GoldenNumber.net serves as a place for sharing insights into the pervasive appearance of Phi in life and the universe. I’d like to recognize and thank the following ‘phriends’ in phi met through this web site for their original contributions to the site:
- Alan Bennett, for his original insights into the relationship of phi in the solar system, summarized here on the Solar System page from his web site Solar Geometry.
- Robert Bartlett, for his original insights into the relationship of phi in the solar system, summarized here on the Solar System page from his web site page on PhiSolCube, and his insights into the appearance of phi in the Bible in the Ark of the Covenant and the number 666, summarized here on the Bible page. Also, for his insights into the resemblance of the heart’s EKG to a graph of Fibonacci convergence, as shown on Heartbeat page.
- William Erman, for his original insights into the application of the golden section to technical stock market analysis, summarized here on the Stock Markets page from his site Ermanometry, and his observation on pi squared in relation to Fibonacci number 987 on the Pi, Phi & Fibonaccis page.
- Dr. Stephen Marquardt, for his original insights into the application of phi in the human beauty analysis mask, summarized here on the Human Beauty page from his web site Marquardt Beauty Analysis.
- Dr. Alexey Stakhov, for his common vision of increasing knowledge, understanding and education of phi as a general foundation to all fields of arts and sciences, as shown in his site “The Museum of Harmony and Golden Section.” See also his essay presented by the Rethinker’s Movement entitled “Mathematical Connections in Nature, Science and Art.”
- Dr. Eddy Levin, for his original insights into the application of the golden section to dental aesthetics, as well as his creation of The Golden Mean Gauge, a wonderful tool for seeing phi in everything around.
- Steve McIntosh, for his original insights into the spiritual/theological implications of phi and the relationship of the Trinity to the golden section, as described on the Theology page. See his perspectives on Integral World Government as well as his unique product offerings at Now&Zen.
- Dr. Ron Knott, for his extensive research and probably the most exhaustive Fibonacci site on the Internet, Fibonacci Numbers and the Golden Section, a great source of insight and learning for anyone interested in this topic.
- Dr. Yosh Jefferson, for his insights and contributions into the role of facial proportions in health, summarized here on the Facial Proportions and Human Health page from his article published in the June 1996 issue of the Journal of General Orthodontics, and also presented on his web site FacialBeauty.
- Ed Oberg and Jay A. Johnson, for their original insights into the pi-phi product, summarized here on the Pi, Phi & Fibonaccis page from their paper The Pi-Phi Product.
- Michael Semprevivo, whose research into a broad range of topics related to phi includes original insights into the application of phi relationships in the spectrum of colors in visible light. His PhiBar program, an interactive application in Visual Basic, illustrates this principle and is summarized and included here on the Color page.
- Norman S. Rose, Ph.D., for his original insights into the application of Fibonacci numbers to the human development process, summarized here on the Development page from his site WhizKidz.
- Valrie Jensen, for her insights into orthogons, summarized here on the Orthogons page from her web site Timeless by Design.
- Steve Lautizar for submitting Sam Kutler’s geometric construction of phi using concentric circles, illustrated here on the Geometric Construction of Phi in Crcles page.
- Erol Karazincir (pcerol@yahoo.com) for his original insight and contribution of a new formula for phi based entirely on 5’s, in that Phi = (5+√5) / (5-√5), illustrated here on the Five and Phi page.
- W. Nathan Saunders for his added insights on the four 5’s in that (5+√5) x (5-√5) = 5 + 5 + 5 + 5 and also that the symbol for phi, or 0.618, in lower case, is available in Symbol font by typing Alt-618! (i.e., hold the Alt key and enter 618 on the numeric pad).
- J.D. Ahmanson for being the first to bring the 2003 discovery of the Phi-based shape of the Universe to my attention and for his original insight into the phi relationship of the colors of the Tabernacle described in the Bible.
- Rick Toews for his original discovery and contribution that the reciprocal of 109 is based on powers of the Fibonacci series, similar to the properties of the reciprocal of 89.
- Stephanie Miller, for her original insight that body temperatures fall at about the phi point between the freezing and boiling temperatures of water.
