Top 131 Pythagorean Theorem Quotes & Sayings - Page 2

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.

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.

It is impossible to decide whether a particular detail of the Pythagorean universe was the work of the master, or filled in by a pupil a remark which equally applies to Leonardo or Michelangelo . But there can be no doubt that the basic features were conceived by a single mind; that Pythagoras of Samos was both the founder of a new religious philosophy, and the founder of Science, as the word is understood today.

MacPherson told me that my theorem can be viewed as blah blah blah Grothendieck blah blah blah, which makes it much more respectable.

The "seriousness" of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.

Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure.

Error is multiform (for evil is a form of the unlimited, as in the old Pythagorean imagery, and good of the limited), whereas success is possible in one way only (which is why it is easy to fail and difficult to succeed - easy to miss the target and difficult to hit it); so this is another reason why excess and deficiency are a mark of vice, and observance of the mean a mark of virtue: Goodness is simple, badness is manifold.

The missing piece in his stomach hurt so much-and eventually he stopped thinking about the Theorem and wondered only how something that isn't there can hurt you.

Carnal embrace is sexual congress, which is the insertion of the male genital organ into the female genital organ for purposes of procreation and pleasure. Fermat’s last theorem, by contrast, asserts that when x, y and z are whole numbers each raised to power of n, the sum of the first two can never equal the third when n is greater than 2.

I took a break from acting for four years to get a degree in mathematics at UCLA, and during that time I had the rare opportunity to actually do research as an undergraduate. And myself and two other people co-authored a new theorem: Percolation and Gibbs States Multiplicity for Ferromagnetic Ashkin-Teller Models on Two Dimensions, or Z2.

Surely in much talk there cannot choose but be much vanity. Loquacity is the fistula of the mind,--ever-running and almost incurable, let every man, therefore, be a Phocion or Pythagorean, to speak briefly to the point or not at all; let him labor like them of Crete, to show more wit in his discourse than words, and not to pour out of his mouth a flood of the one, when he can hardly wring out of his brains a drop of the other.

No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.

One way of looking at Impossibility Theorem is that we proposed some criteria for what a good system should be: what is it you want from a voting system, and impose some conditions. And then ask: can you have a voting system that guarantees that?

To many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples.

... the word "theory" ... was originally an Orphic word, which Cornford interprets as "passionate sympathetic contemplation" ... For Pythagoras, the "passionate sympathetic contemplation" was intellectual, and issued in mathematical knowledge ... To those who have reluctantly learnt a little mathematics in school this may seem strange; but to those who have experienced the intoxicating delight of sudden understanding that mathematics gives, from time to time, to those who love it, the Pythagorean view will seem completely natural.

What we do may be small, but it has a certain character of permanence; and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men.

Combinatorial analysis, in the trivial sense of manipulating binomial and multinomial coefficients, and formally expanding powers of infinite series by applications ad libitum and ad nauseamque of the multinomial theorem, represented the best that academic mathematics could do in the Germany of the late 18th century.

In a world in which the price of calculation continues to decrease rapidly, but the price of theorem proving continues to hold steady or increase, elementary economics indicates that we ought to spend a larger and larger fraction of our time on calculation.

There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.

Science is the one culture that's truly global - protons, proteins and Pythagoras's Theorem are the same from China to Peru. It should transcend all barriers of nationality. It should straddle all faiths, too.

The story does what no theorem can quite do. It may not be "like real life" in the superficial sense: but it sets before us an image of what reality may well be like at some more central region.

For what is important when we give children a theorem to use is not that they should memorize it. What matters most is that by growing up with a few very powerful theorems one comes to appreciate how certain ideas can be used as tools to think with over a lifetime. One learns to enjoy and to respect the power of powerful ideas. One learns that the most powerful idea of all is the idea of powerful ideas.

Poetry is a theorem of a yellow-silk handkerchief knotted with riddles, sealed in a balloon tied to the tail of a kite flying in a white wind against a blue sky in spring.

A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution.

The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules.

All I remember about the examination is that there was a question on Sturm's theorem about equations, which I could not do then and cannot do now.

[Barack] Obama still is in campaign mode. The Limbaugh Theorem explains it. We've had eight years of Obama and he still isn't being held accountable for the horrible policies that he has implemented because he continues to portray himself as not attached to them.

Humanism . . . is not a single hypothesis or theorem, and it dwells on no new facts. It is rather a slow shifting in the philosophic perspective, making things appear as from a new centre of interest or point of sight.

Fourier's theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics.

I think mathematics is a vast territory. The outskirts of mathematics are the outskirts of mathematical civilization. There are certain subjects that people learn about and gather together. Then there is a sort of inevitable development in those fields. You get to the point where a certain theorem is bound to be proved, independent of any particular individual, because it is just in the path of development.

The Limbaugh Theorem is the way Obama gets away with no accountability for anything he's done is he never was perceived as governing. He was always as an outsider campaigning all the time against powerful forces trying to stop whatever it was he wanted to do.

