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Character and Excellence

The Golden Ratio - A Wonder of God's Creation

The golden ratio, mathematically represented as the Greek letter phi (φ) is 1 : 1.618, or more precisely

Leonardo Fibonacci (1175) is commonly cited as having discovered this ratio, although it has existed from the beginning of time, and has been discovered and rediscovered throughout the centuries.  Mathematically, two quantities have the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. Expressed algebraically:

This proportion has been given many different names, the Golden Section, the Golden Ratio, the Golden Mean, the Golden Cut, and the Divine Proportion (I have no problem with this name, for I believe it was divinely designed). And it has inspired many applications, including the Golden Rectangle, the Fibonacci Spiral, the Golden Angle, and the Fibonacci Gauge.

The Fibonacci Sequence (1, 1, 2, 3, 5, 8, 13, 21, 34 55, 89, 144 ...) is derived from the Golden Ratio, and represents a series of ratios which approximate φ with increasing precision as the sequence progresses. For instance, 2:3 equals 1.5, 5:8 equals 1.6, and 89:144 equals 1.6179. The next number in the sequence always equals the sum of the previous two numbers.

So what's so important about this ratio? Only that it keeps popping up in nature, science, and art, and has been identified as the ratio that is the most visually pleasing.

Shells - A Fibonacci Spiral is created by drawing arcs connecting the opposite corners of squares, whose relative sizes follow the Fibonacci Sequence. Many shells follow the shape of the Fibonacci Spiral.

 

Sunflowers and Pinecones - The individual florets of the sunflower (and of the daisy as well) grow in two spirals extending out from the center in opposite directions. The first spiral has 21 arms, while the other has 34. These are Fibonacci numbers, and have the Golden Ratio. Similarly, pinecones have 5 and 8 arms, or 8 and 13 arms depending on their size. This arrangement has been identified as the most efficient way of filling the space on the pinecone with seeds.

 

Daisies - Most daisies have 21, 34, 55, or 89 petals - all Fibonacci numbers.


Spiral Growth - The Golden Angle, also derived from the Golden Ratio, approximates to 137.51°. This is often the angle found between successive florets or leaves, in spiral growth.

 

Moths & Butterflies - The proportions and placement of colorings on a moth's wings follow the Golden Ratio.

Human body - probably God's most amazing use of the Golden Ratio is the human body. Obviously everyone is different, but if you take the average proportions for several people, you will start to find a pattern. Just in the human face, the following Golden Ratios are found:

  • Center of pupil : Bottom of teeth : Bottom of chin = φ
  • Outer & inner edge of eye: Center of nose = φ
  • Outer edges of lips : Upper ridges of lips = φ
  • Width of center tooth : Width of second tooth= φ
  • Width of eye : Width of iris = φ

Examples from the entire body:

  • The human head forms a golden rectangle (width : height = φ)
  • Whole body height : head to fingertips = φ
  • Top of head to fingertips : head to navel and elbows = φ
  • Top of head to navel and elbows : head to pectorals and inside top of arms = φ
  • Top of head to navel and elbows : width of shoulders = φ
  • Top of head to navel and elbows : length of forearm = φ
  • Top of head to navel and elbows : length of shinbone = φ
  • Top of head to pectorals : top of head to base of skull = φ
  • Top of head to pectorals : width of abdomen = φ
  • Length of Forearm : length of hand = φ

"I will praise thee; for I am fearfully and wonderfully made: marvellous are thy works; and that my soul knoweth right well."

Music - How many notes are there in an octave (black and white)? How many white notes? How many black notes? That's right - all of those numbers (5, 8, 13) are Fibonacci numbers!

 

Architecture - Man has long recognized the wisdom of following God's ways, though sadly many do not recognize Jehovah as the true God. Nobody knows quite why (other than God created it so), but things that use the Divine Ratio just look good - plain and simple. Ancient ruins show the use of the Golden Ratio, and designers and architects today still refer to it as the Golden Rule.


Woodworking - The Golden Ratio makes for the most aesthetically pleasing furniture. Want to learn how to use a Fibonacci Gauge in woodworking?

 

And this is just the tip of the iceberg! Other examples where the Golden Ratio has been observed in creation include the size of DNA molecules, ants, dolphins, pineapples, cactus, romanesque cauliflower, fruit seeds, the size of Saturn's ring, and the orbital periods, mean distances, and orbital velocities of the planets in the solar system.

