I once painted a piece called Cutting Squares…
It was for a going-away group show that William H. Miller (Billy Boots) put on before he left Winter Street Studios. Each piece of art was based off an item that Billy gave each of us from his studio as he was cleaning it out. I received a book called Q.E.D. Beauty in Mathematical Proof. A small little book with overly simplified concepts of math that leave the mind boggled with just about every page.
Although there was tons of more understandable and familiar geometry in this book, like the Platonic Solids, the cover image stood out as pleasing yet mysterious… so I just went with that!
The section of the book that talks about the cover art was equally perplexing yet simple, just how I like it. It reads:
Beautiful theorems are often arrived at by coming up with new ways of interpreting old patterns. For a whirlwind tour of some classic examples dating back to the Pythagoreans, let’s consider various ways of dissecting a square array of n times n, or n^2, pebbles.
The first way gives the elementary equality n+n+…+n (n times) = n^2.
The second way translates into the surprising fact that the sum of the first n odd number is equal to n^2. For another proof of this theorem, just note that the numbers of triangles in the columns of tiling n below are the first n odd numbers and that after separating the black and the gray triangles (opposite, bottom), we get a square of n^2 triangles.
Closely related is the third way of dissecting, which corresponds to the equality (n – 1)^2 + (2n – 1) = n^2. Choosing the odd number 2n – 1 to be a square, we get a Pythagorean triple. Fore example, choosing 2n – 1 = 3^2 gives n = 5, and therefore 4^2 + 3^2 = 5^2.
One last way of dissecting the square array shows that n^2 is equal to the sum of the first n natural numbers plus the sum of the first n – 1 natural numbers. Can you see how to derive from this a formula for the sum of the first n natural numbers?
Check out this post to get a better understanding of square numbers.
After I sold the first Cutting Squares painting I decided to try another version of it:
If this piece speaks to you, I invite you to include it in your home. Sacred Geometry like this is mathematically symmetrical, which signals subconsciously the serenity of balance, enhancing positive energy flow and equilibrium to the house and to those who reside.
You can find more about this artwork in the shop.
And so back to my story,
I remember I was in a clusterfuck, as usual, to get there on time. But as I was driving I was psyching myself up for it, saying to myself, “it doesn’t matter what time you arrive, even if late, because you will still make the connection you need to make and sell the art”.
Sure enough, I easily walked in there, saw someone looking at it, approached her, struck up a conversation about it and sold it as well as met for the first time a life long collector, mentor, and dear friend Linda Starr.
I have her book The Genesis Formula and her life coaching has been instrumental in my development. She is more than a business coach, although she is amazing at that, but also gets a lot into the esoteric and that’s where we really get jiving. I want to have her on my podcast/vlog soon, so check back soon for that.
Wow. It’s fun to think back about where some of this art came from and where some of it has lead me.
Some art actually changes your life.
That’s powerful.
I’m so excited to meet you. The next person to see the value in what I am offering the world. To easily step into my life and together we will continue to synergistically heal the world and make our lives more amazing in a feedback loop of love.
What do you think?
What is this geometry named? Leave a comment to inform the rest of us.
Namaste