21. Golden Ratio Search Form Societies, honours, etc. JOC/EFR July 2001. The URL of this page is http//wwwhistory.mcs.st-andrews.ac.uk/HistTopics/golden_ratio.html. http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Golden_ratio.html

The Golden ratio Number theory index History Topics Index Version for printing Euclid , in The Elements , says that the line AB is divided in extreme and mean ratio by C if AB AC AC CB Although Euclid does not use the term, we shall call this the golden ratio . The definition appears in Book VI but there is a construction given in Book II, Theorem 11, concerning areas which is solved by dividing a line in the golden ratio. As well as constructions to divide a line in the golden ratio, Euclid gives applications such as the construction of a regular pentagon, an icosahedron and a dodecahedron . Here is how the golden ratio comes into the construction of a pentagon. First construct an isosceles triangle whose base angles are double the vertex angle. This is done by taking a line AB and marking C on the line in the golden ratio. Then draw a circle with centre A radius AB . Mark D on the circle so that AC CD BD . The triangle ABD has the property that its base angles are double its vertex angle. Now starting with such a triangle ABD draw a circle through A B and D . Then bisect the angle ADB with the line DE meeting the circle at E . Note that the line passes through C , the point dividing AB in the golden ratio. Similarly construct

22. Golden Ratio - Wikipedia, The Free ... - StumbleUpon Someone discovered this in Mathematics •8 reviews since Feb 25, 2005 icon tags mathematics, math, goldenratio •en.wikipedia.org/wiki/golden_ratio http://www.stumbleupon.com/url/en.wikipedia.org/wiki/Golden_ratio

var SERVERDOM = ".stumbleupon.com"; StumbleUpon Discover new sites Home Websites ... Videos Have an account? Login Website review: Golden ratio - Wikipedia, the free ... Someone discovered this in Mathematics reviews since Feb 25, 2005 mathematics math goldenratio en.wikipedia.org/wiki/Golden_ratio People who like this website Show me more (5) People online now Top stumblers Please Login or Join StumbleUpon to see other people who like this site. It takes less than 2 mins to join. Arlington flyingrose Waxahachie MetaphysicalGirl Fort Worth Neferjeane Texas isansu Texas strubie Corpus Christi phantom-avalanch Mountain Grove Manhattan Missouri BatBelfrey Lincoln StumbleUpon is the best way to discover great web sites, videos, photos, blogs and more - based on your interests. Everything is submitted and rated by the community. Discover, share and review the best of the web! Reviews of this website Add Your Review Please Login or Join StumbleUpon to add a review. It takes less than 2 mins to join. shirlyy rated 4 days ago A nice explanation given.

23. MeetMeinTO.com V4 how do you want to ask golden_ratio for their friendship. beg, demand, grovel, seduce, threaten, ask. Message golden_ratio. you are not logged in, http://www.meetmeinto.com/profile.asp?id=479713

24. 9.1 Mathematical Constants sage a = pi + e + golden_ratio + log2 + euler_gamma + catalan + khinchin + twinprime + .. sage gr = golden_ratio sage RR(gr) 1.61803398874989 sage R http://www.sagemath.org/doc/html/ref/module-sage.functions.constants.html

Sage Reference Manual Previous: 9. Constants Up: 9. Constants Next: 10. Functions 9.1 Mathematical constants Module: sage.functions.constants Mathematical constants The following standard mathematical constants are defined in Sage , along with support for coercing them into GAP, GP/PARI, KASH, Maxima, Mathematica, Maple, Octave, and Singular: sage: pi pi sage: e # base of the natural logarithm e sage: NaN # Not a number NaN sage: golden_ratio golden_ratio sage: log2 # natural logarithm of the real number 2 log2 sage: euler_gamma # Euler's gamma constant euler_gamma sage: catalan # the Catalon constant catalan sage: khinchin # Khinchin's constant khinchin sage: twinprime twinprime sage: merten merten sage: brun brun Support for coercion into the various systems means that if, e.g., you want to create in Maxima and Singular, you don't have to figure out the special notation for each system. You just type the following: Arithmetic operations with constants also yield constants, which can be coerced into other systems or evaluated. sage: a = pi + e*4/5; a pi + 4*e/5 sage: maxima(a) %pi+4*%e/5 sage: RealField(15)(a) # 15 *bits* of precision 5.316 sage: gp(a) 5.316218116357029426750873360 # 32-bit 5.3162181163570294267508733603616328824 # 64-bit sage: print mathematica(a) # optional 4 E - + Pi 5

