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         Golden Mean Geometry:     more detail
  1. Geometry of Design: Studies in Proportion and Composition by Kimberly Elam, 2001-08-01

21. Flower Of Life - The Golden Mean Spiral And The Merkaba - Article By Ronald L. H
As we have seen in the article entitled The golden mean Spiral and the Merkaba , Through the golden spiral, all geometry transcends form and moves into
http://www.floweroflife.org/holomatrix01.htm
(Page 1 The Spiral and the Holographic Matrix by Ronald Holt
Director, Flower of Life Research
August, 2000 Foreward When Drunvalo and Dan Winter introduced me to sacred geometry, I passed through a doorway that held a vast new perspective of reality that caused me to grow internally. As I continued to study I found that I was left with many new tools with which I could work. Yet I felt "stuck" (in a good way) inside a geometric puzzle of reality that I intuitively felt was only a portion of what we are or are capable of becoming. I am writing this article with the intention of helping to inspire more people to embrace sacred geometry as a way to move even further beyond it. I hope you all continue to explore until you find your own unique path that leads you to the understanding of sacred geometry on a deeper level that will then allow you to see beyond sacred geometry in order to understand and claim more of your greater being. What is the effect of this study? It results in a greater humility, because it beckons the individual to step beyond our accepted history and definitions of reality and to embrace a greater understanding of who we really are. There will always exist so much more to our being than we can imagine. Creation (and all that exists within it) can be modeled by sacred geometry. Sacred geometry appears to be the blueprint underlying the many aspects of creation. Sacred geometry and the holographic nature of reality are models that enable us to fathom the possibility that we are the universe, but yet we are still more. Our true being defies all descriptions or boundaries. We are boundless beings made of pure principle itself.

22. Golden Mean
The golden mean can be determined via geometry by taking a square with all sidesequal to 1, drawing an arc with the center of radius at the midpoint of one
http://www.halexandria.org/dward101.htm
Golden Mean
The Golden Mean can be construed as the basis of philosophy and Sacred Geometry , one of the Transcendental Numbers , [*] and is typically derived from Fibonacci Numbers [* Technically, from a strictly mathematical standpoint as has been pointed out by several readers the Golden Mean, Phi, is the solution to a polynomial equation and thus not mathematically transcendental. However, if one looks at the other definitions of transcendental, most would agree that it qualifies.] According to Robert Lawlor [1], “Ancient geometry rests on no a priori axioms or assumptions. Unlike Euclidian and the more recent geometries, the starting point of ancient geometric thought is not a network of intellectual definitions or abstractions, but instead a meditation upon a metaphysical Unity, followed by an attempt to symbolize visually and to contemplate the pure, formal order which springs forth from this incomprehensible Oneness. It is the approach to the starting point of the geometric activity which radically separates what we may call the sacred from the mundane or secular geometries. Ancient geometry begins with One , while modern mathematics and geometry being with Zero Other authors have noted that “Both the ancient Greeks and the ancient Egyptians used the Golden Mean when designing their buildings and monuments.” “Artists as diverse as Leonardo da Vinci and George Seurat used the ratio when constructing their paintings. These artists and architects discovered that by utilizing the ratio 1 : 1.618..., they could create a feeling of order in their works.

23. Sacred Geometry
The golden mean (or F) is by its nature the essential ingredient in Sacred geometry is all about, consider just one facet of it, the golden mean or
http://www.halexandria.org/dward095.htm
Sacred Geometry
Tradition holds that over the entrance to Plato’s Academy was written the words: Agewmetrhtoz mhdeiz eisitw Only he who is familiar with geometry shall be admitted here (Apparently a knowledge of the Greek language was also important.) This website is not quite so stringent, and will happily admit any she who is interested in entering. (The guys will, of course, still need some geometry.) Alternatively, anyone who can carry a tune may enter in a bucket or by any other means. Music is, after all, based on geometry and mathematics. For anyone who doesn’t think of themselves as being “familiar with geometry,” the words attributed to Plato’s school might be considering insulting, and thereby construed to have little or no validity. Any grapes from the discourteous must inevitably be sour. This circumstance is indeed unfortunate in that anyone who is not familiar with geometry, anyone who does not appreciate the premise that Philosophy is about understanding the meaning of a mathematical ratio (the Golden Mean ), and anyone who adheres exclusively to a literal interpretation of spiritual teachings...

