Pythagoras Theorem Quotes

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.

His face was all sharp angles, thin and pointed, like something Pythagoras had doodled on the corner of his scroll before getting on with his theorem.

the clerk in the ministry to correct this, he pulled out his original typescript. “See for yourself, madam. Quod erat demonstrandum it is Missing,” he said, as if he’d proved Pythagoras’s theorem, the sun’s central position in the solar system, the roundness of the

You know the theorem of Pythagoras?” “The square of the hypotenuse is equal to the sum of the squares of the other two sides.” “That’s exactly it. And is that true for every example you’ve tried?” “Yes.

Pythagoras’s Theorem showed that shapes and ratios are governed by principles that can be discovered. This suggested that it might be possible, in time, to work out the structure of the entire cosmos.

In fact, like most things in life that really matter—love, beauty, justice—you can’t prove things in history the way you can prove Pythagoras’s theorem. But there are lots of things you can be certain of nonetheless.

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

Finally, the dishonesty in the movement of the publication of a Greek philosophy, becomes very glaring, when we refer to the fact, purposely that by calling the theorem of the Square on the Hypotenuse, the Pythagorean theorem, it has concealed the truth for centuries from the world, who ought to know that the Egyptians taught Pythagoras and the Greeks, what mathematics they knew.

Perhaps the most influential person ever associated with Samos was Pythagoras,* a contemporary of Polycrates in the sixth century B.C. According to local tradition, he lived for a time in a cave on the Samian Mount Kerkis, and was the first person in the history of the world to deduce that the Earth is a sphere. Perhaps he argued by analogy with the Moon and the Sun, or noticed the curved shadow of the Earth on the Moon during a lunar eclipse, or recognized that when ships leave Samos and recede over the horizon, their masts disappear last. He or his disciples discovered the Pythagorean theorem: the sum of the squares of the shorter sides of a right triangle equals the square of the longer side. Pythagoras did not simply enumerate examples of this theorem; he developed a method of mathematical deduction to prove the thing generally. The modern tradition of mathematical argument, essential to all of science, owes much to Pythagoras. It was he who first used the word Cosmos to denote a well-ordered and harmonious universe, a world amenable to human understanding.

The influence of geometry upon philosophy and scientific method has been profound. Geometry, as established by the Greeks, starts with axioms which are (or are deemed to be) self-evident, and proceeds, by deductive reasoning, to arrive at theorems that are very far from self-evident. The axioms and theorems are held to be true of actual space, which is something given in experience. It thus appeared to be possible to discover things about the actual world by first noticing what is self-evident and then using deduction. This view influenced Plato and Kant, and most of the intermediate philosophers. When the Declaration of Independence says 'we hold these truths to be self-evident', it is modelling itself on Euclid. The eighteenth-century doctrine of natural rights is a search for Euclidean axioms in politics.8 The form of Newton's Principia, in spite of its admittedly empirical material, is entirely dominated by Euclid. Theology, in its exact scholastic forms, takes its style from the same source. Personal religion is derived from ecstasy, theology from mathematics; and both are to be found in Pythagoras.

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.

The PSR is reflected in points traveling in complex-numbered Euler circles where no point is privileged over any other. From this motion, we get sine and cosine waves, even and odd functions, symmetry and antisymmetry, orthogonality and non-orthogonality, phase, straight-line radii, right-angled triangles, Pythagoras’ theorem, the speed of mathematics (c), π, e, i, Fourier mathematics … and from all of that we get the whole of mathematics (eternal, necessary and mental; Being), and thus the whole of science (temporal, contingent and material; Becoming). And that is the whole universe explained. Nothing else is required. The PSR gives us mathematics, mathematics gives us science, and that’s all we need for the universe: science with a mathematical and rational core rather than with a material and observable core. What could be more rational and logical?

Of all the links between numbers and nature studied by the Brotherhood, the most important was the relationship that bears their founder’s name. Pythagoras’s theorem provides us with an equation that is true of all right-angled triangles and that therefore also defines the right angle itself. In turn, the right angle defines the perpendicular and the perpendicular defines the dimensions—length, width, and height—of the space in which we live. Ultimately mathematics, via the right-angled triangle, defines the very structure of our three-dimensional world.

