As our circle of knowledge expands, so does the circumference of darkness surrounding it.

De Morgan was explaining to an actuary what was the chance that a certain proportion of some group of people would at the end of a given time be alive; and quoted the actuarial formula, involving p [pi], which, in answer to a question, he explained stood for the ratio of the circumference of a circle to its diameter. His acquaintance, who had so far listened to the explanation with interest, interrupted him and exclaimed, “My dear friend, that must be a delusion, what can a circle have to do with the number of people alive at a given time?”

Energy is the only life ... as Reason is the bound or outward circumference of Energy.

Eratosthenes of Cyrene, employing mathematical theories and geometrical methods, discovered from the course of the sun, the shadows cast by an equinoctial gnomon, and the inclination of the heaven that the circumference of the earth is two hundred and fifty-two thousand stadia, that is, thirty-one million five hundred thousand paces.

Great works are performed, not by strength, but by perserverance. He that shall walk, with vigour, three hours a day, will pass, in seven years, a space equal to the circumference of the globe.

He scarce had ceased when the superior fiend
Was moving toward the shore; his ponderous shield
Ethereal temper, massy, large and round,
Behind him cast; the broad circumference
Hung on his shoulders like the moon, whose orb
Through optic glass the Tuscan artist views
At evening from the top of Fésolè,
Or in Valdarno, to descry new lands,
Rivers or mountains in her spotty globe.

I will venture to say there is more learning and science within the circumference of ten miles from where we now sit [in London], than in all the rest of the kingdom.

Imagine a person with a gift of ridicule [He might say] First that a negative quantity has no logarithm; secondly that a negative quantity has no square root; thirdly that the first non-existent is to the second as the circumference of a circle is to the diameter.

In the human body the central point is naturally the navel. For if a man be placed flat on his back, with his hands and feet extended, and a pair of compasses centered at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle described therefrom.

It is admitted, on all hands, that the Scriptures are not intended to resolve physical questions, or to explain matters in no way related to the morality of human actions; and if, in consequence of this principle, a considerable latitude of interpretation were not allowed, we should continue at this moment to believe, that the earth is flat; that the sun moves round the earth; and that the circumference of a circle is no more than three times its diameter.

Let him look at that dazzling light hung aloft as an eternal lamp to lighten the universe; let him behold the earth, a mere dot compared with the vast circuit which that orb describes, and stand amazed to find that the vast circuit itself is but a very fine point compared with the orbit traced by the stars as they roll their course on high. But if our vision halts there, let imagination pass beyond; it will fail to form a conception long before Nature fails to supply material. The whole visible world is but an imperceptible speck in the ample bosom of Nature. No notion comes near it. Though we may extend our thought beyond imaginable space, yet compared with reality we bring to birth mere atoms. Nature is an infinite sphere whereof the centre is everywhere, the circumference nowhere. In short, imagination is brought to silence at the thought, and that is the most perceptible sign of the all-power of God.
Let man reawake and consider what he is compared with the reality of things; regard himself lost in this remote corner of Nature; and from the tiny cell where he lodges, to wit the Universe, weigh at their true worth earth, kingdoms, towns, himself. What is a man face to face with infinity?

Many errors, of a truth, consist merely in the application of the wrong names of things. For if a man says that the lines which are drawn from the centre of the circle to the circumference are not equal, he understands by the circle, at all events for the time, something else than mathematicians understand by it.

Mathematics, indeed, is the very example of brevity, whether it be in the shorthand rule of the circle, c = πd, or in that fruitful formula of analysis, e^iπ = -1, —a formula which fuses together four of the most important concepts of the science,—the logarithmic base, the transcendental ratio π, and the imaginary and negative units.

Nature … is an infinite sphere of which the center is everywhere and the circumference nowhere.

Passing just lately over this lake, … and examining this water next day, I found floating therein divers earthy particles, and some green streaks, spirally wound serpent-wise, and orderly arranged, after the manner of the copper or tin worms, which distillers use to cool their liquors as they distil over. The whole circumference of each of these streaks was about the thickness of a hair of one's head. … all consisted of very small green globules joined together: and there were very many small green globules as well. [The earliest recorded observation of the common green alga Spyrogyra.]

The 31th of May, I perceived in the same water more of those Animals, as also some that were somewhat bigger. And I imagine, that [ten hundred thousand] of these little Creatures do not equal an ordinary grain of Sand in bigness: And comparing them with a Cheese-mite (which may be seen to move with the naked eye) I make the proportion of one of these small Water-creatures to a Cheese-mite, to be like that of a Bee to a Horse: For, the circumference of one of these little Animals in water, is not so big as the thickness of a hair in a Cheese-mite.

The Biblical value of pi, by comparison, is exactly three, as is clear from a verse in 1 Kings vii 23: 'and he made a molten sea, ten cubits from brim to brim, and his height was five cubit; and a line of thirty cubits did encompass him round about.'

The first quality we know in matter is centrality,—we call it gravity,—which holds the universe together, which remains pure and indestructible in each mote, as in masses and planets, and from each atom rays out illimitable influence. To this material essence answers Truth, in the intellectual world,—Truth, whose centre is everywhere, and its circumference nowhere, whose existence we cannot disimagine,—the soundness and health of things, against which no blow can be struck but it recoils on the striker,—Truth, on whose side we always heartily are. And the first measure of a mind is its centrality, its capacity of truth, and its adhesion to it.

The sun’s rays proceed from the sun along straight lines and are reflected from every polished object at equal angles, i.e. the reflected ray subtends, together with the line tangential to the polished object which is in the plane of the reflected ray, two equal angles. Hence it follows that the ray reflected from the spherical surface, together with the circumference of the circle which is in the plane of the ray, subtends two equal angles. From this it also follows that the reflected ray, together with the diameter of the circle, subtends two equal angles. And every ray which is reflected from a polished object to a point produces a certain heating at that point, so that if numerous rays are collected at one point, the heating at that point is multiplied: and if the number of rays increases, the effect of the heat increases accordingly.

The universe, then, has no circumference, for, if it had a center and a circumference, it would thus have in itself its beginning and its end, and the universe itself would be terminated by relation to something else; there would be outside the universe another thing and a place—but all this contains no truth.

The view of the moon that we’ve been having recently is really spectacular. It fills about three-quarters of the hatch window, and of course we can see the entire circumference even though part of it is in complete shadow and part of it is in earthshine. It’s a view worth the price of the trip.

The world’s the book where the eternal sense
Wrote his own thoughts; the living temple where,
Painting his very self, with figures fair
He filled the whole immense circumference.

To a body of infinite size there can be ascribed neither center nor boundary ... Just as we regard ourselves as at the center of that universally equidistant circle, which is the great horizon and the limit of our own encircling ethereal region, so doubtless the inhabitants of the moon believe themselves to be at the center (of a great horizon) that embraces this earth, the sun, and the stars, and is the boundary of the radii of their own horizon. Thus the earth no more than any other world is at the center; moreover no points constitute determined celestial poles for our earth, just as she herself is not a definite and determined pole to any other point of the ether, or of the world-space; and the same is true for all other bodies. From various points of view these may all be regarded either as centers, or as points on the circumference, as poles, or zeniths and so forth. Thus the earth is not in the center of the universe; it is central only to our own surrounding space.