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 \$8.401. The Golden Ratio: The Story of
 \$34.402. The Golden Ratio and Fibonacci
 \$13.513. The Return of Sacred Architecture:
 \$111.474. The Golden Ratio: The Story of
 \$0.205. The Diet Code: Revolutionary Weight
 6. The Golden Mean or Ratio [(1+sqrt(5))/2]
 \$19.997. Non-Standard Positional Numeral
 8. Golden Ratio the Story of Phi
 \$19.999. Golden Ratio: Golden Ratio Base,
 \$18.9510. The Golden Ratio: The Story of
 11. The Golden Ratio
 \$17.8212. The Glorious Golden Ratio
 \$26.0013. The Golden Ratio
 \$46.9614. Constants: Mathematical Constants,
 \$20.7015. Fractal Universe and the golden
 \$35.7216. Mathematical Constants: E, Pi,
 17. The Golden Ratio, The Story of
 \$17.9918. Golden Ratio the Story of Phi
 \$16.4819. Irrational Numbers: Golden Ratio
 20. The Golden Ratio The Story of

 4. The Golden Ratio: The Story of Phi, the Extraordinary Number of Nature, Art and Beautyby Mario Livio Paperback: 304 Pages (2003-08-04) list price: US\$16.50 -- used & new: US\$111.47 (price subject to change: see help)Asin: 0747249881Canada | United Kingdom | Germany | France | Japan Editorial ReviewProduct DescriptionWhat do the Parthenon in Greece, crosses in graveyards, the ratio of the height of the navel to a woman's total height, sunflowers and Leonardo da Vinci's "Mona Lisa" have in common? The answer is that these disparate elements share a geometrical proportion of ancient origin, commonly known as the 'Golden Ratio', or expressed numerically as phi. In a captivating journey through art and architecture, botany and biology, taking in fractals and DNA on the way, Livio takes us into the heart of this extraordinary number, and gives an account of the phi-obsessed individuals who devoted their lives to discovering its secrets - from the Pythagoreans who believed that the study of the Golden Ratio would reveal the hand of God, to the great astronomer Johannes Kepler who felt that phi was the greatest treasure of geometry, to the modern day scientists who are discovering ever more remarkable ramifications of this strange, almost mystical, number. It is a journey into the heart of beauty itself. ... Read more

 6. The Golden Mean or Ratio [(1+sqrt(5))/2] to 20,000 placesby null Kindle Edition: Pages (2009-10-04) list price: US\$1.99Asin: B002RKSXBOCanada | United Kingdom | Germany | France | Japan Editorial ReviewProduct DescriptionThis book was converted from its physical edition to the digital format by a community of volunteers. You may find it for free on the web. Purchase of the Kindle edition includes wireless delivery. ... Read more

 7. Non-Standard Positional Numeral Systems: Unary Numeral System, Golden Ratio Base, Fibonacci Coding, Quater-Imaginary Base, Negative Base Paperback: 100 Pages (2010-05-06) list price: US\$19.99 -- used & new: US\$19.99 (price subject to change: see help)Asin: 1155771990Canada | United Kingdom | Germany | France | Japan Editorial ReviewProduct DescriptionPurchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Unary Numeral System, Golden Ratio Base, Fibonacci Coding, Quater-Imaginary Base, Negative Base, Factorial Number System, Bijective Numeration, Non-Integer Representation, Balanced Ternary, Mixed Radix, Redundant Binary Representation, Non-Standard Positional Numeral Systems, Pentimal System, Negafibonacci Coding, Signed-Digit Representation, Bubble Babble, Non-Adjacent Form, Complex Base Systems. Excerpt:Numeral systems by culture Balanced ternary is a non-standard positional numeral system (a balanced form ), useful for comparison logic. It is a ternary system, but unlike the standard (unbalanced) ternary system, the digits have the values 1, 0, and 1. This combination is especially valuable for ordinal relationships between two values, where the three possible relationships are less-than, equals, and greater-than. Balanced ternary can represent all integers without resorting to a separate minus sign . Balanced ternary is counted as follows. (In this example, the symbol 1 denotes the digit 1, but alternatively for easier parsing " " may be used to denote 1 and "+" to denote +1.) Decimal: 6: 5: 4: 3: 2: 1: 0: 1: 2: 3: 4: 5: 6 Unbalanced ternary can be converted to balanced ternary notation by adding 1111.. with carry, then subtracting 1111... without borrow (the string of 1s must be the same length, so if the result of the addition has more digits, subtract nothing from these extra digits). For example, 0213 + 1113 = 2023, 2023 1113 = 1113(bal) = 710. Balanced ternary is easily represented as electronic signals, as potential can either be negative, neutral, or positive. Utilizing a third state encompasses more data per digit; linearly approximately 1.5849 (log23) bits per trit. Applications Balanced ternary has other applications besides computing. For example, a classical "2... ... Read more