Man is indeed without excuse, for God has put his signature on all of creation. "For since the creation of the world His invisible attributes, His eternal power and divine nature have been clearly seen, being understood through what has been made, so that they are without excuse" - Romans 1:20.

Published Nov 15 2009, 07:35 PM by Jon

Comments

 

Tim said:

This is very eye opening; I look at God's creation very differently now. Thanks for this post Jon.

I will praise You, for I am fearfully and wonderfully made; Marvelous are Your works, And that my soul knows very well. (Psalm 139:14)

The works of the LORD are great, Studied by all who have pleasure in them. (Psalm 111:2)

So God created man in His own image; in the image of God He created him; male and female He created them. (Genesis 1:27)

November 16, 2009 10:13 PM
 

Donald Staddon said:

I heard about the Fibonacci seven years ago and have never grown tired of learning about it since! Your summary is the clearest I've seen! Keep acknowledging the Lord in all your ways!

December 4, 2009 9:33 PM
 

Bill Dan said:

Which book, chapter and verse is this mathematical sequence unambiguously referred to in the Bible?

January 7, 2010 2:24 AM
 

The Wilkes Team » Blog Archive » Order & Beauty of Williamsburg said:

Pingback from  The Wilkes Team  » Blog Archive   » Order & Beauty of Williamsburg

January 8, 2010 2:07 PM
 

Robert Staddon said:

Wow! This is very insightful and well explained. Isn't God's creation amazing!

January 9, 2010 9:04 PM
 

Tim said:

Bill Dan,

There is no place in the Bible which specifically points out the "Golden Ratio". Like so many areas of life the Bible speaks of the Golden Ratio principally - not directly. If we only accepted the parts of God's word that specifically speak of our specific situations, instead of applying His principles, we would indeed be ignoring most if not all of the Bible. What a big mistake that would be.

January 14, 2010 4:37 PM
 

Math from a Christian Perspective » The Golden Ratio said:

Pingback from  Math from a Christian Perspective » The Golden Ratio

January 27, 2010 11:41 PM
 

B said:

The Golden Ratio and how it works in nature is pretty awesome.

Retrofitting a mathematical discovery to support creationism is not awesome.

February 2, 2010 10:48 PM
 

Jon said:

Mathematical discoveries are simply gaining knowledge of what God created in the beginning, and we should not be surprised when that knowledge reveals that there is a Creator, and reveal properties of that Creator such as order and objective beauty. It was there from the beginning - no retrofitting necessary.

I love how the Holy Spirit (through David) in Psalm 19 reveals God through His creation, then moves directly into to the sufficiency of the scriptures. It says:

"The heavens declare the glory of God; and the firmament sheweth his handywork. Day unto day uttereth speech, and night unto night sheweth knowledge. There is no speech nor language, where their voice is not heard. Their line is gone out through all the earth, and their words to the end of the world..."

In other words, creation is there for everyone to see, almost like a teacher. And if we study and learn from it we will learn of a Creator. This is how Paul says in Romans 1:20:

"For the invisible things of him [God] from the _creation of the world_ are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse:"

But back to Psalm 19 we see a transition from creation directly into the sufficiency of the scriptures:

"The law of the LORD is perfect, converting the soul: the testimony of the LORD is sure, making wise the simple. The statutes of the LORD are right, rejoicing the heart: the commandment of the LORD is pure, enlightening the eyes. The fear of the LORD is clean, enduring for ever: the judgments of the LORD are true and righteous altogether."

Science (the study of His creation) and the Bible (His word to us) are not at odds! As a follower of Christ, we can study His creation for no other reason than to learn of Him and glorify Him. And as I study His creation and His word, I am driven to the knowledge of His holiness and my own inadequacy, and like David to say:

"Who can understand his errors? cleanse thou me from secret faults. Keep back thy servant also from presumptuous sins... Let the words of my mouth, and the meditation of my heart, be acceptable in thy sight, O LORD, my strength, and my redeemer."

February 11, 2010 8:51 PM
 

David said:

I love this scientific information because It gives really a different way to see life !!

And the fact that there is a god who create everything becomes more and more true.

I want to share with you guys this video even If I didn't like totally the way how It was done but It interesting to see !!

March 3, 2010 1:27 AM

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