The Golden Mean and Human Proportion Inspired by Leonardo DaVinci by Valerie Xanos.

The Golden Mean and Human Proportion

Inspired by Leonardo DaVinci

by Valerie Xanos

The Golden Mean Phi 1.618...is simply the ratio of the line

segments that result when a line is divided in one very special way. 1:1.618

Divide a line so that:

Phi appears in:

The proportions of the human bodyThe proportions of many other animals

PlantsDNA

The solar systemArt and architecture

MusicPopulation growthThe stock market

Copyright 1997-2007 PhiPoint Solutions, LLC

Antiochos (signed),

copy of Phidias

Athena of the Parthenos

Golden Mean in ArtGolden Mean in Art

Ancient Greeks used it in sculpture Ancient Greeks used it in sculpture and architecture (Phidias)and architecture (Phidias)

Renaissance artists created a revival Renaissance artists created a revival of its use, calling it Divine Proportion.of its use, calling it Divine Proportion.

Da Vinci used this technique in all of Da Vinci used this technique in all of his paintings.his paintings.

Artists to this day continue to use the Artists to this day continue to use the Golden Mean.Golden Mean.

The Parthenon, Acropolis, Athens, Greece

The Parthenon, Acropolis, Athens, Greece

Leonardo Da Vinci, The Last Supper

Leonardo Da Vinci, The Last Supper

Leonardo Da Vinci, Mona Lisa

Sandro Botticelli, The Birth of Venus

Sandro Botticelli, The Birth of Venus

Golden Mean and LifeGolden Mean and Life

"All life is biology.  All biology is "All life is biology.  All biology is physiology.  All physiology is physiology.  All physiology is chemistry.  All chemistry is physics.  chemistry.  All chemistry is physics.  All physics is math."All physics is math."Dr. Stephen MarquardtDr. Stephen Marquardt

The Golden Mean is found in all The Golden Mean is found in all Life FormsLife Forms

Golden Mean and LifeGolden Mean and Life

The DNA spiral is a The DNA spiral is a Golden SectionGolden Section

The DNA molecule, The DNA molecule, the program for all life, the program for all life, is based on the golden is based on the golden section.  It measures 34 section.  It measures 34 angstroms long by 21 angstroms long by 21 angstroms wide for each angstroms wide for each full cycle of its double full cycle of its double helix spiral.helix spiral.

Our Solar System corresponds to the Golden Mean in measurement of distance from each other, even the rings of Saturn.

Fibonacci NumbersFibonacci Numbers ""Without mathematics thereWithout mathematics there is is no artno art."."

--Luca Pacioli--Luca Pacioli

Leonard of Pisa (1170-1250), better known as Fibonacci, introduced the Fibonacci Series, a sequence of numbers; 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … in which any number is the sum of the two preceding members.

0 + 1 = 11 + 1 = 21 + 2 = 32 + 3 = 53 + 5 = 85 + 8 = 13 etc.

Fibonacci NumbersFibonacci Numbers

The Fibonacci Series and the Golden The Fibonacci Series and the Golden Mean are intimately connected. The Mean are intimately connected. The Fibonacci Series numbers increase at Fibonacci Series numbers increase at a rate equal to (actually, oscillating a rate equal to (actually, oscillating round) the Golden mean. (The larger round) the Golden mean. (The larger the numbers, the closer to the the numbers, the closer to the Golden Mean.)Golden Mean.)

Notice that the proportionate length of each part of a finger bone corresponds with the Fibonacci sequence

0, 1, 1, 2, 3, 5, 8, 13, 21,

Golden SpiralGolden Spiral Draw a golden rectangleDraw a golden rectangle Taking the smaller of the Taking the smaller of the

sections, draw another golden sections, draw another golden rectanglerectangle

Keep doing that ad infinitumKeep doing that ad infinitum A spiral can be drawn through A spiral can be drawn through

the corners of each golden the corners of each golden section.section.

These spirals are found These spirals are found everywhere!!! (shells, galaxies, everywhere!!! (shells, galaxies, hurricanes, human ear)hurricanes, human ear)

Golden Mean and the Human BodyGolden Mean and the Human Body

The Golden The Golden Mean and Mean and Golden Spiral Golden Spiral are evident in are evident in the the proportions of proportions of the human the human body.body.

A template for human beauty is found in phi and the pentagon

The rules of human proportion are often simplifiedTo correspond to thesize of the head.

Adult humans are about8 heads tall

The proportion of infants, children,And adolescents is very different from the adult.