- Albert Poch Huguet, for his original insight on the maximum density of water at 4° C as it relates to the phi points of body temperatures.
- David W. Thomson, for his original insights that the gfactors of electrons and protons may be determined by sine functions involving phi, thus indicating that phi may be a constant produced by time. This is summarized on the Time and Quantum Physics page and presented in detail on his Quantum Physical Model site.
- Sheila Yurick, for her insight on the Fibonacci relationships that appear in the dominant 5th of the major scale, as described on the Music page.
- Melih Yazici, for the insight on the phi proportions that appear in B-DNA, as described on the DNA page.
- Helga Hertsig, for being the first to bring Jain’s discovery of the pattern of 24 infinitely repeating digits in the Fibonacci series.
- Ian Watson, for his insight into the curious riddle on when +V = 5, on the Phi Phonetics page.
- Eric Manning, for being the first to bring the phi relationships in Bucky Balls to my attention and for submitting an AutoCAD BuckyBall file.
- Tassos Spiliotopoulos, for his insights into the pronunciation of phi, on the Phee, Phi, Pho, Phum page.
- Jody Espina, for his contributions to the application of phi in musical instruments as highlighted on the Acoustics page.
- Ben Moon, for his contribution of an original phi-inspired poem, “Golden” on the Poetry page.
- John Sarber, for his contribution of an original phi-inspired poem, “Aurea Mediocritas” on the Poetry page.
- Katherine Field, for her photos of the golden spiral inspired Quincy Park in Cambridge, MA.
- John Owen, for the example of phi in architecture found in the CN Tower.
- Tawfik Mohammed, for his observation on the relationship of lucky 7 and unlucky 13 in the Fibonacci Series.
- Hans J. Dettmer, for his contribution of a new geometric construction of phi found by using an equilateral triangle and circle, on the Geometric constructions of Phi in Circles page. (2005-09-25)
- Phi Corbett, for his contribution of the Phi Mandala.
- Scott Beach, for his contribution of the Phi Formula Geometric Construction.
- Jim T. Henriksen, for his contribution of poetry illustrating the Fibonacci style poetry.
- Bengt Erik Erlandsen, for his contribution of a newly discovered three circle geometric construction on the Circles page that reflects the standard mathematical expression of Phi, also shown on the Phi Formula Geometry page. (2006-01-11)
- Jordan Malachi Dant, for his contribution of a new way to compute Fibonacci numbers using Phi from a simple formula. (2005-04-10)
- Mark Gabriel, for his insight that “room” temperatures that humans find comfortable represent a phi relationship to body temperatures.
- Joseph Turbeville, for his contribution of the repeating pattern of 24 distilled digits that appears in the Fibonacci series, as presented in his book “A Glimmer of Light From the Eye of a Giant” and on his site Eye of a Giant.
- Alex Williams, MD, for his insight and contribution of the application of the Phi and Fives relationship to create an expression for Pi.
- Marty Stange, PE, for his insight and contribution on the Fibonacci right triangles that are based on any four successive numbers in the Fibonacci Series.
- Remi Schulz for his insight and contribution that the numerological value of my first and last name (51 and 83) represents the angle of the Golden Triangle of sacred geometry (51.83 degrees), thought to be angle used in the construction of the Great Pyramid of Cheops. (Never would have thought of that one on my own!)
- Dale Lohr for contribution of a simple relationship between pi and phi using the arccos function.
- Sir Hemlock for contribution of the application of Fibonacci and golden ratios to the Altar in Exodus 27.
- Moein Danesh for bringing to my attention the application of the golden section in the design of the Taj Mahal.
- Patrick “Paddy” Brown for bringing videos on phi to my attention, as listed on the Phi Multimedia Links page.
- Robert Everest for his contribution of a relationship that expresses Phi as a function of Pi and Fibonacci numbers.
- Mikko Bojarsky, who shared that Michelangelo’s “The Creation of Adam” has Adam and God touching at the golden ratio point of the width of the painting. He used our free golden ratio template to discover this.
- Alireza Shafaei for his contribution of a Phi Calculator that computes phi to a user defined level of accuracy, 1,000,000 or more, along with source code in C++.
