Thinking About Circles

“A circle may be small, yet it may be as mathematically beautiful and perfect as a large one.” —Isaac D’Israeli

“If patterns exist in our seemingly patternless lives — and they do — then the law of harmony insists that the most harmonious of all patterns, circles within circles, will most often assert itself.”  — Dean Koontz, Deeply Odd, 2013

“Conversation is a game of circles.” — Ralph Waldo Emerson, Essays, 1841

“Just as a stone flung into the water becomes the centre and cause of many circles, and as sound diffuses itself in circles in the air; so any object, placed in the luminous atmosphere, diffuses itself in circles, and fills the surrounding air with infinite images of itself.” — Leonardo Da Vinci, Notebooks of Leonardo Da Vinci, 1970

Glory is like a circle in the water,
Which never ceaseth to enlarge itself,
Till by broad spreading it disperses to naught.

— William Shakespeare, Henry VI, Part One, 1591

Circles in water as they wider flow
The less conspicuous in their progress grow,
And when at last they trench upon the shore,
Distinction ceases and they’re view’d no more.

— George Crabbe, the Borough: A Poem in Twenty-Four Letters, 1810

As the small pebble stirs the peaceful lake;
The centre mov’d, a circle straight succeeds,
Another still, and still another spreads.

— Alexander Pope, An Essay on Man, 1734

I’m up and down and round about,
Yet all the world can’t find me out;
Though hundreds have employed their leisure,
They never yet could find my measure.

— Jonathan Swift, “Riddles”, 1724

Mathematicians prefer to think of circle as having an infinite number of corners than to view a circle as having no corners. If this may sound confusing to you, you might prefer Mark Twain’s explanation: “A circle is a round straight line with a hole in the middle.”

“Everything the Power of the World does is done in a circle. The sky is round, and I have heard that the earth is round like a ball, and so are all the stars. The wind, in its greatest power whirls. Birds make their nest in circles, for theirs is the same religion as ours. The sun comes forth and goes down again in a circle. The moon does the same and both are round. Even the seasons form a great circle in their changing, and always come back again to where they were. The life of a man is a circle from childhood to childhood, and so it is in everything where power moves. Our tepees were round like the nests of birds, and these were always set in a circle, the nation’s hoop.” — Nicholas Black Elk, quoted in Black Elk Speaks, 1961

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