Infant:

Toddler:

Child:

Adolescent:

Leonardo DaVinciLeonardo DaVinci

Vitruvian ManVitruvian Man

The The Vitruvian ManVitruvian Man is a world renowned is a world renowned drawingdrawing with accompanying notes created with accompanying notes created by by Leonardo Leonardo dada Vinci Vinci around the year around the year 14921492 as recorded in one of his journals. It as recorded in one of his journals. It depicts a nude male figure in two depicts a nude male figure in two superimposed positions with his arms and superimposed positions with his arms and legs apart and simultaneously inscribed in legs apart and simultaneously inscribed in a circle and square. The drawing and text a circle and square. The drawing and text are sometimes called the are sometimes called the Canon of Canon of ProportionsProportions or, less often, or, less often, Proportions Proportions of Manof Man. It is on display in the . It is on display in the Gallerie dell' Gallerie dell' AccademiaAccademia in in VeniceVenice, Italy , Italy

http://en.wikipedia.org/wiki/Vitruvian_man

http://en.wikipedia.org/wiki/Vitruvian_man

DaVinci filled sketchbooks with studies and research about the human body and the natural world. He even wrote in his own code, backwards (mirror-writing).

Leonardo DaVinci

Michelangelo

Michelangelo

http://www.byzarium.com/images/flashImages/Odd_Nerdrum_small.jpg

Odd Nerdrum

Return of the Sun

Artemisia Gentileschi

Susanna and the Elders

Frida Kahlo

Two Fridas

http://www.ibiblio.org/wm/paint/auth/moreau/orpheus.jpg

Gustave Moreau

Orpheus

http://religion-cults.com/Cults/Other/CRISTO2DALI71.JPG

Salvador Dali

Christ Crucified 2

http://odin.himinbi.org/reading_list/dali%20-%20last%20supper.jpg

BibliogaphyBibliogaphy http://goldennumber.net/http://goldennumber.net/ http://community.middlebury.edu/http://community.middlebury.edu/

~harris/Humanities/TheGoldenMe~harris/Humanities/TheGoldenMeanan..

htmlhttp://en.wikipedia.org/wiki/htmlhttp://en.wikipedia.org/wiki/Golden_ratioGolden_ratio

http://en.wikipedia.org/wiki/Phidiahttp://en.wikipedia.org/wiki/Phidiass

http://en.wikipedia.org/wiki/Imagehttp://en.wikipedia.org/wiki/Image:Athena_Parthenos_Altemps_Inv8:Athena_Parthenos_Altemps_Inv8622.jpg622.jpg

http://drawinglab.evansville.edu/phttp://drawinglab.evansville.edu/proportion.htmlroportion.html

http://www.dace.co.uk/proportion.http://www.dace.co.uk/proportion.htmhtm

http://www.mcs.surrey.ac.uk/Pershttp://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.htmlonal/R.Knott/Fibonacci/fibnat.html#spiral#spiral

http://milan.milanovic.org/math/ehttp://milan.milanovic.org/math/english/body/pages/12.dna-b.htmlnglish/body/pages/12.dna-b.html

http://milan.milanovic.org/math/englishttp://milan.milanovic.org/math/english/body/pages/12.dna-b.htmlh/body/pages/12.dna-b.html

http://facultystaff.vwc.edu/~trfanney/http://facultystaff.vwc.edu/~trfanney/golden-mean-WOWslides/gm10a.htmlgolden-mean-WOWslides/gm10a.html

http://www.fjkluth.com/arch.htmlhttp://www.fjkluth.com/arch.html http://www.halexandria.org/http://www.halexandria.org/

dward103.htmdward103.htm http://www.dace.co.uk/http://www.dace.co.uk/

proportion_child.htmproportion_child.htm http://www.artlex.com/ArtLex/g/http://www.artlex.com/ArtLex/g/

goldenmean.htmlgoldenmean.html http://www.mcs.surrey.ac.uk/http://www.mcs.surrey.ac.uk/

Personal/R.Knott/Fibonacci/Personal/R.Knott/Fibonacci/fibInArt.htmlfibInArt.html

http://www.makart.com/resources/http://www.makart.com/resources/artclass/golden.htmlartclass/golden.html

http://odin.himinbi.org/reading_list/dalihttp://odin.himinbi.org/reading_list/dali%20-%20last%20supper.jpg%20-%20last%20supper.jpg

Livio, Mario, The Golden MeanLivio, Mario, The Golden Mean