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.

Additional Information about Phi at this site dedicated to phi

32 thoughts on “On Phi

  1. That Dr. Stephen Marquardt quote makes me understand why I had to study all those disciplines to get where I am. Luckily I enjoyed most of them. Except physics. That one I could have done without. 🙂


  2. What a beautiful piece of music. My understanding of complex mathematics is shaky, but it’s fascinating to me to see the order and patterns in nature, art and music. I suppose I can appreciate even if I don’t fully comprehend. I enjoyed this post very much, Frank. I’m so disappointed to have missed another Colors: The Musical. I’m sure “Purple” was a good one!


    • Debra,
      Aha ha … you are a fine example that one can appreciate the music and the mathematical complexities in nature without understanding them .. .and that’s OK!

      Purple was a tough one and it wasn’t good timing for me … nonetheless, you were missed. Good news is that info about the next act is on the Hear Ye page!

      Liked by 1 person

  3. I am reminded of this Sarah McLachlan’s ‘Building A Mystery’. At the same time reminding me of Ben, a Dutch painter I once knew who painted nothing of but dots of colours based on a mathematical formula – all his paintings had the title of DOG followed by a serial number. This explains Ben better than Ben ever could.

    Liked by 1 person

  4. Thanks for the five thought-provoking quotes. I plan to use #1 in my next abstract painting, #2 when I go to the voting booth this November, #3 as I continue to learn more about Integrative Education, #4 when I discuss with friends the outstanding play “Silent Sky” at the Know Theatre in Cincinnati, and #5 as I look back on my two favorite classes in high school – plane and solid geometry.


    • Tim,
      It appears you have too much time on your hands … meanwhile, sorry to say we missed Silent Sky. I expect an explanation on how you anticipate getting future band directors to implement Integrative Education into marching band.


  5. Pingback: On Exploring a Musical Design – A Frank Angle

Comment with respect.

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.