A special Thank You to Michael Vassalotti, my good friend who shared a book with me, A Million Little Miracles (citation below). It came at a pivotal point in the writing of this post. It helped me bridge any gaps between spirituality, science and math.
If you teeter between these elements of life as I do, you will enjoy powerfully deep, broadening and even humorous aspects of our amazing universe in this book.
(And yes, if you grew up in Landisville, the Vassalotti name is certainly familiar.)
And also: I dedicate this post to my long-time childhood friend Carol who finds so much meaning walking through the rolling hills of Pennsylvania. Along with her husband David, they immerse themselves in the marvelous patterns of nature . . .
. . . . like this spiraling tree trunk.
A spiraling tree trunk shows us nature's creative ability to adapt to environmental stresses. Hmmm. Environmental stresses.
Does that resonate with you and me? We certainly are surrounded by real and imagined stresses, but strength has always been part of the Grand Design.
I can do all this through him who gives me strength. Philippians 4:13
An uneven burden of heavy snow or lack of water will trigger the trunk to spiral itself, strengthening the base while allowing the upper branches to bend and sway with the wind.
Our own burdens may seem to twist us around, but human growth and endurance is also a spiral.
We move upward in strength, our ever building spiral, as we learn, revisit and climb our many steps to fulfillment.
(Hermann Hesse)
The Spiral Pathway
Our soulful journey
toward authenticity,
is a Spiral Pathway.
Searching. Learning. Finding.
In strengthening circles.
Each time around--
Eyes widen. Ears listen.
Growing wiser and stronger.
-----Sarah Ban Breathnach
Eyes Widen; Ears Listen.
Look above you!
Look below you!
God, whom you seek,
Set before your eyes
All His wonders.
Can you ask for a louder voice than that?
Listen! His voice surrounds you.
When heaven and earth shout to you, Listen!
His voice is there.
-------St. Augustine
Look Around. Prepare for the WOW Factor
Immerse yourself into nature's wonders and you will feel the voice of the Creator seeking you, inviting you to marvel in the Bigger than Big, Closer than Close and the of the WoW-Ness of the Almighty.
His fingerprints are all around us in mathematical patterns. How it all fits together is my WOW Factor.
Mark Batterson, A Million Little Miracles. 1
A Little Fun with Spirals, Ratios, and the Fibonacci Sequence2
Remember arithmetic in elementary school? That's when we began the dread of miscalculations. But allow yourself to go beyond that. Math is the language of the universe. It's full of wondrous magic and you and I are part of it. (Neil deGrasse Tyson)
Why should mathematicians have all the fun?
Pearls of Wonders . . .
The Fibonacci Sequence and Spiral
Moon Snail design follows the same mathematical pattern , the Fibonacci Sequence, as the spiral in a pinecone, conch shell, the yellow center of a daisy, our own galaxy, and our own DNA. How does that happen? (Answer: By Grand Design)
Life is a series of tiny everyday miracles
Spiraling around us.
Ours to see, to hear.
Notice them.
― Roald Dahl
Thank you for indulging in this journey into spirals, math, and beyond.
Maybe for you, this is enough.
But there's more below, if you are a seeker, like me. More on Fibonacci. My inner fractal keeps going.
And there will be a Grand Design, Part Two,: The Song of the Universe.
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Want More? Fibonacci and Fractals and Videos
Fibonacci (real name Leonardo Bonacci) (c. 1170 – c. 1240–50), was an Italian mathematician considered to be "the most talented Western mathematician of the Middle Ages". In his Book of the Abacus, he introduced the Hindu-Arabic numerals (arithmetic) to all of Europe replacing Roman numerals.
The Fibonacci Sequence and Spirals are evident everywhere in nature.
Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34.... to infinity.
To find the next number, just add the last two numbers together!
For example, 1 + 1 = 2, 1 + 2 = 3, and 2 + 3 = 5.
Take a few minutes: I provided 2 links below for easy and entertaining shortcuts presenting much more of the Fibonacci Sequence and Spiral, in nature, the human anatomy, art and architecture.
(Prepare to be WoWed!)
And how can this "Bee"? In honeybees, the Fibonacci sequence is evident in their family tree. A male bee has one parent, while a female bee has two. The pattern of ancestors follows the Fibonacci sequence, with each bee having a number of ancestors equal to the sum of the ancestors in the previous two generations.
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Fractals: Repeating Patterns
And don't get me started with fractals . . . repeating patterns to infinity.
We are surrounded by wondrous artistry found in fractal geometry, symmetrical beauty that repeats and repeats, echoing the hand of the Creator.
History is fractal. The closer you look, the more complicated, yet always repeating patterns.
~ Ted Nelson
Fractals of the Heart: Acts of love, compassion, forgiveness, understandings and kindnesses, as taught to us by Christ, over and over again, repeating forever, in ripples of you and me.
---g. hill
Thank you for indulging in this journey into spirals, math, and beyond.
Maybe for you, this is enough.
But there's more below, if you are a seeker, like me. My inner fractal keeps going.
And there will be a Grand Design, Part Two,: The Song of the Universe.
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You are braver than you know, stronger than you think, and smarter than you believe. But the most important thing is, even if we’re apart… I’ll always be with you.
----Christopher Robin (by A. A. Milne)
There are two ways to live your life. One is as though nothing is a miracle. The other is that everything is miraculous.
----Albert Einstein
The heavens declare the glory of God; And the firmament shows His handiwork. Psalm 19:1
The Fibonacci Sequence: Nature’s Code
The Fibonacci Spiral
See how the squares fit neatly together?
For example 5 and 8 make 13, 8 and 13 make 21, and so on.
It is not the ocean that you hear in the empty shell of a nautilus.
It is the echo of your soul.
----Khang Kijarro Nguyen
See Also: The Triumph of Seeds: What Lies Within and Listening for the Echoes
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Fibonacci Sequencehttps://www.mathsisfun.com/numbers/fibonacci-sequence.html
Images are from Pixabay.com or AI generated.
I love this, Gloria. Somehow I missed noticing and learning about spiraling tree trunks! Nature is truly amazing. It’s all a wonder and chorus.
Thank you, Lori. I only touched a small part— the Golden Spiral is also evident in the human embryo and other parts of the anatomy. What a great God. Sometimes I think the mathematicians and scientists come the closest to the greatness of creation.
yes this is awesome Gloria– has made me think of think of things I had not thought of before! as they relate to my own life! thank you, Nance
Nance, I am sure your daily walks and runs in nature inspire thoughts of our amazing world and how we are all connected.
FABULOUS. ❤️🥰 Sandy
Thank you, Sandy! I taught middle school math and had my students graph the Fibonacci Sequence and shade in the rectangles. I wrote a grant to promote math and art. I found my niche when they asked me to teach math. Always loved equations, remember?