The Golden Ratio is a unique number, approximately 1.618033989. It is also known as the Divine Ratio, the Golden Mean, the Golden Number, Divine Proportion and the Golden Section.
The Fibonacci Sequence of Numbers
The Fibonacci numbers are a unique sequence of integers, starting with 1 (twice), each succeeding number the sequence is the sum of the two preceding ones. So the sequence goes 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc. For some mysterious reasons, this sequence of numbers seems to appear in a wide variety of places in the natural world.
The Fibonacci Sequence is an infinite sequence, which means it goes on forever, and as it develops, the ratio of the consecutive terms converges (becomes closer) to the Golden Ratio, ~1.618. For example, to find the ratio of any two successive numbers, take the latter number and divide by the former. So, we will have: 1/1=1, 2/1=2, 3/2=1.5, 5/3=1.66, 8/5=1.6, 13/8=1.625, 21/13=1.615.
In the Arts
Prevalent in the major works of Leonardo Da Vinci and underlying many of his design compositions, is the Golden Ratio. Another artist who deliberately used the golden ratio is the surrealist Salvador Dali.
In nature and the Human Body
The ancients believe these numbers were sacred. And that might have been because the same proportions can be found in nature.
One of nature’s most exquisite forms is the simple curved shell of the Nautilus. Like so much of nature, the beauty of this shape can also be explained with an equation. If you take a series of squares whose sides correspond to numbers in the Fibonacci sequence, you can construct a logarithmic spiral. A curve that corresponds to the shape of the Nautilus shell.
At an average of 100,000 light years across, even the spirals of the galaxies above us are formed with the exact design that the tiny shells form.
The human body proportioned according to the Golden Ratio is also taken as the basis in the Neufert, one of the most important reference books of modern day architects. The ideal proportional relations that are suggested as existing among various parts of the average human body and that approximately meet the Golden ratio values can be set out in a general plan. The first example of the Golden Ratio in the average human body is that when the distance between the navel and the foot is taken as one unit the height of the human being is equivalent to 1.618. Other examples are shown in the clip.
However, it may not always be possible to use a ruler and find this ratio all over people’s faces because it applies to the idealized human form on which scientists and artists agree.
The DNA molecule in which all the physical features of living things are stored. DNA consists of two intertwined perpendicular helixes. The length of the curve in each of these helixes is 34 angstroms and the width, 21 angstroms. 21 and 34 are two consecutive Fibonacci numbers.
This sequence appears to be the trademark of a designer – a proof of a Creator – something left behind, indicating the One who was there- a fingerprint, if you may, of God. Even Michelangelo’s “Creation” falls within this so-called “Divine Proportions”- a good nexus for us.
This golden measure in the sciences and the arts brings us to the core of life: rational relationships.Ratio after all is reason and relationship.
The Divine Ratio (1:1)
♥ Let us consider Psalm 34 of today’s readings. I will bless the Lord at all times; let my soul glory in the Lord; I sought the Lord, and he answered me; Taste and see how good the Lord is. Blessed the man who takes refuge in Him.
♥ This is a thanksgiving psalm spoken in the 1st person point of view. It speaks from: I, me, my, and the singular man. And it speaks of the very personal senses of seeing and tasting.
♥ Then we consider Jesus’ proclamation in today’s Gospel (Jn 6:41-51) Amen, amen, I say to you, whoever believes has eternal life. ( Jn 6:47 )
♥ Again, Jesus’ invitation is directed to whoever, singular and personal, albeit universal and general.
♥ The golden ratio formulated in numbers found in all of nature, albeit a fascinating and astonishing trivia, if at all true, is nothing compared to this Divine Ratio or Relationship that is certainly real.
The divine ratio, the divine ratio of Christian life, the divine measure is: one is to one (1:1).
♥ Just as we are all connected through the golden ratio in the material world, so must we be truly connected to God – not through material numbers and formulas, not through impersonal means and functions, but through Personal Relationship.
♥ The simple point of this lesson is:
Let each of us have, for every human person, a personal relationship with a loving personal eternal God – a One to One Relationship with God.
Q: How Do We Start Living By This Golden Divine Measure? A: By Imitation
♥ The first step to living up to this measure is given by Paul in today’s 2nd reading (Eph 4:30-5:2): by imitation.
♥ Eph 5:1-2 – So be imitators of God, as beloved children, and live in love…
♥ Just survey Paul’s theology of imitation:
✠1 Cor 4:16 Therefore, I urge you, be imitators of me…
✠1 Cor 11:1 Be imitators of me, as I am of Christ…
✠Phil 3:17 Join with others in being imitators of me…
✠1 Thes 1:6 And you became imitators of us and of the Lord…
✠1 Thes 2:14 For you have become imitators of the churches…
✠2 Thes 3:7 For you know how one must imitate us.
✠2 Thes 3:9 we wanted to present ourselves as a model for you, so that you might imitate us.
♥ And other scripture passages too:
✠ Heb 6:12 so that you may not become sluggish, but imitators of those who, through faith and patience, are inheriting the promises.
✠ Heb 13:7 Remember your leaders who spoke the word of God to you. Consider the outcome of their way of life and imitate their faith.
✠ 3 Jn 1:11 Beloved, do not imitate evil but imitate good.
The Bread of Life is the True Golden Measure
♥ Eucharist: Love without Measure.
What more could Jesus have done for us? Truly, in the Eucharist, He shows us a love which goes “to the end” (cf. Jn 13:1), a love which knows no measure. (JPII, Ecclesia de Eucharistia,6)
♥Eucharist: Measure of Faith.
The measure of our Faith is our belief that Jesus Christ is now on earth in the Holy Eucharist. In the measure that we believe in His Real Presence, He will teach us the truth, and work miracles in our favor. Our relationship to Jesus in the Eucharist is the measure of the validity of our Catholic faith.
♥ Eucharist: the Measure of Hope.
The measure of our Hope is in how we live the teachings of Christ (kerygma) and the shared life (koinonia) to be instruments of hope to others.
1) Do you have a One to One Relationship with God that goes beyond the math of how many times you received holy communion?
2) Are all bitterness, fury, anger, shouting, and reviling removed from you, along with all malice (Eph 4:31)?
3) Are you kind, compassionate, forgiving as God has forgiven you in Christ (Eph 4:32)?