25. 9.1 Mathematical Constants sage a = pi + e + golden_ratio + log2 + euler_gamma + catalan + khinchin + twinprime + . sage gr = golden_ratio sage RR(gr) 1.61803398874989 sage R http://sage.scipy.org/sage/doc/html/ref/module-sage.functions.constants.html

Sage Reference Manual Previous: 9. Constants Up: 9. Constants Next: 10. Functions 9.1 Mathematical constants Module: sage.functions.constants Mathematical constants The following standard mathematical constants are defined in Sage , along with support for coercing them into GAP, GP/PARI, KASH, Maxima, Mathematica, Maple, Octave, and Singular: sage: pi pi sage: e # base of the natural logarithm e sage: NaN # Not a number NaN sage: golden_ratio golden_ratio sage: log2 # natural logarithm of the real number 2 log2 sage: euler_gamma # Euler's gamma constant euler_gamma sage: catalan # the Catalon constant catalan sage: khinchin # Khinchin's constant khinchin sage: twinprime twinprime sage: merten merten sage: brun brun Support for coercion into the various systems means that if, e.g., you want to create in Maxima and Singular, you don't have to figure out the special notation for each system. You just type the following: Arithmetic operations with constants also yield constants, which can be coerced into other systems or evaluated. sage: a = pi + e*4/5; a pi + 4*e/5 sage: maxima(a) %pi+4*%e/5 sage: RealField(15)(a) # 15 *bits* of precision 5.316 sage: gp(a) 5.316218116357029426750873360 # 32-bit 5.3162181163570294267508733603616328824 # 64-bit sage: print mathematica(a) # optional 4 E - + Pi 5

26. E_mod_main.c 2007/03/31 090630 1.8 +++ E_mod_main.c 2007/08/20 (*h)) *h = 0; + /* Apply the golden ratio to the popup */ + if ((double) *w / *h golden_ratio) { + *h = *w / golden_ratio; + } else if ((double) *w / *h http://www.enlightenment.org/viewvc/e_modules/forecasts/e_mod_main.c?r1=1.8&r2=1

27. Libraries - LIBS = Compiler Flags combinatorial combinatorial_cc rm f euclid.o euclid euclid_cc rm -f fast_sum.o fast_sum rm -f fast_sum.o fast_sum rm -f golden_ratio.o golden_ratio rm http://dehesa.freeshell.org/NCSE/PROGRAMS/NCSE/01_num_comp/makefile

