Quotes About Euclid

If Euclid's point, though incapable of being drawn by any human agency, has an imperishable value, my picture has its own for mankind to live.

Benoit Mandelbrot can be considered the Euclid of fractal geometry. He has collected the observations of mathematicians concerned with monsters, or objects not definable by euclidean geometry. By combining the work of these mathematicians with his own insight, he has created a geometry of nature that thrives on asymmetry and roughness. Mandelbrot has said that mountains are not cones, and clouds are not spheres.

In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.

As to writing another book on geometry [to replace Euclid] the middle ages would have as soon thought of composing another New Testament.

The once-surprising existence of non-Euclidean models of Euclid's first four axioms can be seen as a sort of mathematical joke.

Euclid aloneHas looked on Beauty bare. Fortunate theyWho, though once only and then but far away,Have heard her massive sandal set on stone.

In other words, to put it into Euclid, or old-fashioned plane geometry, a straight line is not the shortest distance between two points.

APODICTICAL  (APODI'CTICAL)   adj.[from    evident truth; demonstration.]Demonstrative; evident beyond contradiction. Holding an apodictical knowledge, and an assured knowledge of it; verily, to persuade their apprehensions otherwise, were to make Euclid believe, that there were more than one centre in

it was not a] circle—just a concrete platform with a pay phone and a sign that read EUCLID CIRCLE. I thought Euclid would have been mad. "That's so typical of your attitude," Svetlana said. "You always think everyone is angry. Try to have some perspective. It's over two thousand years after his death, he's in Boston for the first time, they've named something after him—why should his first reaction be to get pissed off?

While Euclid himself may not have been the greatest mathematician who ever lived, he was certainly the greatest teacher of mathematics.

Euclid discovered that perfect numbers are always the multiple of two numbers, one of which is a power of 2 and the other being the next power of 2 minus 1.

It was in Alexandria that the circumference of the earth was first measured, the sun fixed at the center of the solar system, the workings of the brain and the pulse illuminated, the foundations of anatomy and physiology established, the definitive editions of Homer produced. It was in Alexandria that Euclid had codified geometry.

The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry.

1. An 'unit' is that by virtue of which each of the things that exist is called one. 2. A 'number' is a multiple composed of units.

A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.

He thought that when he had healed sufficiently, and withdrawn from the capital, he might write the magus a letter and open a correspondence on Euclid, or Thales, or the new idea from the north, that the sun and not the Earth might be the centre of the universe.

At the age of eleven, I began Euclid, with my brother as my tutor. ... I had not imagined that there was anything so delicious in the world. After I had learned the fifth proposition, my brother told me that it was generally considered difficult, but I had found no difficulty whatsoever. This was the first time it had dawned on me that I might have some intelligence.

At the Stourbridge Fair in 1663, at age twenty, he purchased a book on astrology, "out of a curiosity to see what there was in it." He read it until he came to an illustration which he could not understand, because he was ignorant of trigonometry. So he purchased a book on trigonometry but soon found himself unable to follow the geometrical arguments. So he found a copy of Euclid's Elements of Geometry, and began to read. Two years later he invented the differential calculus.

The proof is by reductio ad absurdum, and reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons5. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

It seems that mathematical ideas are arranged somehow in strata, the ideas in each stratum being linked by a complex of relations both among themselves and with those above and below. The lower the stratum, the deeper (and in general more difficult) the idea. Thus the idea of an 'irrational' is deeper than that of an integer; and Pythagoras's theorem is, for that reason, deeper than Euclid's.

Now we can see what makes mathematics unique. Only in mathematics is there no significant correction—only extension. Once the Greeks had developed the deductive method, they were correct in what they did, correct for all time. Euclid was incomplete and his work has been extended enormously, but it has not had to be corrected. His theorems are, every one of them, valid to this day.

Mother Nature did not attend high school geometry courses or read the books of Euclid of Alexandria. Her geometry is jagged, but with a logic of its own and one that is easy to understand.

Spinoza is not to be read, he is to be studied; you must approach him as you would approach Euclid, recognizing that in these brief two hundred pages a man has written down his lifetime's thought with stoic sculptury of everything superfluous.

If you have ever studied geometry, you remember that by a course of reasoning Euclid proves that all the angles in a triangle are equal to the two right angles. Euclid has shown how to work it out. Now, if you undertake to disprove that proposition, and to show that it is erroneus, would you prove it to be false by calling Euclid a liar?