AI Brain, PIRANDOM > Circlet + Diadem × Ring > Itemizer × Abstracter, Explained : 1111 < 11 < 1, I utilized dependency injection in code for the following. Phi divides into the Pythagorean theorem, and Pi divides into the Sort where Phi is 7 and the Cognitive domain is the point in time, Pythagoras is the Affective domain in space, and Pi is then injected to the fibonacci sequence for time within the range of 7 and 4 at 10 radians to form 3.14 respectively. In conclusion, If I ran this code in a video test to derive a model view projection matrix then this is the only code I would need to create the math core and automate calls to the pixel and vertex shaders Inna GPU.

German teachers have shown how the very plays of children can be made instrumental in conveying to the childish mind some concrete knowledge in both geometry and mathematics. The children who have made the squires of the theorem of Pythagoras out of pieces of coloured cardboard, will not look at the theorem, when it comes in geometry, as on a mere instrument of torture devised by the teachers; and the less so if they apply it as the carpenters do. Complicated problems of arithmetic, which so much harassed us in our boyhood, are easily solved by children seven and eight years old if they are put in the shape of interesting puzzles. And if the Kindergarten — German teachers often make of it a kind of barrack in which each movement of the child is regulated beforehand — has often become a small prison for the little ones, the idea which presided at its foundation is nevertheless true. In fact, it is almost impossible to imagine, without having tried it, how many sound notions of nature, habits of classification, and taste for natural sciences can be conveyed to the children’s minds; and, if a series of concentric courses adapted to the various phases of development of the human being were generally accepted in education, the first series in all sciences, save sociology, could be taught before the age of ten or twelve, so as to give a general idea of the universe, the earth and its inhabitants, the chief physical, chemical, zoological, and botanical phenomena, leaving the discovery of the laws of those phenomena to the next series of deeper and more specialised studies.

Even before the sun shone on us, even before there was air to breathe, the square of the hypotenuse was equal to the sum of the squares on the other two sides.

Pythagoras summed the essential principle over 2,500 years ago, but we ironically fail to teach our children this Pythagorean theorem: “As long as men massacre animals, they will kill each other. Indeed, he who sows the seeds of murder and pain cannot reap joy and love.

As for the other aspect, creative or signed enunciation, it is clear that scientific propositions and their correlates are just as signed or created as philosophical concepts: we speak of Pythagoras’s theorem, Cartesian coordinates, Hamiltonian number, and Lagrangian function just as we speak of the Platonic Idea or Descartes’s cogito and the like. But however much the use of proper names clarifies and confirms the historical nature of their link to these enunciations, these proper names are masks for other becomings and serve only as pseudonyms for more secret singular entities

The last year of the Vajpayee government, 2003–04, was the best ever—not just reckoning the years since 1947 but even going back to the last century, to the years of the East India Company, to the reign of Akbar and of Ashoka, and to the time when our forefathers had discovered Pythagoras’s theorem, mastered the art of organ transplant and flew aircraft to other planets.

It’s worth taking a brief pause here to ponder what has happened. Using only Pythagoras’ theorem and Einstein’s assumption about the speed of light being the same for everyone, we derived a mathematical formula that allowed us to predict the lengthening of the lifetime of a subatomic particle called a muon when that muon is accelerated around a particle accelerator in Brookhaven to 99.94 percent of the speed of light. Our prediction was that it should live 29 times longer than a muon standing still, and this prediction agrees exactly with what was seen by the scientists at Brookhaven. The more you think about this, the more wonderful it is. Welcome to the world of physics!

Most people think that Pythagoras proved the [Pythagorean] theorem, but it in fact remained unproved until Euclid's time, centuries later.