 8. Golden Ratio the Story of Phi the Worldsby Mario Livio Hardcover: Pages (2002) Asin: B00128Y79YCanada | United Kingdom | Germany | France | Japan

 9. Golden Ratio: Golden Ratio Base, List of Works Designed With the Golden Ratio, Pentagram, Proportion, Golden Section Search, Golden Spiral Paperback: 104 Pages (2010-09-15) list price: US\$19.99 -- used & new: US\$19.99 (price subject to change: see help)Asin: 1155555090Canada | United Kingdom | Germany | France | Japan Editorial ReviewProduct DescriptionChapters: Golden Ratio Base, List of Works Designed With the Golden Ratio, Pentagram, Proportion, Golden Section Search, Golden Spiral, Golden Rectangle, Jay Hambidge, Golden Angle, Golden Triangle, Golomb Sequence, Lute of Pythagoras, Mark Barr. Source: Wikipedia. Pages: 103. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to (=) the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.6180339887. Other names frequently used for the golden ratio are the golden section (Latin: sectio aurea) and golden mean. Other terms encountered include extreme and mean ratio, medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, golden number, and mean of Phidias. The golden ratio is often denoted by the Greek letter phi, usually lower case (). The figure on the right illustrates the geometric relationship that defines this constant. Expressed algebraically: This equation has as its unique positive solution the algebraic irrational number At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratioespecially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratiobelieving this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties. Construction of a golden rectangle:1. Construct a unit square (red).2. Draw a line from the midpoint of one side to an opposite corner.3. Use that line as the radius to draw an arc that defines the long dimension of the rectangl...More: http://booksllc.net/?id=12386 ... Read more

 10. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number   [GOLDEN RATIO] [Paperback] Unknown Binding: Pages (2003-09-30) -- used & new: US\$18.95 (price subject to change: see help)Asin: B002VK3EC8Canada | United Kingdom | Germany | France | Japan

 11. The Golden Ratioby Mario Livio Unknown Binding: Pages (2002) Asin: B003HFRHX8Canada | United Kingdom | Germany | France | Japan

 12. The Glorious Golden Ratioby Alfred S. Posamentier, Ingmar Lehmann Hardcover: Pages (2011-06) list price: US\$27.00 -- used & new: US\$17.82 (price subject to change: see help)Asin: 1616144238Canada | United Kingdom | Germany | France | Japan

