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Topic: Golden function

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Golden mean base

Trigonometric identity

Golden ratio

Golden mean

Fibonacci number

Golden angle

Trigonometric function

Table of integrals

List of coshes

Phi (letter)

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	Golden ratio - Wikipedia, the free encyclopedia
		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.
		The golden ratio was first studied by ancient mathematicians due to its frequent appearance in geometry and may have even been understood and used as far back in history as the Egyptians.
		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 (1492 words)

	Golden ratio - Encyclopedia, History, Geography and Biography (Site not responding. Last check: 2007-10-08)
		The golden ratio was first studied by ancient mathematicians due to its frequent appearance in geometry.
		The golden ratio is typically symbolized by the Greek letter φ (phi), with τ (tau) being less common.
		The American mathematician Mark Barr first conceived of the use of the symbol φ to represent the golden ratio, taking it from the first letter in the name of the Greek sculptor Phidias, who was long believed to have used the golden ratio in his designs.
	www.arikah.com /encyclopedia/Golden_mean (1924 words)

	Golden ratio -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		The golden ratio is an (A real number that cannot be expressed as a rational number) irrational number, approximately 1.618, that possesses many interesting properties.
		The golden ratio was first studied by ancient mathematicians due to its frequent appearance in (The pure mathematics of points and lines and curves and surfaces) geometry.
		The name "golden ratio" appears in the form sectio aurea, "golden section", by (Italian painter and sculptor and engineer and scientist and architect; the most versatile genius of the Italian Renaissance (1452-1519)) Leonardo da Vinci.
	www.absoluteastronomy.com /encyclopedia/g/go/golden_ratio.htm (1833 words)

	Encyclopedia: Golden function (Site not responding. Last check: 2007-10-08)
		Graph of a quadratic function: y = x2 - x - 2 = (x+1)(x-2) The x-coordinates of the points where the graph crosses the x-axis, x = -1 and x = 2, are the roots of the quadratic equation: x2 - x - 2 = 0.
		The golden function is connected to the hyperbolic sine by the identity In mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
		In mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
	www.nationmaster.com /encyclopedia/Golden-function (345 words)

	Chapter5
		Golden section search sacrifices being a minimax technique to relax the requirement that the number of experiments be specified in advance.
		Then the function is evaluated at the two points, and the third and subsequent experiments are placed symmetrically in the interval remaining.
		Golden section search will be used to illustrate the procedures to bound the optimum on an open interval.
	www.mpri.lsu.edu /textbook/Chapter5-a.htm (3817 words)

	The Golden Retriever Club of America
		The Golden is a medium sized dog, with males ranging from 23 to 24 inches at the withers and weighing 65 to 75 pounds, while bitches stand 21 ½ to 22 ½ inches and weigh 55 to 65 pounds.
		A Golden with a muzzle that is not straight in profile (one that shows a Roman nose, for example) or one with heavy flews is also incorrect.
		The function of the tail is to act as a rudder both in the water and on land, not as a sail.
	www.grca.org /judgesed/judging_goldens.html (2379 words)

	The Purdue Exponent (Site not responding. Last check: 2007-10-08)
		Golden is working to uncover the mysteries of RNA, which for several years was believed to be a duplicate of DNA’s blueprints for proteins.
		According to Golden, with the discovery that RNA molecules could catalyze biological reactions came the realization that a single biopolymer could perform all of the functions required for life: coding and storage of genetic information and biological catalysis.
		Golden said even in the modern, protein-driven world, RNA molecules continue to perform a variety of cellular functions because, in the presence of magnesium ion, many RNAs can fold into stable three-dimensional structures that support biological functions much like protein enzymes.
	www.purdueexponent.org /2000/07/24/features (391 words)

	STABILITY
		The golden mean phenomenon allows us to establish the dual analogy in mechanisms of resonance and procedures of decision-making as “the entropy-information pendulum” in the cellular organization activity and to consider oncogenesis as a deviation or lag in its function.
		Furthermore, the golden mean and cancer may be defined in the meta-game concepts (Howard, 1966) as equilibrium (in contrast to a gray zone) points in the prisoner’s dilemma of tumor cells between the group (Pareto) and individual (Nash) rationalities and the corresponding strategies of de-escalation and escalation (Saaty, 1968).
		The golden mean and cancer may be presented as the decidable and undecidable relations between the epistemology of the measure of irreversibility and the ontology of the limit of reversibility (resonance/nonresonance conditions).
	www.geocities.com /metadoxy/svc_xiinl_site.html (9861 words)

