Circles
simple curve of Euclidean geometry
Circles are simple shapes of Euclidean geometry consisting of those points in a plane which are equidistant from a given point, the centre. They can be described as closed curves which divide the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is the former and the latter is called a disk.
Quotes
edit- Quotes are arranged alphabetically by author
A - F
edit- Do not disturb my circles!
- Archimedes, in last words before being killed by a soldier, as quoted in World Literature : An Anthology of Human Experience (1947) by Arthur Christy, p. 655
- 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.
- Black Elk in Black Elk Speaks (1961), Chapter 17 : The First Cure
- Circles and right lines limit and close all bodies, and the mortal right-lined circle must conclude and shut up all.
- Sir Thomas Browne, Hydriotaphia, Chapter V. Reported in Hoyt's New Cyclopedia Of Practical Quotations (1922), p. 119.
- If people stand in a circle long enough, they'll eventually begin to dance.
- George Carlin, Napalm and Silly Putty (2001)
- All my life's a circle;
But I can't tell you why;
Season's spinning round again;
The years keep rollin' by.- Harry Chapin in "Circle" on Sniper and Other Love Songs (1972).
- A circle may be small, yet it may be as mathematically beautiful and perfect as a large one.
- Isaac D'Israeli, Miscellanies. Reported in Hoyt's New Cyclopedia Of Practical Quotations (1922), p. 119.
- Our task must be to free ourselves... by widening our circle of compassion to embrace all living creatures and the whole of nature and its beauty.
- Albert Einstein, in a letter of 1950, as quoted in The New York Times (29 March 1972).
- The eye is the first circle; the horizon which it forms is the second; and throughout nature this primary figure is repeated without end. It is the highest emblem in the cipher of the world.
- Ralph Waldo Emerson, Essays. Circles. Reported in Hoyt's New Cyclopedia Of Practical Quotations (1922), p. 119.
G - L
edit- Never, never rest contented with any circle of ideas, but always be certain that a wider one is still possible.
- Richard Jefferies, Story of My Heart : My Autobiography (1901).
- Circularity is a powerful concept, the idea of a closed loop even more so. In circular motion there is magic, just as there is in electro-magnetism. But it only manifests itself when it is, like (shall we say for the moment, rather than a 'reflection' of) its 'neighboring head', truly three-dimensional. ...We can induce current into the one [coil] from the other by means totally unintelligible to us, but to which we give the name 'electromagnetic induction'. But if I place one coil with its axis at right-angles to that of the other, there is no induced voltage. It is as if the two circuits lived in different worlds... What is the meaning of perspective in a four-dimensional space?
- Eric Laithwaite, Engineer Through the Looking-Glass (1980) Ch. 4, The Jabberwock, pp. 41-42.
- The next best thing to being wise oneself is to live in a circle of those who are: that good fortune I have enjoyed for nearly twenty years.
- C. S. Lewis, in They Asked for a Paper: Papers and Addresses (1962), p. 63.
M - R
editHeretic, rebel, a thing to flout.
But Love and I had the wit to win:
We drew a circle that took him in. ~ Edwin Markham
- He drew a circle that shut me out —
Heretic, rebel, a thing to flout.
But Love and I had the wit to win:
We drew a circle that took him in.- Edwin Markham, "Outwitted", from The Shoes of Happiness, and Other Poems (1913).
- There must be a positive and negative in everything in the universe in order to complete a circuit or circle, without which there would be no activity, no motion.
- John McDonald, in The Message of a Master : A Classic Tale of Wealth, Wisdom and the Secret of Success (1929), Chapter 11.
- And the seasons they go round and round,
And the painted ponies go up and down,
We're all captive on the carousel of time
We can't return we can only look behind
From where we came
And go 'round and 'round and 'round
In the circle game.- Joni Mitchell, "The Circle Game," from Ladies of the Canyon (1970).
- No one ever squared the circle with so much genius, or, excepting his principal object, with so much success.
- Attributed to Jean-Étienne Montucla in Augustus De Morgan, A Budget of Paradoxes, (London, 1872): About Gregory St. Vincent, described by De Morgan as "the greatest of circle-squarers, and his investigations led him into many truths: he found the property of the arc of the hyperbola which led to Napier's logarithms being called hyperbolic."
- Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.
- Friedrich Nietzsche, as quoted in The Puzzle Instinct : The Meaning of Puzzles in Human Life (2004) by Marcel Danesi, p. 71.
- Rust Cohle: Someone once told me, 'Time is a flat circle.' Everything we've ever done or will do, we're gonna do over and over and over again. And that little boy and that little girl, they're gonna be in that room again and again and again forever.
- Nic Pizzolatto, True Detective (TV series) The Secret Fate of All Life
- 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 (1733-34), Epistle IV, line 364. Reported in Hoyt's New Cyclopedia Of Practical Quotations (1922), p. 119.
- As on the smooth expanse of crystal lakes
The sinking stone at first a circle makes;
The trembling surface by the motion stirr'd,
Spreads in a second circle, then a third;
Wide, and more wide, the floating rings advance,
Fill all the watery plain, and to the margin dance.- Alexander Pope, Temple of Fame, line 436. Reported in Hoyt's New Cyclopedia Of Practical Quotations (1922), p. 119.
S - Z
edit- The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover a miracle — another circle, drawn kilometers downstream of the decimal point. There would be richer messages farther in. It doesn't matter what you look like, or what you're made of, or where you come from. As long as you live in this universe, and have a modest talent for mathematics, sooner or later you'll find it. It's already here. It's inside everything. You don't have to leave your planet to find it. In the fabric of space and in the nature of matter, as in a great work of art, there is, written small, the artist’s signature. Standing over humans, gods, and demons, subsuming Caretakers and Tunnel builders, there is an intelligence that antedates the universe.
- Carl Sagan, in Contact : A Novel (1985), Ch. 24.
- Until he extends his circle of compassion to include all living things, man will not himself find peace.
- Albert Schweitzer, in Kulturphilosophie (1923), translated as Philosophy of Civilisation (1949).
- 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, On a Circle. Reported in Hoyt's New Cyclopedia Of Practical Quotations (1922), p. 119.
- I watch'd the little circles die;
They past into the level flood.- Alfred Tennyson, The Miller's Daughter, stanza 10. Reported in Hoyt's New Cyclopedia Of Practical Quotations (1922), p. 119.
- On the lecture slate
The circle rounded under female hands
With flawless demonstration.- Alfred Tennyson, The Princess (1847), II, line 349. Reported in Hoyt's New Cyclopedia Of Practical Quotations (1922), p. 119.
- A circle is a round straight line with a hole in the middle.
- Mark Twain, quoting a schoolchild in "English as She Is Taught", Century Magazine, May 1887, as reprinted in Essays and Sketches of Mark Twain (1995), ed. Stuart Miller, ISBN 1566198798 .
- Circles are praised, not that abound
In largeness, but the exactly round.- Edmund Waller, Long and Short Life Reported in Hoyt's New Cyclopedia Of Practical Quotations (1922), p. 119.