 13. The Golden Ratioby Keith Flynn Hardcover: 160 Pages (2007-02-15) list price: US\$26.00 -- used & new: US\$26.00 (price subject to change: see help)Asin: 0916078949Average Customer Review: Canada | United Kingdom | Germany | France | Japan Editorial ReviewProduct DescriptionKeith Flynn's fourth and most innovative collection of poems to date, The Golden Ratio, is filled with themes of music and balance, creating a literary world in opposition to our discordant contemporary times, where the human population is at odds with one another and the Natural World, out of sync and unfocused, spiritually and physically adrift. The book's six sections deal separately with the state of our government, our art forms, and our relationship and responsibility to the society that surrounds us. This book is a tour de force by one of our most distinctive poetic voices, seeking to redefine what it means to be human and creative in the face of overwhelming opposition. ... Read moreCustomer Reviews (2) Flynn Spins The World Into A Beautiful Balance Keith Flynn's latest book, The Golden Ratio, is one of the most compelling and inventive collections of poetry that I have ever read. From the exquisite imagery in "Mysterium," the book's intro poem, through the historical masterpiece, "Chang and Eng," and the political theater of "Hitler's Yacht in America," the poems coalesce to create a multi-faceted picture of the contemporary world. In the last section, Flynn shows us how music is the real moral law in the brilliant rhythmic jazz profiles of giants such as Duke Ellington, Chet Baker, Herbie Hancock, Ellis Marsalis and others, by using surreal juxtapositions, intricate wordplay, and thought-provoking descriptions to bring these lives and the music they play into fuller focus. Flynn is one of our best contemporary poets and this book shows his incredible talents in full flower. The poems about divorce in the book's mid-section will break your heart as the poet struggles to find a proper balance in his relationship with the new landscape alone, and the ways to reconcile his artistic growth with the personal process of aging and loving again. This might be the first real Baby Boomer coming-of-age collection that defines this era in clear, unflinching terms. This book creates an entirely new world between its covers and builds sentences that are unforgettable. Don't miss it... When the Mountain Boy becomes the Intellectual Keith Flynn is a mountain boy at heart, but there is an urbanite rolling around under the surface. His poems reflect the duality of his nature: the hillbilly and the intellectual. In this collection there are poems that honor nature, jazz, and variety.The set of poems from the voices of Chang and Eng (the legendary Siamese twins who retired to NC) are fascinating as are the poems that delve into the world of jazz, hoping to honor the narrator's heroes of that world as well. My favorite was Welsh Fantasia with lines such as "Only mystery enables us to live." This is a long collection of over 150 pages and many of the poems are lengthy with long lines as well so you will certainly get your money's worth.My only complaint with this collection is that at times the author's lust for language overpowers me as so many complex words are strung together. Or maybe, I'm just not as smart as Mr. Flynn :) I'd defintiely suggest this collection for Southern Literature fans and for anyone out there who has a love of the world of jazz. ... Read more

 14. Constants: Mathematical Constants, Physical Constants, Dimensionless Quantity, Avogadro Constant, Pi, Golden Ratio, Gas Constant Paperback: 400 Pages (2010-09-15) list price: US\$46.96 -- used & new: US\$46.96 (price subject to change: see help)Asin: 1157808913Canada | United Kingdom | Germany | France | Japan Editorial ReviewProduct DescriptionChapters: Mathematical Constants, Physical Constants, Dimensionless Quantity, Avogadro Constant, Pi, Golden Ratio, Gas Constant, Stefan-boltzmann Constant, Faraday Constant, Brun's Constant, Catalan's Constant, Feigenbaum Constants, de Bruijn-Newman Constant, Euler-mascheroni Constant, Parts-Per Notation, Bohr Radius, Planck Mass, Planck Time, Planck Temperature, Square Root of 2, Time Constant, Square Root of 5, Silver Ratio, Particle Data Group, Schnirelmann Density, Astronomical Constant, Elementary Charge, Apéry's Constant, Degree, Electron Rest Mass, Zeta Constant, Madelung Constant, Euler Product, Gaussian Gravitational Constant, Khinchin's Constant, G-Factor, Particular Values of the Gamma Function, Electron Magnetic Dipole Moment, Rydberg Constant, Loschmidt Constant, Representations of E, Viswanath's Constant, Champernowne Constant, Plastic Number, Classical Electron Radius, Mrb Constant, Period, Bohr Magneton, Mills' Constant, Molar Mass Constant, 6174, Square Root of 3, Gelfond's Constant, Golomb-dickman Constant, Twelfth Root of Two, Gelfond-schneider Constant, Parabolic Constant, Astronomical Almanac, Fransén-robinson Constant, Cahen's Constant, Reciprocal Fibonacci Constant, Komornik-loreti Constant, Stieltjes Constants, Omega Constant, Gauss's Constant, Somos' Quadratic Recurrence Constant, Prouhet-thue-morse Constant, Glaisher-kinkelin Constant, Feller's Coin-Tossing Constants, Conic Constant, Bernstein's Constant, Curie Constant, Niven's Constant, Hartree, Meissel-mertens Constant, Hilbert Number, Hafner-sarnak-mccurley Constant, Landau's Constants, Embree-trefethen Constant, Erdős-borwein Constant, Laplace Limit, Legendre's Constant, Ramanujan-soldner Constant, Atomic Mass Constant, Heath-Brown-moroz Constant, Backhouse's Constant, Lieb's Square Ice Constant, Landau-ramanujan Constant, Lévy's Constant, Seshadri Constant, Sierpiński's Constant, Kepler-bouwkamp Constant, Oort Constants, Favard Constant, Lebesg...More: http://booksllc.net/?id=12386 ... Read more

 15. 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. Paperback: Pages (2008) -- used & new: US\$20.70 (price subject to change: see help)Asin: 5397000450Canada | United Kingdom | Germany | France | Japan

