How do you know the Golden Ratio?

• Literature

• Art

• Music

• Science

• Nature

• ????

Great Pyramids

ParthenonThe Golden Ratio has been represented by the Greek letter (phi), after Phidias, who is said to have employed it. 480BC-430BC

Phi is the first letter of Phidias, who used the golden ratio in his sculptures, as well as the Greek equivalent to the letter "F," the first letter of Fibonacci.

Can you show me a Golden Rectangle?

Anything???

Islamic Renaissance 700AD-1200AD

• Leonardo Fibonacci wrote - Liber Abaci• Arabic Numbering – The glyphs most commonly

used in conjunction with the Latin alphabet since Early Modern times are 0 1 2 3 4 5 6 7 8 9.

• Other developments from Islamic mathematicians were algebra and algorithms.

• The invention of spherical trigonometry.• The addition of the decimal point notation to the

Arabic numerals.

1, 1, 2, 3, 5, …Once a month…

In a year?

…, 55, 89, 144, 233, …

…, 8, 13, 21, 34,…

Fibonacci’s rabbits.

A New Number

• 1202AD

• It's not certain that Fibonacci even realized the sequences connection to phi and the Golden Mean.

• 3/5, 5/8, 8/13, 13/21,…

• 1.618033988749894…

• A new – Irrational constant

The division of a line into extreme and mean ratio.

It is equal to the constant Phi.

(1.618033988749894…)

The Golden Ratio is Divine Proportion.

Golden Ratio

Golden Ratio

Golden Ratio

Golden Ratio

Golden Ratio

Golden Ratio

Creation

• The description of this proportion as Golden and Divine is fitting perhaps because it is seen by many to open the door to a deeper understanding of beauty and spirituality in life.

• This one number has played an incredible role in human history and in the universe at large.

• The mathematical constant of 1.618…, is found throughout all of creation.

• Represented by the symbol Phi, which is the symbol 0 for nothing split in two by the symbol 1 for unity and one.

• The scriptures of all the major monotheistic religions is that God is One, Who created the universe from nothing, splitting nothingness into offsetting forces and elements.

Creation’s Number

In the beginning God created the heaven and the earth. And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. And God said, Let there be light: and there was light. And God saw the light, that it was good: and God divided the light from the darkness. And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.

Arc of the Covenant

Noah’s Ark

Book of John

In the beginning was the Word, and the Word was with God, and the Word was God.

God is one, without diversification

within God's self.

St. Thomas Aquinas, 1225-1274

Johannes Kepler, 1571-1630

"Geometry has two great treasures: one is the theorem of Pythagoras;

the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a

precious jewel."

European Renaissance

• 1300AD to 1600AD – Popular Culture began using Phi, and commonly called it the Divine Proportion.

• Famous People

• New World

• Reformation

• Industrial Age – Global Standardization

Famous People

• Marco Polo, 1254-1324• Johannes Gutenberg, 1398-1456• Christopher Columbus, 1451-1506• Leonardo Da Vinci, 1452-1519• Michelangelo, 1475-1564• Martin Luther, 1483-1546• Others???

Johannes Gutenberg• By 1450, the Gutenberg press was in operation,

and a German poem had been printed, possibly the first item to be printed there.

• In 1455 Gutenberg published his 42-line Bible, commonly known as the Gutenberg Bible. About 180 were printed, most on paper and some on vellum.

Most Books are Divine Proportion

Martin Luther

• In 1522, he completed his extraordinary translation of the Bible from Latin to German.

• The King James Bible is 75 per cent the work of English Reformer William Tyndale, 1494-1536.

• Even the notes on the margin of Tyndale's Bible are exactly the same as Luther's translation.

• Martin Luther also had a tremendous influence on the Spanish translation as most educated Spaniards spoke German.

Nature

• Sequential

Animals

• Head

• Trunk

Humans

• Arms

• Hands

• Fingers

• Face

• Head

• Eyes

• Nose

Art

Why PHI? – Some current uses of Phi.

• It wasn't until the 20th Century, that American mathematician Mark Barr used the Greek letter phi to designate this proportion.

• By this time this ubiquitous proportion was known as the – golden mean

– golden section

– golden ratio

– Divine Proportion.

• There has only been a Global Standard for a few decades, but it has been here all along.

Current Discoveries• Phi continues to open new doors in our understanding of

life and the universe.

• It appeared in Roger Penrose's discovery in the 1970's of "Penrose Tiles," which first allowed surfaces to be tiled in five-fold symmetry. (Fringe Science)

• It appeared again in the 1980's in quasi-crystals, a newly discovered form of matter. (sand nor glass)

• Mandlebrot Set - Chaos Mathematics

Plants

• Seed Rotation