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.

Diatonic, he heard the word in his head. Chromatic, pentatonic, hexatonic, heptatonic, octatonic, each iteration of the scale opening innumerable possibilities for harmony. He thought about the Pythagorean major third, the Didymus comma, the way the intervals sound out of tune rather than as though they were different notes. This, he thought, was where his brilliance at mathematics bled into his love of music; music was the realm in which his mathematical brain danced.

Fourier's theorem has all the simplicity and yet more power than other familiar explanations in science. Stated simply, any complex pattern, whether in time or space, can be described as a series of overlapping sine waves of multiple frequencies and various amplitudes.

I just enjoy calculating, and it's an instrument I know how to play. It's almost an athletic performance, in a way. I was just watching the Olympics, and that's how I feel when proving a theorem.

Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. Fermat's Last Theorem is the most beautiful example of this.

One would normally define a "religion" as a system of ideas that contain statements that cannot be logically or observationally demonstrated... Gödels theorem not only demonstrates that meathematics is a religion, but shows that mathematics is the only religion that proves itself to be one!

This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.

I think it is said that Gauss had ten different proofs for the law of quadratic reciprocity. Any good theorem should have several proofs, the more the better. For two reasons: usually, different proofs have different strengths and weaknesses, and they generalise in different directions - they are not just repetitions of each other.

For me, science is just a bunch of tools - it's like playing the violin. I just enjoy calculating, and it's an instrument I know how to play. It's almost an athletic performance, in a way. I was just watching the Olympics, and that's how I feel when proving a theorem.

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.

My favourite fellow of the Royal Society is the Reverend Thomas Bayes, an obscure 18th-century Kent clergyman and a brilliant mathematician who devised a complex equation known as the Bayes theorem, which can be used to work out probability distributions. It had no practical application in his lifetime, but today, thanks to computers, is routinely used in the modelling of climate change, astrophysics and stock-market analysis.

I have a basic theorem as to how I do my jokes. Growing up, I knew when to cross the line and when not to cross the line. It's the same with my comedy. I know what my audience will take and how much they won't take. I can't give you a formula for it. It's my own personal formula inside my head. Somebody else's might be different.

Any effect, constant, theorem or equation named after Professor X was first discovered by Professor Y , for some value of Y not equal to X.

The primes are the raw material out of which we have to build arithmetic, and Euclid's theorem assures us that we have plenty of material for the task.

If true, the Pythagorean principles as to abstain from flesh, foster innocence; if ill-founded they at least teach us frugality, and what loss have you in losing your cruelty? It merely deprives you of the food of lions and vultures...let us ask what is best - not what is customary. Let us love temperance - let us be just - let us refrain from bloodshed.

A mathematician experiments, amasses information, makes a conjecture, finds out that it does not work, gets confused and then tries to recover. A good mathematician eventually does so - and proves a theorem.

The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument.

I loved doing problems in school. I'd take them home and make up new ones of my own. But the best problem I ever found, I found in my local public library. I was just browsing through the section of math books and I found this one book, which was all about one particular problem - Fermat's Last Theorem.

Words are the children of reason and, therefore, can't explain it. They really can't translate feeling because they're not part of it. That's why it bugs me when people try to analyze jazz as an intellectual theorem. It's not. It's feeling.

Toward the end of his life, Gödel feared that he was being poisoned, and he starved himself to death. His theorem is one of the most extraordinary results in mathematics, or in any intellectual field in this century. If ever potential mental instability is detectable by genetic analysis, an embryo of someone with Kurt Gödel's gifts might be aborted.

I think I have met nearly all the Laureates in Economics. Among the few I haven't met, I suppose I'd most like to meet Ronald Coase because of his legendary power to persuade his colleagues of the validity of the Coase Theorem.

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.

There is nothing that has caused me to meditate more on Plato's secrecy and sphinx-like nature, than the happily preserved petit fait that under the pillow of his death-bed there was found no 'Bible,' nor anything Egyptian, Pythagorean, or Platonic - but a book of Aristophanes. How could even Plato have endured life - a Greek life which he repudiated - without an Aristophanes!

There is a theorem that colloquially translates, You cannot comb the hair on a bowling ball. ... Clearly, none of these mathematicians had Afros, because to comb an Afro is to pick it straight away from the scalp. If bowling balls had Afros, then yes, they could be combed without violation of mathematical theorems.

The Limbaugh Theorem was not about me giving me credit for something. It was simply sharing with you when the light went off.

Those who have more power are liable to sin more; no theorem in geometry is more certain than this.

Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they?

The proof of Fermat's Last Theorem underscores how stable mathematics is through the centuries - how mathematics is one of humanity's long continuous conversations with itself.

Human rights are an aspect of natural law, a consequence of the way the universe works, as solid and as real as photons or the concept of pi. The idea of self- ownership is the equivalent of Pythagoras' theorem, of evolution by natural selection, of general relativity, and of quantum theory. Before humankind discovered any of these, it suffered, to varying degrees, in misery and ignorance.