- Leonairo Pencue-Fierro for his contribution of the relationship of the cosine of 6 x 6 x 6 or 216 degrees to phi, as shown on the Bible page.
- Dominique Cressatti, Travis Moore, John Devlin, Stephen Paul King and others for sending news of the announcement of the appearance of Phi and the Golden Ratio at quantum levels in solid state matter and the E8 symmetry.
- Sathimantha Malalasekera for bringing to my attention the Phi relationship in the dimensions of the Earth and Moon, as presented in “Hidden Nature” by Alick Bartholomew.
- Eric Polster for bringing to my attention some additional phi relationships in dimensions of Saturn, including the relationship of the diameter of Saturn to the diameter of its rings.
- Bill Cummins for providing an AutoCad version of the Golden Ratio Gauge template on the Do It Yourself page.
- Jo Niemeyer for her contribution of a new and very elegant geometric construction of the Golden Ratio based on just three straight lines.
- Yosi Spater for his bringing to my attention the golden ratio relationships in the Tetragrammaton and Jewish scriptures about creation.
- David Sterner for his discovery and contribution of the DOR, a new and unique patented geometric solid with a relationship to phi.
- Christopher Ricci for his discovery and contribution of a new geometric construction which uses Phi in responding to a classic challenge of geometry, Squaring the Circle.
- Tim Fisher for contributing his observations on the appearance of the Golden Ratio in the entry winning the Rose Award for Photography at the 2012 Royal Academy Summer Exhibition.
- Shaman Aka for contributing his observations on the appearance of the Golden Ratio in car manufacturer logos, including Honda, Mazda, Hyundai and Mercedes Benz.
- Kevin Muldoon for his article “The Geometry of Starship Design – Star Trek” which inspired this article and the search for additional golden ratios in the design of Star Trek’s USS Enterprise.
- Miika Kuisma for the observations on the iterative calculation of phi as an insight to deeper spiritual connection and oneness.
- John Gury for his observation that Seurat’s “Le Jardiner” was painted on a panel of golden rectangle proportions. This resulted in my review of all 103 Seurat paintings for golden rectangles in the dimensions of the canvases or panels, and the finding that Seurat chose these for at least two dozen of his paintings.
- David Kapuschinsky for his research confirming Martin Ohm as the first one known to use the term “golden” when referring to the golden ratio as the goldener schnitt, or golden section. Also for his link to the online version of “The Curves of Life”, which mentioned the origin of the use of Phi to refer to the golden ratio. See both on the History page.
- Oliver Brady for his astute analysis of the illustrations on “Is the Nautilus shell spiral a golden spiral,” which led to improvements in the accuracy and clarity of the article.
- Alex Leach for his analysis and application of the golden ratio in football decision strategy for the point after touchdown.
- Lucien Khan for his insights into the 60 digit pattern based on the last digits of the Fibonacci sequence numbers, and Bernie Dobovicnik for bringing his work to my attention.
- Gerben Schwab for his concepts and YouTube video presentation of the Fibonacci relationship found in musical scales.
- Kalana Dido of France for his research and discoveries that unite the visual spectrum of light, the proportions of the human body, the chakras and the Golden Ratio.
- Bert de Groot for his research and discoveries on the golden ratio patterns that appear in the economic cycles of Gross Domestic Product in over 25 countries.
- Abe Ihmeari for his contribution that Φ * √5 = 3.6180339… = Φ + 2, shown on the Mathematics of Phi and Power of Phi pages, and the Fibonacci sequence property f(n)-f(n-5)-f(n-10) = 10 ∙ f(n-5), shown on the Mathematics of Phi page.
I welcome any new contributions of original or unique insights into phi which will serve to add to our understanding and appreciation of its relationship to the world around us. I’d also like to thank everyone else who has written, especially those whose insights I haven’t yet incorporated into the site.
Gary Meisner
Author, editor and developer of Phi: The Golden Number at www.GoldenNumber.net.
Developer of “The Golden Ruler™” and “The Golden Grid™.”
Developer of PhiMatrix golden ratio design and analysis software at www.PhiMatrix.com