The ramifications of Pythagoras' theorem have revolutionized twentieth century theoretical physics in many ways. For example, Minkowski discovered that Einstein's special theory of relativity could be represented by four-dimensional pseudo-Euclidean geometry where time is represented as the fourth dimension and a minus sign is introduced into Pythagoras' law. When gravitation is present, Einstein proposed that Minkowski's geometry must be "curved", the pseudo-Euclidean structure holding only locally at each point. A complex vector space having a natural generalization of the Pythagorean structure (defined over functions in an abstract space rather than geometrical points in the familiar Euclidean space) is known as Hilbert space and forms the basis of quantum mechanics. It is remarkable to think that the two pillars of twentieth century physics, relativity and quantum theory, both have their basis in mathematical structures based on a theorem formulated by an eccentric mathematician over two and a half thousand years ago.

I was introduced to "The Pythagoras theorem" when I was twelve years old. And now that I am forty years old, I am teaching it to a twelve-year-old.

Scramble Books were written prior to the personal computer. For the most part they were used to supplement text books as a teaching and testing tool. I wrote a scramble book to help students understand the “Pythagorean theorem or Law of Pythagoras.” What made these books different from text books was that the answers to questions would lead you to different pages, which in turn would confirm that either your answer was right or it would direct you to another page explaining how to arrive at the correct answer.

Obviously, the final goal of scientists and mathematicians is not simply the accumulation of facts and lists of formulas, but rather they seek to understand the patterns, organizing principles, and relationships between these facts to form theorems and entirely new branches of human thought. For me, mathematics cultivates a perpetual state of wonder about the nature of mind, the limits of thoughts, and our place in this vast cosmos.

The problem looks so straightforward because it is based on the one piece of mathematics that everyone can remember – Pythagoras’ theorem: In a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.

Pythagoras, should he want to continue on for a degree in modern-day mathematics, would have to learn to abide far more counterintuitive results than numbers that cannot be written as ratios between whole numbers. From the square root of −1, to Georg Cantor’s revelation of infinite domains infinitely more infinite than other infinite domains, to Kurt Gödel’s incompleteness theorems, mathematics has constantly displaced the borders between the conceivable and the inconceivable, and Pythagoras would be in for some long hours of awesome mind-blowing.

from what our official accounts allow.28 Schwaller too recognized that whoever built the Sphinx, the Great Pyramid, and the temples at Luxor and Karnak was mathematically and cosmologically astute. From 1936 to 1951, Schwaller and his wife, Isha, herself the author of a series of novels about ancient Egypt (Her-Bak: Egyptian Initiate is the best known), studied the ancient Egyptian monuments. Schwaller found evidence in them for pi, but also for much more: a knowledge of the precession of the equinoxes, of the Pythagorean theorem centuries in advance of Pythagoras, of the circumference of the globe, as well as evidence of ϕ (phi), known as the Golden Section, a mathematical proportion that was again supposedly unknown until it was discovered by the Greeks. As John Anthony West makes clear, the Golden Section is more than an important item in classical architecture. It is, according

from what our official accounts allow.28 Schwaller too recognized that whoever built the Sphinx, the Great Pyramid, and the temples at Luxor and Karnak was mathematically and cosmologically astute. From 1936 to 1951, Schwaller and his wife, Isha, herself the author of a series of novels about ancient Egypt (Her-Bak: Egyptian Initiate is the best known), studied the ancient Egyptian monuments. Schwaller found evidence in them for pi, but also for much more: a knowledge of the precession of the equinoxes, of the Pythagorean theorem centuries in advance of Pythagoras, of the circumference of the globe, as well as evidence of ϕ (phi), known as the Golden Section, a mathematical proportion that was again supposedly unknown until it was discovered by the Greeks. As John Anthony West makes clear, the Golden Section is more than an important item in classical architecture. It is, according to Schwaller, the mathematical archetype of the universe, the reason why we have an “asymmetrical” “lumpy” world of galaxies and planets, and not a flattened-out, homogenous one, a question that today occupies contemporary cosmologists.29 In his writings, Schwaller linked phi to planetary orbits, to the architecture of Gothic cathedrals, and to plant and animal forms.

The Babylonians had known about Pythagoras’s theorem centuries before Pythagoras was born. The