pin down: it's the most difficult to express as any kind of fraction and its digits - 10 million of which were computed in 1996 - never repeat.
		It was this elusive nature that led the 15th-century Italian friar and mathematician Luca Pacioli to equate the golden ratio with the incomprehensibility of God.
	technology.guardian.co.uk /online/science/story/0,12450,875198,00.html (1004 words)

	The Fountain Magazine
		This golden number is the basic number at work in aesthetics; there are even claims that the Golden Ratio was used by Leonardo da Vinci when painting the Mona Lisa, and by the Greeks in building the Parthenon.
		It was the elusive nature of the Golden Ratio that led the Italian friar and mathematician Luca Pacioli to equate it with the incomprehensibility of God.
		The most common angle between successive leaves is 137.5 degrees – the Golden Angle; 137.5=3d 360-360/G, where G is the Golden Ratio.
	www.fountainmagazine.com /articles.php?SIN=cf8377aeff&k=222&762967487&show=part1 (1376 words)

	More True Applications of the Golden Number by Huylebrouck and Labarque for the Nexus Network Journal vol.4 no.1 ... (Site not responding. Last check: 2007-10-20)
		he golden number (or golden section, mean, or ratio, or divine proportion, etc.) arises when a line segment of length x (>1) is divided into two pieces of lengths 1 and x-1, such that the whole length is to 1, as 1 is to the remaining piece, x-1.
		Therefore, the related angle of 36° is perhaps appropriately called the "golden angle" (Figure 1).
		Nevertheless, psychological golden section tests may be reformulated as "finding the rectangle such that the added area is maximal when compared to two squares constructed on the diagonal".
	www.nexusjournal.com /Huy-Lab.html (3505 words)

	Golden Ratio
		The blue triangle has its sides in the golden ratio with its base, and the red triangle has its base in the golden ratio with one of the sides.
		If we divide a circle into two arcs in the proportion of the Golden ratio, the central angle of the smaller arc marks off the Golden Angle, is 137.5 degrees.
		If we take the isoceles triangle that has the two base angles of 72 degrees and we bisect one of the base angles, we should see that we get another Golden triangle that is similar to the first (Figure 1).
	jwilson.coe.uga.edu /emt669/Student.Folders/Frietag.Mark/Homepage/Goldenratio/goldenratio.html (2304 words)

	Fibonacci Numbers in Nature
		This angle is called the golden angle, and it divides the complete 360 degree circle in the golden section, 0.618033989.
		Look at almost any Christian cross; the ratio of the vertical part to the horizontal is the golden ratio.
		The spiral inside a nautilus shell is remarkably close to the golden section, and the ratio of the lengths of the thorax and abdomen in most bees is nearly the golden ratio.
	www.e-telescope.gr /en/cat04/art04_040616.htm (1270 words)

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