MAY 2018

1.618

VISUAL EXPRESS PRODUCTIONS

GOLDEN

& logos The Golden Ratio Phi Î¦ 1.618

GOLDEN & LOGOS

CONTENTS Intro ......................................... 5 Ratios & Number Series ..... 6 Tools ........................................ 7 Being Golden ........................ 8 Golden Shapes ................... 10 Golden Rectangle .............. 12 Golden Spiral ...................... 13 Logo - Twitter ...................... 14 Logo - Pepsi ......................... 15 Logo - BP ............................. 16 Logo - NatGeo .................... 17 Music .................................... 18 References & Resources ... 20

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HIGH Lights geometric shapes

This book contains a brief but spectacular introduction to simple geometric shapes. Shapes that have been used to create masterpieces like the Mona Lisa, to build magnificent architectural structures like the Chartres Cathedral, along with many of the most popular logos today like Apple, Toyota, and Google.

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1:1618 vs. 1:2:3:5:8

The Golden Ratio

Geometry & Golden

The Golden Ratio Phi vs. the Fibonacci number sequence 3, 5, 8, 13, etc..

Creating the golden rectangle from squares and generating the golden spiral..

This book contains the steps to divide a line (a straight line, of course) into the golden section, which supports the drawing of the golden rectangle and the golden spiral. With these basic steps, you will be able to create balance, harmony, and beauty in designs.

The golden ratio is also called the golden mean or golden section. Artists and architects use golden ratio because it produces aesthetically pleasing work.

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Logos & Golden

Music

References

Various logos created using the golden ratio.

Both the golden ratio and Fibonacci sequences abound in nature, geometry, and the arts including music.

https://www.goldennumber.net/art-composition-design/

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INTRODUCTION Notes from My Art School Journal

These fundamentals along with the well proven and reliable Gestaltâ&#x20AC;&#x2122;s Principles and Laws, the Bauhaus House practices, and Maitland Graves Visual Design Elements and Tools provide valuable insight into what makes a piece work.

This book along with my other two, The Art of Prepress and the Printing Process and My Art Reference Notebook, provide highlights of my journey, with all its divergences and meandering, into the wondrous and complex universe of the study of art. It has been such a fantastic adventure. I have fallen hard for the discipline and look forward to expanding my understanding, appreciation, knowledge, and love of art, and, actually applying it to my future endeavors.

All my struggles and do-overs of my class assignments have provided me with a wealth of experience and knowledge. The hours of study and creating art have taught me how to observe, analyze, and critique work. These traits are paramount when developing work, and they make one think and purposely place every line, shape, and color out of respect and with awareness of the known practices and theories of good design.

My initial objective was to learn to draw, which to my surprise takes a great deal of patience and a whole lot of practice. I am still a beginner at drawing; however, I now have a powerful toolkit that includes a vast array of fundamentals such as:

Best Wishes, Susan

1. The golden ratio, 2. A horizon line and 1, 2, 3 points for perspective, 3. Composition, layout, and positive-negative space, 4. Color and its tints, tones, values, and saturation, 5. The power of light and dark, also known as, chiaroscuro, and 6. The direction & the intensity of the light source and its effect.

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Golden Ratio & Fibonacci Pi (Phi Φ) Day is an annual celebration of the mathematical constant π. Pi Day is observed on March 14 since 3, 1, and 4 are the first three significant digits of π.

The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it. Starting with 0 and 1, the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth.

Dividing A Line into the Golden Ratio 1.618:1

Vi Hart illustrates the series in nature.

R. A. Dunlap’s basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry. Versus the generation of the Fibonacci series and generalized Fibonacci series and their relationship to the golden ratio. The Fibonacci sequence is viewed as a one-dimensional aperiodic, lattice and these ideas are extended to twoand three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms in terms of Fibonacci sequences.

APERIODIC

APERIODIC CRYSTALS

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Tools PENCIL RULER COMPASS PROTRACTOR T-SQUARE CALIPER ADOBE AI Examples in Nature: Φ Pine-cones Φ Seashells

Examples in Architecture: Φ The Great Pyramid of Giza Φ The Roman Parthenon Φ Stonehenge Φ The Chartres Cathedral

Examples in the Human Body: Φ The joints Φ The fingers Φ The arms Φ The legs

Individuals who used the ratio: Φ Leonardo da Vinci Φ Stradivari Φ Piet Mondrian

THE CHARTRES CATHEDRAL

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Being Golden

The Apple Computer Logo and the Golden Rectangles and Circles

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Using the golden circles.