24. Sacred Geometry Exercise-Nautilus Shell Spiral
as the golden mean or phi spiral, but with slightly different proportions.A close approximation of a golden mean spiral, based on the Fibonacci whole
http://www.sacredarch.com/sacred_geo_exer_shell.htm
The Nautilus Shell Spiral
Sunflower Mandala
Snowflake Pattern Six-Around-One The shell of the chambered nautilus is a symbol of beauty and proportional perfection. In this exercise you will experience the essence and energy of the spiral displayed in the unfolding of the nautilus shell. The proportion of this nautilus shell is consistent through all of the relationships of the shell, so once you discover the secret ratio, you will see clearly why this particular gem of nature is such a treasure. The nautilus shell spiral is a logarithmic spiral similar to other spirals such as the Golden Mean or phi spiral, but with slightly different proportions. A close approximation of a Golden Mean spiral, based on the Fibonacci whole number sequence is illustrated below.
The spiral of the chambered nautilus as well as other logarithmic spirals can be found throughout the human body and nature. The drawing of the inner ear and the photo image of a star cluster nebula shown to the right are just two examples which can be seen with a microscope or a telescope. There are many examples which can be seen without magnification. See what you can find.
This beautiful spiral can be easily drawn on a piece of grid paper with a pencil. Refer to the drawings below as you work.

25. The Math Forum - Math Library - Golden Ratio/Fibonacci
Includes geometric applications of the golden ratio; Fibonacci puzzles; the Great golden Pyramid, because its geometry is that of the golden mean.
http://mathforum.org/library/topics/golden_ratio/
Browse and Search the Library
Home
Math Topics Arithmetic/Early Number Sense/About Numbers : Golden Ratio/Fibonacci

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Selected Sites (see also All Sites in this category
  • Fibonacci Numbers and the Golden Section - Ron Knott
    Information about the Fibonacci series, including a brief biography of Fibonacci, the numerical properties of the series, and the ways it is manifested in nature. Fibonacci numbers are closely related to the golden ratio (also known as the golden mean, golden number, golden section) and golden string. Includes: geometric applications of the golden ratio; Fibonacci puzzles; the Fibonacci rabbit binary sequence; the golden section in art, architecture, and music; using Fibonacci bases to represent integers; Fibonacci Forgeries (or "Fibonacci Fibs"); Lucas Numbers; a list of Fibonacci and Phi Formulae; references; and ways to use Fibonacci numbers to calculate the golden ratio. more>>
  • The Fibonacci Series - Matt Anderson, Jeffrey Frazier, and Kris Popendorf; ThinkQuest 1999
    more>>

  • Aesthetics, dynamic symmetry, equations, the Divine Proportion, the Fibonacci sequence, the Golden rectangle, logarithmic spirals, formulas, links to other MathSoft pages mentioning the Golden Mean, and print references. Also available as MathML more>>
  • Golden Ratio, Fibonacci Sequence - Math Forum, Ask Dr. Math FAQ
  • 26. Geometry Forum: Winter 95 Outposts - III
    The geometry Forum Newsletter. Winter 1995, page 3 Now, about the golden mean.The golden mean is the ratio of successive Fibonacci numbers. The series
    http://mathforum.org/Outposts/W95p3text.html
    Forum Outposts
    The Geometry Forum Newsletter
    Winter 1995, page 3
    Ask Dr. Math!, continued
    Look at the sequence 1/(-1/2), 1/(-1/3), 1/(-1/4), and notice again that the denominators -1/2, -1/3, -1/4, ..., are going to zero. Again, we would want the limit of this sequence to be 1/0, but looking at the sequence, it simplifies to -2, -3, -4, ..., and it goes to negative infinity. So which would we assign to 1/0? Negative infinity or positive infinity? Instead of just assigning one of these willy nilly, we say that infinity isn't a number, and that 1/0 is indeterminate. I hope this helps. Ken "Dr." Math Dear Dr. Math: My name is Erica Anderson and I need to know examples of where the Fibonacci sequence is found in nature and how that relates to the Golden Mean. This is for Pre Calculus class. Thanks for your help. Hey Erica, I love this problem. The Fibonacci sequence happens all the time in nature, so much it is amazing. I am having trouble not just sitting here and listing all the occurrences that I can think of, but I will try to resist sending you a seven-page e-mail message. A few examples:
    • Think about a pine cone. Have you ever noticed that the petals spiral up in two directions? Well, the number of petals it takes to get once around is almost always a Fibonacci number.