# # libraries # - # LIBS = # # compiler flags # # FLAGS = # # # binary # # binary: binary.f f77 -o binary binary.f $(LIBS) # # bits # # bits: bits.f f77 -o bits bits.f bits_cc: bits.o ipow.o g++ -o bits_cc bits.o ipow.o ipow.o: ipow.cc g++ -c ipow.cc bits.o: bits.cc g++ -c bits.cc # # combinatorial # - # combinatorial: combinatorial.f f77 -o combinatorial combinatorial.f combinatorial_cc: combinatorial.cc g++ -o combinatorial_cc combinatorial.cc # # cubic # - # cubic: cubic_dr.o cubic.o f77 -o cubic cubic_dr.o cubic.o cubic_dr.o: cubic_dr.f f77 -c cubic_dr.f cubic.o: cubic.f f77 -c cubic.f # # cluster_2d # # OBJCL = cluster_2d_dr.o cluster_2d.o cluster_2d_link.o cluster_2d: $(OBJCL) f77 -o cluster_2d $(OBJCL) cluster_2d.o: cluster_2d.f f77 -c $(FLAGS) cluster_2d.f cluster_2d_dr.o: cluster_2d_dr.f f77 -c $(FLAGS) cluster_2d_dr.f cluster_2d_link.o: cluster_2d_link.f f77 -c $(FLAGS) cluster_2d_link.f # # euclid # # euclid: euclid.f f77 -o euclid euclid.f euclid_cc: euclid.cc g++ -o euclid_cc euclid.cc # # # fast_sum # # fast_sum: fast_sum.o f77 -o fast_sum fast_sum.o # # golden ratio # # golden_ratio: golden_ratio.o f77 -o golden_ratio golden_ratio.o # # hello # - # hello_cc: hello.cc c++ -o hello_cc hello.cc # # mapping # - # mapping: mapping.f f77 -o mapping mapping.f mapping_cc: mapping.cc c++ -o mapping_cc mapping.cc # # # matrix_mult # - # matrix_mult: matrix_mult.f f77 -o matrix_mult matrix_mult.f # # pie # - # pie: pie.f f77 -o pie pie.f # # # prime # - # prime: prime.f f77 -o prime prime.f prime_cc: prime.cc c++ -o prime_cc prime.cc # # ran_bsort # - # ran_bsort: ran_bsort.o random.o f77 -o ran_bsort ran_bsort.o random.o random.o: random.f f77 -c random.f # # ran_sort # # ran_sort: ran_sort.o random.o f77 -o ran_sort ran_sort.o random.o # # richardson # # richardson: richardson.o f77 -o richardson richardson.o # # # von_koch # # von_koch: von_koch.o f77 -o von_koch von_koch.o # # clean # - # clean: rm -f PLOTDAT core xyunit AAA* rm -f bits.o bits bits_cc bits_cc.o ipow.o rm -f binary.o binary rm -f $(OBJCL) cluster_2d rm -f combinatorial.o combinatorial combinatorial_cc rm -f euclid.o euclid euclid_cc rm -f fast_sum.o fast_sum rm -f fast_sum.o fast_sum rm -f golden_ratio.o golden_ratio rm -f hello_cc rm -f matrix_mult.o matrix_mult rm -f mapping.o mapping mapping_cc rm -f pie.o pie rm -f prime.o prime rm -f ran_bsort.o ran_bsort random.o rm -f ran_sort.o ran_sort random.o rm -f richardson.o richardson rm -f von_koch.o von_koch # # all fortran # - # all: make bits make binary make cluster_2d make combinatorial make euclid make fast_sum make fast_sum make golden_ratio make matrix_mult make mapping make pie make prime make ran_bsort make ran_sort make richardson make von_koch # # # all c++ # - # # all_cc: make bits_cc make combinatorial_cc make mapping_cc make hello_cc make prime_cc

28. MathConstants (CroftSoft Core) static double, golden_ratio. static long, MILLISECONDS_PER_DAY golden_ratio. static final double golden_ratio. See Also Constant Field Values http://www.croftsoft.com/library/code/javadoc/core/com/croftsoft/core/math/MathC

Overview Package Class Use Tree Deprecated Index ... FIELD DETAIL: FIELD com.croftsoft.core.math Interface MathConstants public interface MathConstants A collection of constants to supplement java.lang.Math. Since: Version: $Date: 2006/01/07 04:57:31 $ Author: David Wallace Croft Field Summary static double static double static long static long static long static long static double static double Field Detail static final long See Also: Constant Field Values static final long See Also: Constant Field Values static final long See Also: Constant Field Values static final long See Also: Constant Field Values static final double See Also: Constant Field Values static final double See Also: Constant Field Values static final double See Also: Constant Field Values static final double See Also: Constant Field Values Overview Package Class Use Tree Deprecated Index ... FIELD DETAIL: FIELD CroftSoft Core Javadoc (2006-11-12 23:24:04)

29. Golden Ratio (phi) A remarkable number that, like pi and e, pops up all over the place in mathematics but, in some ways, has a more human connection in that it seems to be http://www.daviddarling.info/encyclopedia/G/golden_ratio.html

