I spotted my old “Pre-Calculus” textbook on the bookshelf yesterday and smiled as I recalled that I had never put that knowledge to practical use in my life. Dad had strongly suggested that I should try to develop a love of mathematics similar to his. He was a civil engineer and utilized complex mathematics every day of his career. On the other hand, math was not my strong suit. Although I respected mathematics for its value to civilization, I did not love it, in fact, I struggled with it. I did not become enmeshed with it until I aced a remedial algebra course much later in life.
Anyhow, as I flipped through the pages of the old “Pre-Calculus” book I paused at some descriptions of circles. Circles being defined as “round plane figures” whose circumference (boundaries) consist of equidistant points from one fixed point (center). [( x – h )^2 + ( y – k )^2 = r^2, where ( h, k ) is the center and r is the radius.] Along with equilateral triangles and squares, circles are considered as highly symmetrical, geometric shapes.
I skimmed a few more pages of the book, then set it aside to review later. I intend to replace the battery in my handheld calculator later this week after going shopping for one at the hardware store. I’m eager to see how much I remember. I’d do the calculations by hand, but that makes my brain hurt.
Aside from geometric circles, there are other types. We have family circles, friendship circles, professional circles, and so forth. The word “circle” is also used as a verb. For example, “The hawk circles its prey.”
As people age and enter new phases of life, ideally our circles of knowledge and wisdom broaden. We continue to learn about different things and try out fresh concepts in our minds. We better understand that there are negative and positive qualities regarding everything in our vast Universe. Without a complete circuit (circle) there would be no action nor movement. Electricity being only one example of this requirement.
We see circuits in social interactions whether they be in commerce or within friendships. When someone shows loyalty to us, we take care of our comrads. If one member of the friends circle strays and becomes disloyal to the group, the group eventually parts company from that person. The friends circle shrinks by one person, but the common loyalty of the remaining members ensures that the circuit still operates.
“And I say the sacred hoop of my people was one of the many hoops that made one circle, wide as daylight and as starlight, and in the center grew one mighty flowering tree to shelter all the children of one mother and one father.”–Oglala Lakota elder, Black Elk
I feel fortunate to belong to a small, tight circle of friends. I feel emotionally close to them, even closer than with my biological family. I’ve encountered many people throughout life, but have only befriended a limited number of them. Furthermore, I’ve only made a few true-blue friends–this makes me feel quite fortunate and lucky. My current friends circle contributes to the meaningfulness of life.
Artie, one of the guys in my small friends circle, is an amateur mathematician. He likes to study buildings and bridges. Reverse engineering is one of his strong points. During his career, he was an architect’s assistant. Artie admires the work of J. Buckminster Fuller. Fuller’s style was elegant and simple–utilizing geometric circles and spheres. His famous circle domes minimized structural strains and stresses. The design elements worked in concert to maintain structural integrity and strength. In addition, his works have a timeless quality about them.
So, we have come full circle in today’s little ramble.
The Blue Jay of Happiness quotes French novelist, playwright, and poet, Jules Verne. “In spite of the opinions of certain narrow-minded people, who would shut up the human race upon this globe, as within some magic circle it must never outstep, we shall one day travel to the Moon, the Planets, and the stars, with the same facility, rapidity, and certainty as we now make the voyage from Liverpool to New York!”