After the class have exhausted their energies on the theorem of the right triangle, tell them something about its discoverer – how Pythagoras, jubilant over his great accomplishment, sacrificed a hecatomb to the Muses who inspired him.
The Eudemian Summary ascribes to Thales the invention of the theorems on the equality of vertical angles, the equality of the angles at the base of an isosceles triangle, the bisection of a circle by any diameter, and the congruence of two triangles having a side and the two adjacent angles equal respectively. The last theorem he applied to the measurement of the distances of ships from the shore. Thus Thales was the first to apply theoretical geometry to practical uses.
The theorem on the sum of the three angles of a triangle, presumably known to Thales, was proved by the Pythagoreans after the manner of Euclid. They demonstrated also that the plane about a point is completely filled by six equilateral triangles, four squares, or three regular hexagons, so that it is possible to divide up a plane into figures of either kind.
We completely ignore the human value of the information. A selection of 100 letters is given a certain information value, and we do not investigate whether it makes sense in English, and, if so, whether the meaning of the sentence is of any practical importance. According to our definition, a set of 100 letters selected at random (according to the rules of Table 1.1), a sentence of 100 letters from a newspaper, a piece of Shakespeare or a theorem of Einstein are given exactly the same informational value.léon brillouin
That little monkey. The theorem was that he was too small to play in the NFLhoward cosell
A mathematician, then, will be defined in what follows as someone who has published the proof of at least one non-trivial theorem.
As a boy of six I could understand the proof of a mathematical theorem more readily than that meat had to be cut with one's knife, not one's fork.ferdinand eisenstein
A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution.richard arnold epstein
A theorem is a proposition which is a strict logical consequence of certain definitions and other propositionsAnatol Rapoport
It is not so much whether a theorem is useful that matters, but how elegant it is.stanislaw ulam
We may consequently state the fundamental theorem of Natural Selection in the form:;: The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time.ronald fisher
Professor Eddington has recently remarked that 'The law that entropy always increases the second law of thermodynamics holds, I think, the supreme position among the laws of nature'. It is not a little instructive that so similar a law [the fundamental theorem of natural selection] should hold the supreme position among the biological sciences.ronald fisher
In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.martin gardner
To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.
...a theorem of propositional logic if and only if f(p1, p2 ,..., pn) is a tautology . ... He (Emil L.Post) uses the word to discuss the adequacy of a system of functions to express all the possible truth tables (this is nowadays called truth-functional completeness). In this way he shows not only that through the connectives of Principia (? and ?) one can generate all possible truth tables but also that there are only two connectives which can, singly generate all the truth tables.
We completely ignore the human value of the information . A selection of 100 letters is given a certain information value, and we do not investigate whether it makes sense in English, and, if so, whether the meaning of the sentence is of any practical importance. According to our definition, a set of 100 letters selected at random (according to the rules of Table 1.1), a sentence of 100 letters from a newspaper, a piece of Shakespeare or a theorem of Einstein are given exactly the same informational value.
A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution.
Unfortunately for Pythagoras, his theorem led at once to the discovery of incommensurables , which appeared to disprove his whole philosophy. So long as no adequate arithmetical theory on incommensurables existed, the method of Euclid was the best that was possible in geometry. When Descartes introduced co-ordinate geometry, thereby again making arithmetic supreme, he [Descartes] assumed the possibility of a solution of the problem of incommensurables, though in his day no such solution had been found.
Of the theorems generally ascribed to the Italian school, some cannot be attributed to Pythagoras himself, nor to his earliest successors. The progress from empirical to reasoned solutions must, of necessity, have been slow. It is worth noticing that on the circle no theorem of any importance was discovered by this school.
Analysis and natural philosophy owe their most important discoveries to this fruitful means, which is called induction. Newton was indebted to it for his theorem of the binomial and the principle of universal gravity.
Bell’s theorem is the most profound discovery of science.
Physicists continue to debate whether Bell's theorem is airtight or not. However, the real question is not whether Bell can prove beyond doubt that reality is non-local, but whether the world is in fact non-local.
Let us now (at last) state the basic theorem: If God exists, then God is identical to the Universe. That is, the theorem is a statement of conditional pandeism. If God exists at all, God must be absolutely everything that exists.
A deist who believes in God that is the Universe is a pandeist, and is not only compatible with the theorem, but is now affirmed in their conditional belief as being demonstrably proven as a theorem of information theory.
Our offense is like the pythagorean theorem: There is no answer!
I confess that Fermat's theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.carl friedrich gauss
Geometry has two great treasures; one is the theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.johannes kepler
Comparatively few of the propositions and proofs in the Elements are his [Euclid's] own discoveries. In fact, the proof of the "theorem of Pythagoras" is the only one directly ascribed to him.