NOTABLE NUMBERS MATHEMATICS A B ... CONTACT entire Web this site A remarkable number that, like pi and e , pops up all over the place in mathematics but, in some ways, has a more "human" connection in that it seems to be linked to aesthetics. Its name, which is also given as the golden mean , the golden section , the golden number , and the divine proportion , reflects this sense of a harmonious or pleasing ideal. The golden ratio is an irrational number of the type known as an algebraic number (in contrast with pi and e Fibonacci sequence ; in fact, F n F n ) gets closer and closer to phi as n continued fraction Two quantities are said to be in the golden ratio, if the ratio of the larger one, a , to the smaller one, b , is the same as the ratio of the smaller one to their difference, i.e. a b b a b ). The so-called golden rectangle is one whose sides a and b stand in the golden ratio. It is famously said to have great aesthetic appeal and is closely approximated by the dimensions of the front of the Parthenon in Rome. Leonardo da Vinci's masterpiece the Mona Lisa is said to have a face that is framed by a golden rectangle; what is certain is that Leonardo was a The golden ratio appears in Dali's The Last Supper close personal friend of Luca Pacioli , who published a three-volume treatise on the golden ratio, Divina Proportione , in 1509. The Swiss-French architect and painter Le Corbusier designed an entire proportional system called the "Modulor," that was based on the golden ratio. The Modulor was supposed to provide a standardized system that would automatically confer harmonious proportions to everything, from door handles to high-rise buildings. Another artist who deliberately used the golden ratio is the surrealist Salvador Dali. The ratio of the dimensions of Dali's Sacrament of the Last Supper is equal to the golden ratio. Dali also incorporated in the painting a huge dodecahedron (a twelve-faced Platonic solid in which each side is a pentagon) engulfing the supper table.

30. Python Script To Generate Patterson Map Animations For The inch, golden_ratio * inch) def showPage(self) if (not self.closing) canvas.Canvas. golden_ratio) self.circle(0, 0, radius, stroke, fill) self. http://cci.lbl.gov/~rwgk/ccp4sw2001/build_pattersons.py

<= x <= 3. + eps and 0. - eps <= y

31. 6.1 Mathematical Constants sage pi Pi sage e base of the natural logarithm e sage NaN Not a number NaN sage golden_ratio golden_ratio sage log2 natural logarithm of the http://www.dms.umontreal.ca/~math/logiciels/Sage/ref/module-sage.misc.constants.

SAGE Reference Manual Previous: 6. Special Constants and Up: 6. Special Constants and Next: 6.2 Computation of transcendental 6.1 Mathematical constants Module: sage.misc.constants The following standard mathematical constants are defined in SAGE , along with support for coercing them into GAP, GP/PARI, KASH, Maxima, Mathematica, Maple, Octave, and Singular: sage: pi Pi sage: e # base of the natural logarithm e sage: NaN # Not a number NaN sage: golden_ratio golden_ratio sage: log2 # natural logarithm of the real number 2 log2 sage: euler_gamma # Euler's gamma constant euler_gamma sage: catalan # the Catalon constant K sage: khinchin # Khinchin's constant khinchin Suppose for coercion into the various systems means that if, e.g., you want to create in Maxima and Singular, you don't have to figure out the special notation for each system. You just type the following: Arithmetic operations with constants also yield constants, which can be coerced into other systems or evaluated. sage: a = pi + e*4/5; a (Pi + ((e*4)/5)) sage: maxima(a) %pi + 4*%e/5 sage: a.str(15) # 15 *bits* of precision '5.31616' sage: gp(a) 5.316218116357029426750873360 # 32-bit 5.3162181163570294267508733603616328824 # 64-bit sage: mathematica(a) # optional (4*E)/5 + Pi

32. R Mathematical Constants The Following Standard Mathematical RDF(1.61803398874989484820458) def _mpfr_(self,R) is this OK for _mpfr_ ? return (R(1)+R(5).sqrt())*R(0.5) golden_ratio = GoldenRatio() class http://sage.math.washington.edu/home/bogart/sage_src_code/functions/constants.py

33. Golden Ratio - CreationWiki, The Encyclopedia Of Creation Science Retrieved from http//creationwiki.org/index.php/golden_ratio . Categories Intelligent design Physics Mathematics http://creationwiki.org/index.php/Golden_ratio