    27. E-z Geometry Project Topics
    Games Math; Geodesic Domes; golden mean; golden Ratio; History of Math;Magic Squares Mona Lisa the golden Rectangle Some golden geometry
    http://www.e-zgeometry.com/links/plinks.htm
    e-zgeometry Project Topics A to F G to M N to R S to Z
    Binary #'s Cartography Centers of Triangles Constructions ... Topology
    Binary Numbers: Go to Top Cartography: Go to Top Centers of Triangles: Go to Top Constructions: Go to Top Cyrptography: Go to Top Fermat's Last Theorem: Go to Top Fibonacci Numbers: Go to Top Figurative Numbers: Go to Top Four Color Theorem: Go to Top Fractals:

    28. Golden Mean 3
    Page 2 Euclid Page 3 Repeating geometry Page 4 golden Rectangle Page 5golden rectangles entangled golden mean in Art and Nature
    http://facultystaff.vwc.edu/~trfanney/golden-mean-WOWslides/gm3.html
    Page 1: Intro Page 2: Euclid Page 3: Repeating geometry Page 4: Golden Rectangle ... Page 11: Golden mean and Fibonacci Numbers
    Again:
    If a straight line is cut in extreme and mean ratio, then as the whole is to the greater segment, the greater segment is the lesser segment.

    29. Golden Ratio - Wikipedia, The Free Encyclopedia
    The golden ratio is also referred to as the golden mean, golden section, The number f turns up frequently in geometry, in particular in figures
    http://en.wikipedia.org/wiki/Golden_mean
    Golden ratio
    From Wikipedia, the free encyclopedia.
    (Redirected from Golden mean It has been suggested that this article or section be merged with Golden Mean Discuss
    This article is about the mathematical ratio. For the Aristotelian concept of "golden mean" see Nicomachean Ethics
    The golden ratio is an irrational number , approximately 1.61803..., that possesses many interesting properties. Shapes defined by the golden ratio have long been considered aesthetically pleasing in Western cultures, reflecting nature's balance between symmetry and asymmetry and the ancient Pythagorean belief that reality is a numerical reality, except that numbers were not units as we define them today, but were expressions of ratios. The golden ratio is still used frequently in art and design. The golden ratio is also referred to as the golden mean golden section golden number divine proportion or sectio divina
    Contents
    edit
    History
    The golden ratio was first studied by ancient mathematicians due to its frequent appearance in geometry . The golden ratio may have been understood and used by the Egyptians. The discovery of irrational numbers, numbers that cannot be represented as an exact ratio of two

    30. CG: Sacred Geometry: Mandalas: The Golden Mean Rectangle And The Phi Ratio
    golden mean Rectangle Phi Ratio by World renowned Mandala artist Charles Gilchrist.
    http://www.charlesgilchrist.com/SGEO/Gal1101.html
    Charles Gilchrist Mandalal: Gallery #11
    The Golden Mean Rectangle and The Phi Ratio
    LDV Phi Ratio Geometry: by Charles Gilchrist

    A beautiful print on fine watercolor paper is now available of this popular Gilchrist Mandala based on Leonardo Da Vinci's famous masterpiece. Charles personally creates these prints. The paper size is 13 inches by apox. 19 inches. The price is #39.95, plus $14.00 insurance, shipping, and handling anywhere in the continental USA.
    The low wholesale price is:
    One print - only $39.95 - plus $14.00 I/S/H
    This print is shipped flat
    See (Order Form)
    The Golden Mean Rectangle and The Phi Ratio
    An Interview With The Artist - Number 11
    by Leslie Page Sacred Sequence: Number 11 L.P. "Tape running, here we are again, Charles, continuing our ongoing conversation on Sacred Geometry and all the unbelievable connections it has to our everyday lives. I'm amazed, Charles, I truly am. This is our eleventh tape and I promised you our subject would be your choice this time. What are we going to talk about today?" C.G. "Thank you, Leslie. Generally, when I take on a really bright student, like yourself, I begin by letting them ask the questions that first come to their minds. It seems to work pretty well. And so far we have been doing just that, but this is, as you just mentioned, our eleventh conversation and it feels pretty special to me."