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Golden Shapes

According to astrophysicist and mathematics popularizer Mario Livio, since the publication of Luca Pacioli’s Divina Proportione in 1509, when “with Pacioli’s book, the Golden Ratio started to become available to artists in theoretical treatises that were not overly mathematical, that they could actually use”, many artists and architects have been fascinated by the presumption that the golden rectangle is considered aesthetically pleasing. The proportions of the golden rectangle have been observed in works predating Pacioli’s publication. 10

The Vitruvian Man

Circles from the Golden Rectangle

Squares from the Golden Rectangle

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Golden Rectangle

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Golden Spiral

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Logo - Pepsi

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1:1.618

1.618 15

Logo - BP

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Logo - NatGeo

1.618

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Music Music and the Fibonacci Sequence and Phi Music and the Fibonacci Sequence and Phi By Gary Meisner (May 4, 2012) . Musical frequencies are based on Fibonacci ratios. Notes in the scale of western music are based on natural harmonics that are created by ratios of frequencies. Ratios found in the first seven numbers of the Fibonacci series ( 0, 1, 1, 2, 3, 5, 8 ) are related to key frequencies of musical notes. https://www.goldennumber.net/music/

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Five Classical Pieces with the Golden Ratio Five Classical Pieces with the Golden Ratio By Angelica Frey (July 16, 2015). ♪ Mozart’s Sonata n. 1 in C Major ♪ Beethoven’s Fifth Symphony, first movement ♪ Bartok’s for strings, percussion & celesta, first movement ♪ Erik Satie and the Sonneries de la Rose+Croix ♪ Claude Debussy’s Dialogue du vent et de la mer www.cmuse.org/classical-pieces-with-the-golden-ratio/

In the thirteenth century, Italian mathematician Leonardo Bonacci (also known as Fibonacci) posed and solved a problem regarding the growth of rabbit population, by illustrating a series of numbers where each number is the sum of the previous two numbers. This sequence nears 1.618, namely the golden ratio. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377

Both the golden ratio and Fibonacci sequences abound in art, nature and geometry. These five compositions, which reference the golden ratio and the Fibonacci sequence.

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References & Resources MATHEMATICAL PROPERTIES OF THE GOLDEN RATIO ALONG WITH CERTAIN BIOLOGICAL ORGANISMS IN TERMS OF FIBONACCI SEQUENCES. VICTORIA HART, (VI HART) IS A "RECREATIONAL MATHEMUSICIAN" WHO IS WELL KNOWN FOR HER MATHEMATICAL VIDEOS . DUNLAP, RICHARD. THE GOLDEN RATIO AND FIBONACCI NUMBERS. WORLD SCIENTIFIC PUBLISHING (WSPC), SINGAPORE. 1997.

HART, VI. HTTP://VIHART.COM

BRINGHURST COMBINES PRACTICAL, THEORETICAL, AND HISTORICAL INFO ON TYPOGRAPHY.

PACIOLI, LUCA. DE DIVINA PROPORTIONE, LUCA PAGANINEM DE PAGANINUS DE BRESCIA (ANTONIO CAPELLA) 1509, VENICE. HTTP://SPENCERMORTENSEN.COM/ARTICLES/ TYPOGRAPHIC-SCALE/

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FAVORITE DOCUMENTARIES

BOOKS:

Guest of Cindy Sherman. A documentary on art-scene commentator Paul H-Oâ&#x20AC;&#x2122;s (Hasegawa-Overacker) relationship with enigmatic photographer Cindy Sherman. 2009.

Allen, Jon. Drawing Geometry. Floris Books, UK. 2007. Boole, George. The Mathematical Analysis of Logic. Forgotten Books, UK. 2009.

The Machine That Made Us. A documentary in which Stephen Fry examines the story behind the first media entrepreneur, printing press inventor Johann Gutenberg, to find out why he did it and how, a story which involves both historical inquiry and hands-on craft and technology. 2008.

Olsen, Scott. The Golden Section: Natureâ&#x20AC;&#x2122;s Greatest Secrets. Wooden Books, 2006. YouTube VIDEOS:

Understanding Art. Is a four-part documentary with art critic Waldemar Januszczak. He reveals that in their time, the impressionists were artistic rebels. 2011.

Achraf, Mohamed. How to design a logo with golden ratio. Speed Arts & Tutorials. 2017. Achraf, Mohamed. How to design a logo with golden ratio #2. Speed Arts & Tutorials, Ai. 2017. Websites: Phi Matrix Software https://www.phimatrix.com

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THE AMERICAN INSTITUTE OF GRAPHIC ARTS IS THE PROFESSIONAL ASSOCIATION FOR DESIGN

SPIEKERMANN RAN A LETTERPRESS PRINTING PRESS AND HE & HIS TWO PARTNERS FOUNDED METADESIGN. HTTPS://WWW.AIGA.ORG

HTTPS://WWW.EDENSPIEKERMANN.COM

IDEO IS A GLOBAL DESIGN COMPANY THAT CREATES POSITIVE IMPACT THROUGH DESIGN.

IDEO

THE INDEPENDENT DOCUMENTARY FILM ABOUT TYPOGRAPHY AND GRAPHIC DESIGN, CENTERED ON THE TYPEFACE OF HELVETICA.

HTTPS://WWW.IDEO.COM

HTTPS://EN.WIKIPEDIA.ORG/WIKI/HELVETICA_(FILM)

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PAULA SCHER SAYS DO WHAT YOU DO BEST—BUT CHANGE WITH THE TIMES.

PAULA SCHER

AIGA.ORG/SEARCH?SEARCHTEXT=PAULA%20SCHER

IT'S A CLICHÉ, BUT SAUL BASS REALLY HAS DONE IT ALL. FILMS. PACKAGING. PRODUCTS. ARCHITECTURE. CORPORATE IDENTIFICATION. GRAPHICS. HIS WORK SURROUNDS US.

SAUL BASS