Golden ratio From CreationWiki, the encyclopedia of creation science Jump to: navigation search The golden ratio , otherwise known as the Divine Proportion or Phi , is a mathematical ratio with special properties and aesthetic significance. An enormous number of things in the universe are engineered around the ratio, ranging from the human body to the ark of the covenant to snail shells to the orbits of the planets. Some argue that the prevalence of the Golden Ratio is positive evidence of a common design plan uniting a wide variety of phenomena which share only their creator in common. Contents Calculating Examples Architecture Biology ... See Also Calculating Phi is derived by dividing a line segment into two parts in such a way that the ratio of the smaller segment to the larger segment is the same as the ratio of the large segment to the whole. The number is irrational, meaning it never ends or repeats in a decimal system. To the first ten decimals, it is 1.6180339887 ... A golden rectangle is one in which the ratio of length to height is 1:phi. The divine ratio also makes an appearance in the Fibonacci sequence . The fibonacci sequence is derived by starting with and 1, and then calculating the next number in the sequence by adding the last two togther. Thus the sequence is 0, 1, 1 (0+1), 2(1+1), 3(1+2), 5(2+3), 8(3+5) and so on. The ratio of a number to the previous number in the sequence approximates the golden ratio, and comes to approximate it more closely as the values increase. Thus:

34. Golden Ratio - Culture See Art and Popular Culture s copyright notice. Retrieved from http//www. artandpopularculture.com/golden_ratio . Views. Article; Discussion; Edit; History http://www.artandpopularculture.com/Golden_ratio

var skin = 'monobook';var stylepath = '/skins'; Golden ratio From Culture Jump to: navigation search google_ad_client = "pub-7609450558222968"; google_ad_slot = "7009642393"; google_ad_width = 468; google_ad_height = 60; Related e Wikipedia Wiktionary Wikiquote ... Shop Featured visual Centrale elettrica ) by Antonio Sant'Elia who stated that "the decorative value of Futurist architecture depends solely on the use and original arrangement of raw or bare or violently colored materials". In mathematics and the arts , two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is approximately 1.6180339887 At least since the Renaissance , many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle , in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties..

35. Golden Ratio - Indopedia, The Indological Knowledgebase Retrieved from http//www.indopedia.org/golden_ratio.html . This page has been accessed 1687 times. This page was last modified 1417, 30 Nov 2004 by http://www.indopedia.org/Golden_ratio.html

Indopedia Main Page FORUM Help ... Log in The Indology CMS In other languages: Deutsch Categories Algebraic numbers Irrational numbers ... Wikipedia Article Golden ratio ज्ञानकोश: - The Indological Knowledgebase The golden ratio is a number, approximately 1.618, which when considered as a ratio posseses many interesting properties. It was studied by ancient mathematicians due to its frequent appearance in geometry . Shapes defined by the golden ratio have long been considered aesthetically pleasing in western cultures, reflecting nature's balance between symmetry and asymmetry. The ratio is still used frequently in art and design. The golden ratio is also known as the golden mean golden section golden number or divine proportion It is usually denoted by the Greek letter (phi). Two quantities are said to be in the golden ratio if "the whole is to the larger as the larger is to the smaller". This can be easily visualized using a line that is divided into two segments, as in the diagram. MI Golden_ratio_line.png A line is divided into two segments a and b . The entire line is to the a segment as a is to the b segment Contents showTocToggle("show","hide")

36. !+ Subroutine To Perform A Search By Golden Sections. ! ! Method F1) THEN X0=X1 X1=X2 X2=golden_ratio*X1+GOLDEN_COMPLEMENT*X3 F0=F1 F1=F2 F2=RESIDUAL_POLYNOMIAL(N_DATA, WEIGHT, RESIDUAL, U, X2) ELSE X3=X2 X2=X1 http://www.met.reading.ac.uk/~marc/ellie_rad/fort/golden.f

37. Re: Re: Eek! Goto? perl slw use strict; use constant golden_ratio = 0x9e3779b9; use constant A = 0; use constant B = 1; use constant C = 2; sub mix ($$$) { $_A -= $_B http://www.perlmonks.org/index.pl?node_id=234705