    31. CG: Sacred Geometry: Mandalas: The Golden Mean Rectangle And The Phi Ratio: Part
    golden mean Rectangle Phi Ratio by World renowned Mandala artist Charles Gilchrist.
    http://www.charlesgilchrist.com/SGEO/Gal1102.html
    Charles Gilchrist Mandala: Gallery #11
    The Golden Mean Rectangle and The Phi Ratio - Part 2
    (Fig. 1) A New Painting
    Author's note: since we created Gallery #11 and our interview #11 part one, Charles has created another major painting celebrating the Golden Mean Rectangle. This wonderful work is entitled, 1.6180339. It is a painting panel measuring 36 '' by 22.25" (Phi Ratio proportions) covered with deep and rich acrylic glazes.
    A beautiful rich print is now available of this important Gilchrist Mandala. Charles personally creates and signs these prints. The watercolor paper size is 19 inches by 13 inches. The price is #39.95, plus $14.00 insurance, shipping, and handling anywhere in the continental USA..
    The low wholesale price is:
    One print - only $39.95 - plus $14.00 I/S/H
    This print is shipped flat
    See (Order Form)
    An Interview With The Artist by Leslie Page - Number 11 Part 2
    Cipher L.P. "It's beautiful Charles. Tell us about this painting, 1.6180339. Of course the title is the Phi Ratio to nine places, the Golden Mean proportions of the painting, but there's obviously a lot more going on in this piece." C.G. "That's true, Leslie. This is a contemplative Mandala, based on Sacred Geometric Principles

    32. Golden Ratio: Information From Answers.com
    For the Aristotelian concept of golden mean see Nicomachean Ethics. The number f turns up frequently in geometry, in particular in figures involving
    http://www.answers.com/topic/golden-ratio
    showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Best of Web Mentioned In Or search: - The Web - Images - News - Blogs - Shopping golden ratio Wikipedia golden ratio
    This article is about the mathematical ratio. For the Aristotelian concept of "golden mean" see Nicomachean Ethics
    The golden ratio is an irrational number , approximately 1.618, that possesses many interesting properties. Shapes defined by the golden ratio have long been considered aesthetically pleasing in Western cultures, reflecting nature's balance between symmetry and asymmetry and the ancient Pythagorean belief that reality is a numerical reality, except that numbers were not units as we define them today, but were expressions of ratios. The golden ratio is still used frequently in art and design. The golden ratio is also referred to as the golden mean golden section golden number or divine proportion The golden ratio was first studied by ancient mathematicians due to its frequent appearance in geometry . The golden ratio may have been understood and used by the Egyptians. The discovery of irrational numbers, numbers that cannot be represented as an exact ratio of two

    33. Excerpts From The Golden Mean Book And Calipher Set
    Like geometry itself, the golden mean Calipers begin with the vesica piscissacredsymbol of the creative act. The vesica piscis (which literally means
    http://www.heall.com/products/nowandzen/goldmeannbookexcerpts.html

    34. The Geometry Junkyard: Pentagonal Geometry And The Golden Ratio
    The golden section and geometry. Somehow leading to questions like how many starsthere are on the US Penrose tilings and the golden mean, K. Wiedman.
    http://www.ics.uci.edu/~eppstein/junkyard/pent.html
    Pentagonal Geometry and the Golden Ratio This page includes geometric problems defined on regular pentagons, involving pentagonal angles, or based on the golden ratio (the ratio of diagonal to side length in a regular pentagon).
    • A Brunnian link . Cutting any one of five links allows the remaining four to be disconnected from each other, so this is in some sense a generalization of the Borromean rings. However since each pair of links crosses four times, it can't be drawn with circles.
    • Constructing a regular pentagon inscribed in a circle, by straightedge and compass. Scott Brodie. Also described by M. Gallant
    • Cut-the-knot logo . With a proof of the origami-folklore that this folded-flat overhand knot forms a regular pentagon.
    • Digital Diffraction , B. Hayes, Amer. Scientist 84(3), May-June 1996. What does the Fourier transform of a geometric figure such as a regular pentagon look like? The answer can reveal symmetries of interest to crystallographers.
    • The downstairs half bath . Bob Jenkins decorated his bathroom with ceramic and painted pentagonal tiles.
    • Equilateral pentagons . Jorge Luis Mireles Jasso investigates these polygons and dissects various polyominos into them.
    • Equilateral pentagons that tile the plane , Livio Zucca.