	Encyclopedia: Golden Mean (Site not responding. Last check: 2007-10-08)
		The Golden Mean is a mathematical expression of proportion that ancient Greek philosophers observed throughout the natural world.
		The simplest geometrical example of the Ratio is the golden rectangle, whose sides have unequal length but whose shape the Greeks found particularly pleasing.
		The two parts of the Golden Mean which can be seen in the Golden rectangle, has two parts; the major and minor parts which are unequal.
	www.nationmaster.com /encyclopedia/Golden-Mean (2608 words)

	Chapter 8 M-Files
		function E = TE(theta) % E = TE(theta) % % theta is a real number in the interval [-pi/2,pi/2] % E is a negative multiple of the total edge length of a tetrahedron % that is inscribed in the unit sphere.
		function f = rho(z,plist) % f = rho(z,plist) % z is a 2-vector whose components are the orbit parameters A and P % respectively.
		function J = Jrho(z,plist) % J = Jrho(z,plist) % J is the Jacobian of the function rho at z.
	www.cs.cornell.edu /cv/Books/SCMV/Mfiles/chap8.htm (2623 words)

	[No title]
		c c it is not actually the distribution function but rather c the often used l function as in johnson and kotz c function returns prob(x>a,y>b) where x,y standard normal c rvs with corr rho c c the first subroutine fn calcs the standard normal density and c distribution function.
		the abscissa of the minimum is returned as xmin, c and the minimum function value is returned as golden, c the returned fucntion value.
		c given a function func, and given distinct initial points c ax and bx, this routine searches in the downhill direc - c tion (defined by the function as evaluated at the initi- c al points returns new points ax, bx, cx which bracket a c minimum of the function.
	www.people.virginia.edu /~sns5r/resint/imputstf/m-estim.f (4889 words)

	ipedia.com: Golden ratio Article (Site not responding. Last check: 2007-10-08)
		The golden mean was found throughout nature, in the structure of nautilus shells, the size of leaves, the branching patterns of trees, and in the human body.
		The Greeks thought that the golden mean described the dimensions of average, and by inference "ideal", body features such as the face and the torso, and the proportions of arms and legs to the size of the body.
		Many paintings are arranged according to golden ratios; buildings and courtyards were designed with golden rectangles, as were great monuments (e.g., the Parthenon and the Great Pyramid at Giza).
	www.ipedia.com /golden_ratio.html (1094 words)

	1.5.2 Brent's Method (Golden Section Search in one dimension) (Site not responding. Last check: 2007-10-08)
		The golden section search (Brent's method) is designed to handle, in effect, the worst possible case of function minimization in one dimension, with the uncooperative minimum hunted down and cornered like a scared rabbit.
		If the function is nicely parabolic near its minimum - surely the generic case for sufficiently smooth functions - then the parabola fitted through any three points ought to take us in a single leap to the minimum, or at least very near ´ it.
		Careful attention must be given to the ''endgame'', where the function is being evaluated very near to the roundoff limit of Equation (1.12).
	linneus20.ethz.ch:8080 /1_5_2.html (1342 words)

	Golden Ponds Restaurant Perth Western Australia - Weddings (Site not responding. Last check: 2007-10-08)
		The Golden Ponds Restaurant is known for creating a magical experience for everyone who visits, whether it is an intimate dinner for two or a large group.
		The Golden Ponds Function Coordinator will assist you with any requests you may have for breakfast, lunch or dinner and will prepare a team to fulfil the best service available on the day.
		Golden Ponds cater for all manner of functions, supporting the event with great service and dedicating the venue to whatever suits the occasion.
	www.goldenponds.com.au /restaurant-weddings-perth.shtml (460 words)

