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Golden Ratio:     more books (52)

Fractal Universe and the golden ratio structural and rhythmic unity of the world - ("Relata Refero") / Fraktalnaya Vselennaya i zolotoe otnoshenie Strukturnoe i ritmicheskoe edinstvo mira - ("Relata Refero") by Yakimova N.N., 2008 Mathematical Constants: E, Pi, Golden Ratio, Brun's Constant, Catalan's Constant, Feigenbaum Constants, de Bruijn-Newman Constant The Golden Ratio, The Story of Phi the World's Most Astonishing Number - 2002 publication by Maro Lvo, 2002-01-01 Golden Ratio the Story of Phi the Worlds by Mario Livio, Irrational Numbers: Golden Ratio The Golden Ratio The Story of PHI the Worlds Most Astonishing Number 2003 publication. by Mario Livio, 2003 Alishev C. x. Bulgarian-Kazan and the Golden ratio in the XIII-XVI in / Alishev S.Kh. Bolgaro-kazanskie i zolotoordynskie otnosheniya v XIII-XVI v by Alishev S., 2009 Variance amplification and the golden ratio in production and inventory control [An article from: International Journal of Production Economics] by S.M. Disney, D.R. Towill, et all 2004-08-18 The Return of Sacred Architecture: The Golden Ratio and the End of Modernism Golden Ratio by MarioLivio, 2002 Golden Section: An entry from Macmillan Reference USA's <i>Macmillan Reference USA Science Library: Mathematics</i> by Philip Edward Koth, William Arthur Atkins, 2002 Fibonacci Trading, Chapter 1: Fibonacci Numbers and the Golden Ratio by Carolyn Boroden, 2008-02-25 The Golden Mean or Ratio[(1+sqrt(5))/2] by Jerry Bonnell, 2010-07-06 Golden ratio geometry: A book of research by Joan Moore, 1996

lists with details

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
    
    Extractions: 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.

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
    
    Extractions: 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! 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
    
    Extractions: Sage Reference Manual Previous: 9. Constants Up: 9. Constants Next: 10. Functions 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
    
    Extractions: Sage Reference Manual Previous: 9. Constants Up: 9. Constants Next: 10. Functions 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
    
    Extractions: # # 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

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
    
    Extractions: 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. 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

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.
    
    Extractions: SAGE Reference Manual Previous: 6. Special Constants and Up: 6. Special Constants and Next: 6.2 Computation of transcendental 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
    
    Extractions: 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. 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
    
    Extractions: 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
    
    Extractions: Categories Algebraic numbers Irrational numbers ... Wikipedia Article 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

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
    
    Extractions: #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 >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

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