    35. Under Siege: The Golden Mean In Architecture By Michael Ostwald For The Nexus Ne
    Michael Ostwald briefly describes the golden mean and its history before A ScrollDown Lesson in the golden mean The Sacred geometry HomePage
    http://www.nexusjournal.com/Ostwald.html
    Abstract. Michael Ostwald briefly describes the Golden Mean and its history before examining the stance taken by a number of recent authors investigating the Golden Mean in architecture. He addresses the theories of Husserl, Derrida and Ingraham, who separately affirm that tacit assumptions about the relationship between geometric forms and other forms - say geometry and architecture - must be constantly questioned if they are to retain any validity.
    Under Siege: The Golden Mean in Architecture Michael J. Ostwald
    Department of Architecture
    Faculty of Architecture, Building and Design, University of Newcastle
    University Drive, Callaghan, NSW 2308 AUSTRALIA Introduction
    E
    dmund Husserl's Origin of Geometry was originally written as an appendix to his The Crisis of European Sciences and Transcendental Phenomenology . Significantly, in the Origin of Geometry Husserl examines geometry from a historical perspective not a mathematical one. For Husserl the elevation of geometric forms to transcendental status (as, for example, the basis of universal beauty) presupposes the connection between such forms and some "ideal" or "original" form. An example of this is found in Vitruvius, who maintains that th

    36. *Golden Mean*
    ASIS provides a starting point a golden mean from which to embark on your With these illustrations, using simple geometry of line and arc we are able
    http://www.asis.com/asis/golden.html
    The Golden Mean -
    We find in the ASIS logo, two methods of constructing the golden proportion using Euclidean tools. The logo represents a system or series of systems that ever resolve themselves in harmony and usefulness. The golden proportion was selected to be an integral part of the logo representing Access Solutions Information Services. The construction is a network of scribed arcs and straight lines that resolve themselves in useful relationship. We are able to arrive, through technological, conceptual, human based rationality at a relationship that nature exudes. Nature can't help herself, it's just how the flower grows. But man can stray and create abominations. So many of us live far removed from natural structure and as we venture into cyber space we are even further removed from order that can keep us sane. Our logo pays homage to nature's wisdom and serves as a reminder that with a little care, we can structure our world in a way that gives us beauty and peaceful resolve. Information requires perspective or context. The relevance of information is based on its usefulness.

    37. BrainPhire?Fractal Golden Ratio Harmonics In BrainWaves As Mechanism Of Euphoria
    And this confirms why so many peoples HEART s choose a golden mean Ratio (the There is only one sonic geometry the PHI ray caddeuceus (which is also
    http://www.soulinvitation.com/brainphire/
    If the Source of Becoming Informed, and of Knowing - Lies in How Much CHARGE Information can Be Contained or Embedded in the Body.. And - Peak Awareness is Peak Charge- Then The Goal of EDUCATION Should be that Peak.. Consider - the Physics of Euphoria and Peak Awareness ( even BLISS) as the Ultimate Educator BrainPhire? Study in Russia Indicates Fractal Golden Ratio Harmonics in BrainWaves as Mechanism of Euphoria / Active Visualization / Bliss? May Support Neurofeedback Solutions to ATTENTION DISORDERS Based on IMPLOSION. notes from Dan Winter and James Barrett, Oct 17,2001, Index Study in Russia (Konstantin Korotkov, Gas Discharge Visualization Group) http://www.heartbeat2000.com/korotkov.htm , kindly reprinted by James Barrett (HeartLink Project), heartbeat2000.com , shows that Bliss / Euphoria - active visualization states, measureably correspond to Golden Mean Fractal Ratio between EEG contained harmonics
    see BLISS TUNER Above: Dr Korotkov- shows by GDV measurement that the altered state / bliss / euphoria which accompanies increased perception - has consistent qualities. The GDV area (aura size) should correlate to increased heart coherence. "I am reminded of the day Dr.Ed Wilson, Research Director Monroe Institute, decided to quit Bob Monroe and travel to my farm to make our film, when he discovered Fibonacci (Phi directed) audio heterodynes in ear headphones measureably induced (Lexicor's) 'definition' of transcendance in Brain Wave Mapping. He was so excited we had found parallels in the Heart EKG for compassion." Dan Winter