	GOLDEN IRIS MOBILE DISCO
		Golden Iris Mobile Disco, is based in South East London/West Kent, but has travelled as far as Bristol, Portsmouth, Dover, and Colchester!!!.
		Golden Iris has provided music at Weddings, Wedding Anniversaries, Christmas Parties, Club Functions, Childrens Parties, Family 18th & 21st parties, also 30th, 40th, 50th and even at 60th birthday parties, as a wide range of music is provided.
		Golden Iris specialises in 60's, 70's and 80's music, but we have available 800 CD's with about 10,000 tracks right up to the latest chart sounds.
	uk.geocities.com /golden_iris_disco (289 words)

	Golden function -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, the golden function is the upper branch of the (An open curve formed by a plane that cuts the base of a right circular cone) hyperbola
		Applying the (An equation in which the highest power of an unknown quantity is a square) quadratic equation to the above quadratic in a makes it immediately obvious that gold(x) furnishes the positive root of the equation, with -gold(-x) giving the negative solution.
		The golden function is connected to the (Click link for more info and facts about hyperbolic sine) hyperbolic sine by the identity
	www.absoluteastronomy.com /encyclopedia/g/go/golden_function.htm (188 words)

	The Golden Mean
		The Golden Mean (or Golden Section), represented by the Greek letter phi, is one of those mysterious natural numbers, like e or pi, that seem to arise out of the basic structure of our cosmos.
		When you swing the long side of a Golden Rectangle around to create a new rectangle, the line it forms with the short side is made up of two sections having lengths of phi and one, respectively.
		This entire 'Golden Mean' site is dedicated to Liane Hansen of National Public Radio, whose honesty about her unfamiliarity with the 'Golden Section' during a 1995 interview inspired the original version of this page, and to Ken Beattie, who first got me thinking seriously about the signifcance of phi.
	www.vashti.net /mceinc/golden.htm (831 words)

	GOLDEN Home Page - Top Professional Entertainment Service Providers and Booking Agency
		Golden Canadian Productions is a full service entertainment provider and one of the most established and highly regarded Entertainment Agencies in Canada.
		For over 30 years Golden has built up a comprehensive database of talented performers and a great variety of entertainment to bring your event to life.
		Golden has gained an enviable reputation for offering the best independent advice in this field; we will identify and direct you to the finest entertainers most suited to your event and budget.
	www.goldencdnproductions.com (350 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		function [x, xiter]= steepest(x0,tol,maxiter,act,func,grad,varargin) % % Gradient search (steepest descent) algorithm for min/max f(x): % Golden section is used at each iteration to find step-length.
		end function h = f1d(t,f,x,p,varargin) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Evaluate the univariant function % h(t) = f(x + tp) % for given multi-variant function* f % and given vectors x and p.
		h = feval(f, x+tp, varargin{:}); function* [x,f] = golden(xlo, xhi, tol, act, func, varargin) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % This function implements golden section to search % for an optimum of func(x) in the interval [xlo, xhi].
	www.caam.rice.edu /~yzhang/caam378/nlp/steep.m (90 words)

	Golden Key South Africa (Site not responding. Last check: 2007-10-08)
		Also present at the function will be a number of honorary members from the Wits chapter and the event is open to all Golden Key members currently studying at Wits, although places for the event are limited.
		The Golden Key Society Executive Committee of the UKZN Chapter, Howard College campus decided to have a Book Drive Initiative to assist disadvantaged communities in starting up libraries and thus giving people in the community a chance to enrich their lives with knowledge.
		Silvia Constanza Auger was inducted as a member of Golden Key in 2001, during the 2nd year of her LLB degree at the University of Johannesburg (then RAU).
	www.goldenkey.org.za (997 words)

	The 'Golden Mean' in number theory (Site not responding. Last check: 2007-10-08)
		Castro's observation possibly linking the 'Golden String' to a function central to the behaviour of certain eigenvalues in random matrix theory (which in turn appears to be deeply linked to the behaviour of the nontrivial zeros of the Riemann zeta function).
		The choice of the golden mean is dictated by number theory: the golden mean is the irrational number for which it is hardest to give good rational approximants.
		Such wave packets scaled in powers of the golden mean have to be understood as numbers with directions, where bifurcations occur at the edge of chaos, i.e.
	www.maths.ex.ac.uk /~mwatkins/zeta/goldenmean.htm (1193 words)