 16. Mathematical Constants: E, Pi, Golden Ratio, Brun's Constant, Catalan's Constant, Feigenbaum Constants, de Bruijn-Newman Constant Paperback: 278 Pages (2010-09-15) list price: US\$35.72 -- used & new: US\$35.72 (price subject to change: see help)Asin: 1157608906Canada | United Kingdom | Germany | France | Japan Editorial ReviewProduct DescriptionChapters: E, Pi, Golden Ratio, Brun's Constant, Catalan's Constant, Feigenbaum Constants, de Bruijn-Newman Constant, Euler-mascheroni Constant, Mathematical Constant, Square Root of 2, Square Root of 5, Silver Ratio, Schnirelmann Density, Apéry's Constant, Degree, Zeta Constant, Madelung Constant, Euler Product, Khinchin's Constant, Particular Values of the Gamma Function, Representations of E, Viswanath's Constant, Champernowne Constant, Plastic Number, Mrb Constant, Period, Mills' Constant, 6174, Square Root of 3, Gelfond's Constant, Golomb-dickman Constant, Twelfth Root of Two, Gelfond-schneider Constant, Parabolic Constant, Fransén-robinson Constant, Cahen's Constant, Reciprocal Fibonacci Constant, Komornik-loreti Constant, Stieltjes Constants, Omega Constant, Gauss's Constant, Somos' Quadratic Recurrence Constant, Prouhet-thue-morse Constant, Glaisher-kinkelin Constant, Feller's Coin-Tossing Constants, Conic Constant, Bernstein's Constant, Niven's Constant, Meissel-mertens Constant, Hilbert Number, Hafner-sarnak-mccurley Constant, Landau's Constants, Embree-trefethen Constant, Erdős-borwein Constant, Laplace Limit, Legendre's Constant, Ramanujan-soldner Constant, Heath-Brown-moroz Constant, Backhouse's Constant, Lieb's Square Ice Constant, Landau-ramanujan Constant, Lévy's Constant, Seshadri Constant, Sierpiński's Constant, Kepler-bouwkamp Constant, Favard Constant, Lebesgue Constant, Linnik's Constant. Source: Wikipedia. Pages: 277. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to (=) the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.6180339887. Other names frequently ...More: http://booksllc.net/?id=12386 ... Read more

 17. The Golden Ratio, The Story of Phi the World's Most Astonishing Number - 2002 publicationby Maro Lvo Hardcover: Pages (2002-01-01) Asin: B003JGEVNYCanada | United Kingdom | Germany | France | Japan

 18. Golden Ratio the Story of Phi the Worldsby Mario Livio Hardcover: Pages -- used & new: US\$17.99 (price subject to change: see help)Asin: B000UDHJCYCanada | United Kingdom | Germany | France | Japan

 19. Irrational Numbers: Golden Ratio Paperback: 104 Pages (2010-09-15) list price: US\$19.99 -- used & new: US\$16.48 (price subject to change: see help)Asin: 1156506913Canada | United Kingdom | Germany | France | Japan Editorial ReviewProduct DescriptionChapters: Golden Ratio. Source: Wikipedia. Pages: 103. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to (=) the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.6180339887. Other names frequently used for the golden ratio are the golden section (Latin: sectio aurea) and golden mean. Other terms encountered include extreme and mean ratio, medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, golden number, and mean of Phidias. The golden ratio is often denoted by the Greek letter phi, usually lower case (). The figure on the right illustrates the geometric relationship that defines this constant. Expressed algebraically: This equation has as its unique positive solution the algebraic irrational number At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratioespecially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratiobelieving this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties. Construction of a golden rectangle:1. Construct a unit square (red).2. Draw a line from the midpoint of one side to an opposite corner.3. Use that line as the radius to draw an arc that defines the long dimension of the rectangle. Two quantities a and b are said to be in the golden ratio if: This equation unambiguously defines . The right equation shows that a = b, which can be substituted in the left part, giving Dividing out b yields Multiplying...More: http://booksllc.net/?id=12386 ... Read more

 20. The Golden Ratio The Story of PHI the Worlds Most Astonishing Number 2003 publication.by Mario Livio Paperback: Pages (2003) Asin: B003ZPGKWOCanada | United Kingdom | Germany | France | Japan

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