    38. Great Golden Pyramid
    has golden geometry of the golden mean. What does it look like? to call itthe Great golden Pyramid, because its geometry is that of the golden mean.
    http://www.valdostamuseum.org/hamsmith/Gpyr.html
    The Great Pyramid
    has Golden Geometry of the Golden Mean
    What does it look like ? What are its Purposes
    Ikonos satellite image PBS NOVA has an Online Exploration of the Giza Pyramids and Sphinx with commentary by Mark Lehner and Zahi Hawass, who advocate an age of about 4,600 years for the Giza pyramids. Mark Lehner says "... we know ... the date of the pyramids ... mostly by context. The pyramids are surrounded by cemeteries of other tombs. ... we find organic materials ... that can be radiocarbon dated ... But primarily we date the pyramids by their position in the development of Egyptian architecture and material culture over the broad sweep of 3,000 years. ..." I agree with the dates of the materials found in the area of the Giza pyramids, but I do NOT agree that those materials, tombs, etc., are the materials, tombs, etc., of the builders of the Giza Pyramids and Sphinx. In my opinion, the builders were either the Ice Age Civilization of 36,525 to 11,600 years ago, or, at the latest, a part of a global Early Human Civilization that broke up about 6,000 years ago, and that the Giza Sphinx and Pyramids were already built about 5,100 years ago when Menes reunited Lower Egypt, including Giza, with Southern Upper Egypt.

    39. ENC Online: ENC Features: Classroom Calendar: Golden Mean Day (Grades 7-12)
    There s Pi Day and Mole Day, so it seems only right that the golden mean geometry Use visualization, spatial reasoning, and geometric modeling to solve
    http://www.enc.org/features/calendar/unit/0,1819,152,00.shtm
    Skip Navigation You Are Here ENC Home ENC Features Classroom Calendar Search the Site More Options Don't lose access to ENC's web site! Beginning in August, goENC.com will showcase the best of ENC Online combined with useful new tools to save you time. Take action todaypurchase a school subscription through goENC.com Classroom Calendar By Category By Month ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Find detailed information about thousands of materials for K-12 math and science. Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants.
    Golden Mean Day (Grades 7-12)
    August 13 Graphic: Ji Sun An There's Pi Day and Mole Day, so it seems only right that the Golden Mean should have its own day. The Golden Mean, or Golden Ratio, is 1.6180339 rounded off to eight digits, or approximately 1.618. That makes August 13the day that is 61.8 percent of way through the yeara fitting day to proclaim Golden Mean Day. (Of course, if you prefer to celebrate during the traditional school year, you could have students figure out what 61.8 percent of your school year would be, or 61.8 percent of a specific month.) The Golden Mean represents an aesthetically pleasing proportion of height to width: 1 to 1.618 . . . . Like pi, it's an irrational number. It's often represented by the Greek letter Phi.

    40. ENC Online: Curriculum Resources: Browse: Mathematics> Geometry> Golden Ratio
    Browse Mathematics geometry golden ratio The introductory section explainswhat the golden mean, or golden Ratio, represents.
    http://www.enc.org/resources/browse/0,,0-100-294-1123_1_0-0-0,00.shtm
    Skip Navigation You Are Here ENC Home Curriculum Resources Browse Search the Site More Options Don't lose access to ENC's web site! Beginning in August, goENC.com will showcase the best of ENC Online combined with useful new tools to save you time. Take action todaypurchase a school subscription through goENC.com Classroom Calendar Digital Dozen ENC Focus ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse Frequently Asked Questions Resource of the Day ... About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants.
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    http://nlvm.usu.edu/en/nav/frames_asid_133_g_4_t_3.html?open=instructions
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