	ICAI :: Vision :: (Site not responding. Last check: 2007-10-08)
		The Golden Jubilee celebrations of the Institute were inaugurated by Hon’ble Shri Atal Behari Vajpayee on this day at the Siri Fort Auditorium, New Delhi.
		The Prime Minister, Hon’ble Shri Atal Behari Vajpayee who had inaugurated the Golden Jubilee Celebrations of the Institute at the Siri Fort Auditorium on the 1st of July, 1998, also graced the Golden Jubilee Function held in the main hall of Vigyan Bhawan on July 1, 1999.
		While inaugurating the Golden Jubilee Function Shri Vajpayee said “Misuse and wrong use of public funds is a chronic problem affecting implementation of government schemes.
	www.icai.org /institute/a_landmark.html (1734 words)

	Nat' Academies Press, Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003)
		The first, dated 1849, is titled “On the Function that Determines the Totality of Prime Numbers Less Than a Given Limit”; notice the similarity to the title of Riemann’s paper of 10 years later.
		The thesis itself—it is titled “On the representability of a function by a trigonometric series”—is a landmark paper, giving the world the Riemann integral, now taught as a fundamental concept in higher calculus courses.
		A function was not, for Riemann, a mere set of points; still less was it any of its pictorial representations as a graph or a table; and still less a collection of expressions involving algebraic formulas.
	www.nap.edu /books/0309085497/html/118.html (5799 words)

	Happy Together » Full of flaws by using golden function (Site not responding. Last check: 2007-10-08)
		Around the middle of the semester, the teacher asked us to practice “golden function,” which means that we should use a sentence to rephrase others’ sentences during the conversation.
		In his view, the golden function has two functions: first, it can help the conversation keep going.
		If your partner did not agree with your rephrasing, they should also rephrase their words, and then you should use golden function again to negotiate the meaning with your partner, until you reach the consensus.
	schoolof.info /rolcoco/index.php?p=53 (427 words)

	Golden function - Encyclopedia, History, Geography and Biography (Site not responding. Last check: 2007-10-08)
		Golden function - Encyclopedia, History, Geography and Biography
		Applying the quadratic formula to the above quadratic equation in a makes it immediately obvious that gold(x) is the positive root of the equation and −gold(−x) is the negative solution.
		gold(1) gives the golden ratio and gold(2) gives the silver ratio 1 + √2.
	www.arikah.com /encyclopedia/Golden_function (152 words)

	Manideepam - Absar Abdul Azeez Manjiyil
		The awards were announced at a function held at the ICRC Majlis hall on Saturday to commemorate the second death anniversary of Absar Abdul Azeez Manjiyil, a child prodigy who was a former student of Ideal Indian school.
		Subramaniyan, a supervisor at the Pareeksha Bhavan of Calicut University in Kerala presented the awards at the function.
		The golden award will be sent to the winner, the organisers said.
	www.freewebs.com /manideepam/news.htm (1474 words)

	Effects of testosterone, pregnenolone, progesterone and cortisol on pituitary and testicular function in male golden ... (Site not responding. Last check: 2007-10-08)
		Effects of testosterone, pregnenolone, progesterone and cortisol on pituitary and testicular function in male golden hamsters with gonadal atrophy induced by short photoperiods -- Bartke et al.
		Testicular regression was induced in adult golden hamsters by exposure to a short photoperiod (5 h light:19 h darkness).
		Administration of cortisol did not alter any of the parameters of reproductive function that were examined.
	joe.endocrinology-journals.org /cgi/content/abstract/90/1/97 (272 words)

	Golden Ratio Search (Site not responding. Last check: 2007-10-08)
		in a given interval is to evaluate the function many times and search for a local minimum.
		To reduce the number of function evaluations it is important to have a good strategy for determining where
		The next example compares the secant method for root-finding with the golden ratio search method.
	math.fullerton.edu /mathews/n2003/GoldenRatioSearchMod.html (403 words)

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