# On Phi

The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. (Albert Einstein)

Nature hides her secrets because of her essential loftiness, but not by means of ruse. (Albert Einstein)

All life is biology – All biology is physiology – All physiology is chemistry – All chemistry is physics – All physics is math. (Dr. Stephen Marquardt)

Measure what is measurable, and make measurable what is not so. (Galileo Galilei)

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. (Johannes Kepler)

This post is about Phi (Φ) – 21st letter of the Greek alphabet

Phi – but not fi fo and fum

Phi, in traditional Greek numerals a value of 500 (φʹ) or 500 000 (φ)

Phi – the ratio of each successive pair of numbers in the Fibonacci Sequence

Phi – the symbol for the golden ratio and on other occasions in math and science

Phi – applicable in mathematics, art, architecture, biology, astronomy, music, physics, navigation, geology, engineering, economics, philosophy, and more

Phi – squared is a number exactly 1 greater than itself: 2.618

Phi – the ratio in the length of a DNA molecule

Phi – the ratio of the diameter of Saturn to the diameter of its rings

Phi – the sound of this song if the numbers were assigned to piano keys. Enjoy.

# On Exploring Nature

This is episode 4 of this holiday’s Exploring series. With yesterday’s focus on light, there is a logical connection between light and nature. After all, light is the foundation for life as we know it on Earth … and nature is the center stage for each of our lives.

Nature is all around us. We interact with it, sense it, we explore it, and even ignore it. Thankfully, not everyone chooses to ignore it. As a matter of fact, they share what they’ve learned with anyone who is willing to learn.

Nature is a fascinating place and even linked to numbers. After watching this video, share your thoughts in the comments. Do you have a favorite pattern in nature?

# Flashbacks: On Grandness Around Us

Earth and the universe provide countless wonders. I uncovered flashbacks so you can enjoy some of the grandness around us. Enjoy, visit as many as you want, and I hope you comment on the post you visited.

# On A to Z

Someone declared April as A-to-Z Challenge Month. Sure, the challenge’s intent is to have a separate post for each letter, but hey – I have a streak of independence.

With 1,167 posts before this one, why not use my archives to meet the challenge? After all, even frequent readers aren’t aware of some of the posts.

Therefore, I present A Frank Angle’s A-to-Z. Visit as many as you like, because as in my tradition, there is something for all …. so hopefully you’ll visit at least one.

A is for Acquaintance – People that were not in my graduation class: set 1 and set 2

B is for Ballroom – … and ballroom dance delivers benefits

C is for Cruising – We like cruising, so start your trip with a click

D is for Dinner Group – … We hosted a night of Chopped

E is for Education Reform – Although the need is obvious, here are the obstacles

F is for Frank – Yep, that’s my name, but these are the All-Time Franks in baseball

G is for God and Government – I must say that this post about the separation of church and state is pretty darn good

H is for Handbells – It takes many bells to make one instrument

I is for Italian – I’m 100% Italian heritage, and Ellis Island is an important place

J is for Joys – To whatever give you joy, but for some of us, it’s reliving the cartoons of our youth, and here is where the series started, which led to the first honoree

K is for Knowledge – What do you know about supersonic kangaroos?

L is for LearnerLearning should never stop

M is for Moderate – This early post defines an independent moderate, thus shows why neither party wants me … well, except for my vote

N is for News – Staying informed is important, but there is something more biased than the media

O is for Ohio River – A story from my hometown on a river during my youth.

P is for Politics – I wrote this shortly after the 2008 election, but before the Tea Party’s emergence (which is what makes this post interesting)

Q is for Quantum – Actually, this past post was On a Quantum Thought

R is for Recipes – I’m sort of a Foodie, so try Cranberry Sausage Spaghetti or my own spaghetti sauce that offers a little crunch

S is for Science – Like sports, science has players, plays, rules, and boundaries

T is for Trieste – A beautiful city on the Adriatic Sea that is the place of my birth

U is for Universe – The universe is vast and inspiring, and this post includes one of my absolute favorite videos

V is for Victory – The raised arm created an unexpected moment in college

W is for Wonders – There are many wonders in our world, and let’s not forget Fibonacci, Pi, and Tau

X is for X-Factor – and one X-factor in life is forgiveness

Y is for Why because I can – This is the first main post about the religion-science interchange; now there are 44, plus here is the very first post

Z is for Zinfandel – I enjoy a wide spectrum of wines, especially reds, but zins were the first to capture my fancy – and cheers to the wine group at church

AAA+++ Bonus for the bloggers on my sidebar and on the More Bloggers page, for as without them and you, I wouldn’t be here, so try to visiting someone soon that you don’t know, and tell them I sent you.

# On Fibonacci in Nature

Nature has many patterns, and they come in a variety of ways. Patterns can be simple, inspiring, microscopic, overt, sudden, gradual, and who knows how many ways as seasons, tides, anatomical structures, life created, processes, and behaviors. Patterns are associated with animals, plants, and the microscopic world.

For instance, the chambered nautilus is a biological relative to snails, squids, and octopi. Even though it is a simple organism, we stare with wonder at its shell and subsequent design. This mollusk also inspired Oliver Wendell Holmes to write the words below (taken from this poem named for its inspiration).

Build thee more stately mansions, O my soul,
As the swift seasons roll!
Leave thy low-vaulted past!
Let each new temple, nobler than the last,
Shut thee from heaven with a dome more vast,
Till thou at length art free,
Leaving thine outgrown shell by life’s unresting sea!

The Fibonacci sequence is a mathematical pattern linked to many patterns in nature. Tied to Leonardo of Pisa work in the early 1200s, the sequence appears in eastern cultures even earlier. The sequence can appear as a mathematical equation, a graphic representation, or in a photograph that may be just an image to the untrained eye.

Nonetheless, patterns in nature speak in their own language to help us understand the glories of the creation in which we live. Maybe this is one of the messages Dr. Seuss’s professes in these words:

I am the Lorax. I speak for the trees. I speak for the trees for they have no tongues.” —Dr. Seuss (The Lorax)

Enjoy this wonder video about the Fibonacci sequence in nature … and a special thanks to Kellie at The Beaglez for sharing this video with me. Below the video, I posted several photography links for anyone wanting to see more wonderful images.

Photography