38. Ifndef ISAAC_HPP Define ISAAC_HPP /* C++ TEMPLATE VERSION OF const UINT32 golden_ratio = UINT32(0x9e3779b9); typedef UINT32 ISAAC_INT; else // ISAAC64 typedef unsigned int64 UINT64; const UINT64 golden_ratio http://www.burtleburtle.net/bob/cplus/isaac.hpp

#ifndef ISAAC_HPP #define ISAAC_HPP /* C++ TEMPLATE VERSION OF Robert J. Jenkins Jr.'s ISAAC Random Number Generator. Ported from vanilla C to to template C++ class by Quinn Tyler Jackson on 16-23 July 1998. quinn@qtj.net The function for the expected period of this random number generator, according to Jenkins is: f(a,b) = 2**((a+b*(3+2^^a)-1) (where a is ALPHA and b is bitwidth) So, for a bitwidth of 32 and an ALPHA of 8, the expected period of ISAAC is: 2^^(8+32*(3+2^^8)-1) = 2^^8295 Jackson has been able to run implementations with an ALPHA as high as 16, or 2^^2097263 */ #ifndef ISAAC64 typedef unsigned long int UINT32; const UINT32 GOLDEN_RATIO = UINT32(0x9e3779b9); typedef UINT32 ISAAC_INT; #else // ISAAC64 typedef unsigned int64 UINT64; const UINT64 GOLDEN_RATIO = UINT64(0x9e3779b97f4a7c13); typedef UINT64 ISAAC_INT; #endif // ISAAC64 template QTIsaac QTIsaac void QTIsaac inline T QTIsaac void QTIsaac inline T QTIsaac inline void QTIsaac void QTIsaac <11; d+=a; b+=c; b^=c>>2; e+=b; c+=d; c^=d

39. Koders Code Search: Vnl_bracket_minimum.cxx - C++ swap(fa,fb); } // Initial guess at c c = b+ golden_ratio*(ba); fc = f(c); so try a default step u = c+golden_ratio*(cb); fu = f(u); http://www.koders.com/cpp/fid8CE804323FD2BC0DCE8F7DBB62BA6F5958670960.aspx?s=mde

40. PC Pitstop Forums > 2004/05 Stock Pitstop Challenge QUOTE(golden_ratio @ December 15th, 2004, 1018 PM) golden_ratio welcome to the pit, the glitch is related to the chipset drivers your running. IntelGuy http://forums.pcpitstop.com/lofiversion/index.php/lofiversion/t74193-150.html

Help Search Members Calendar Full Version: 2004/05 Stock Pitstop Challenge PC Pitstop Forums Community Custom PCs, case mods, overclocking ... HWbot Benchmark Scores Pages: ManiaK 11:59pm Tue Dec 14 2004 http://service.futuremark.com/compare?2k1=8304151 http://www.pcpitstop.com/techexpress.asp?id=GQ8J9WVTE3RS41F7 http://service.futuremark.com/compare?pcm04=2714697 AMD 3400+ @ 2417mhz Air Cooling ISP = 100 Total: 7213 crossfire 12:03am Wed Dec 15 2004 http://service.futuremark.com/compare?2k1=8304151 http://www.pcpitstop.com/techexpress.asp?id=GQ8J9WVTE3RS41F7 http://service.futuremark.com/compare?pcm04=2714697 AMD 3400+ @ 2417mhz Air Cooling ISP = 100 Total: 7213 looks good.. now youve gone and forced me to come up with a better score i wonder what this thing will do in 3dmark when i really cut it loose ManiaK 12:10am Wed Dec 15 2004 Raptor 12:12am Wed Dec 15 2004 QUOTE "The Force is with you" Intel Guy just got shot down That had to hurt ManiaK 12:20am Wed Dec 15 2004 "The Force is with you" Intel Guy just got shot down That had to hurt crossfire 12:48am Wed Dec 15 2004 after a bios flash, and a driver update.. this is what i come up with..

Page 2     21-40 of 75    Back | 1  | 2  | 3  | 4  | Next 20