Pythagorean Theorem Quotes

Rachel bit her lip. "I hope you're right. I'm a little worried. What if someone asks what's on the next math test and I start spouting a prophecy in the middle of geometry class? The Pythagorean theorem shall be problem two...Gods, that would be embarrassing.

You forget all of it anyway. First, you forget everything you learned-the dates of the Hay-Herran Treaty and Pythagorean Theorem. You especially forget everything you didn't really learn, but just memorized the night before. You forget the names of all but one or two of your teachers, and eventually you'll forget those, too. You forget your junior class schedule and where you used to sit and your best friend's home phone number and the lyrics to that song you must have played a million times. For me, it was something by Simon & Garfunkel. Who knows what it will be for you? And eventually, but slowly, oh so slowly, you forget your humiliations-even the ones that seemed indelible just fade away. You forget who was cool and who was not, who was pretty, smart, athletic, and not. Who went to a good college. Who threw the best parties Who could get you pot. You forget all of them. Even the ones you said you loved, and even the ones you actually did. They're the last to go. And then once you've forgotten enough, you love someone else.

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.

Do people believe in human rights because such rights actually exist, like mathematical truths, sitting on a cosmic shelf next to the Pythagorean theorem just waiting to be discovered by Platonic reasoners? Or do people feel revulsion and sympathy when they read accounts of torture, and then invent a story about universal rights to help justify their feelings?

Thus the thought, for example, which we expressed in the Pythagorean theorem is timelessly true, true independently of whether anyone takes it to be true. It needs no bearer. It is not true for the first time when it is discovered, but is like a planet which, already before anyone has seen it, has been in interaction with other planets.

I began to study trigonometry. There was solace in its strange formulas and equations. I was drawn to the Pythagorean theorem and its promise of a universal—the ability to predict the nature of any three points containing a right angle, anywhere, always. What I knew of physics I had learned in the junkyard, where the physical world often seemed unstable, capricious. But here was a principle through which the dimensions of life could be defined, captured. Perhaps reality was not wholly volatile. Perhaps it could be explained, predicted. Perhaps it could be made to make sense.

Uh-oh," Moni sang, and nodded her head in Chantal's direction. "I think someone's a wee bit upset with us." She turned and walked a few steps backward. "Careful," I said. "We're not out of range." "Have no fear, Super Brain is here." Moni whipped out her calculator, holding it up like a shield. "What are you going to do, daze her with denominators?" "Maybe. But first I'm going to pummel her with my Pythagorean theorem.

There is much creativity underlying math and science problem solving. Many people think that there’s only one way to do a problem, but there are often a number of different solutions, if you have the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean theorem.

One Washington axiom, proved more times than the Pythagorean theorem, states that in the presence of oxygen, one loud fart with an obvious culprit will cover many small emissions in the same room, provided they are nearly simultaneous.

I smiled. Mom laughed, shaking her head. “That’s the punchline? Why is that even funny?” “It’s the Pythagorean theorem,” said Lauren. “It’s a math formula for . . . something.” “Right triangles,” I said, and looked pointedly at Margaret. “I told you I’d already done geometry.

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.

I don’t see him much.” “It happens, baby. You forget all of it anyway. First, you forget everything you learned – the dates of the Hay-Herran Treaty and the Pythagorean theorem. You especially forget everything you didn’t really learn, just memorised the night before. You forget the names of all but one or two of your teachers, and eventually you’ll forget those, too. You forget your junior year class schedule and where you used to sit and your best friend’s home phone number and the lyrics to that song you must have played a million times. For me, it was something by Simon & Garfunkel. Who knows what it will be for you? And eventually, but slowly, oh so slowly, you forget your humiliations – even the ones that seemed indelible just fade away. You forget who was cool and who was not, who was pretty, smart, athletic, and not. Who went to a good college. Who threw the best parties. Who could get you pot. You forget all of them. Even the ones you said you loved, and the ones you actually did. They’re the last to go. And then once you’ve forgotten enough, you love someone else.

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.

Or think of the tale of the blind men who encounter an elephant for the first time. One wise man, touching the ear of the elephant, declares the elephant is flat and two-dimensional like a fan. Another wise man touches the tail and assumes the elephant is like rope or a one-dimensional string. Another, touching a leg, concludes the elephant is a three-dimensional drum or a cylinder. But actually, if we step back and rise into the third dimension, we can see the elephant as a three-dimensional animal. In the same way, the five different string theories are like the ear, tail, and leg, but we still have yet to reveal the full elephant, M-theory. Holographic Universe As we mentioned, with time new layers have been uncovered in string theory. Soon after M-theory was proposed in 1995, another astonishing discovery was made by Juan Maldacena in 1997. He jolted the entire physics community by showing something that was once considered impossible: that a supersymmetric Yang-Mills theory, which describes the behavior of subatomic particles in four dimensions, was dual, or mathematically equivalent, to a certain string theory in ten dimensions. This sent the physics world into a tizzy. By 2015, there were ten thousand papers that referred to this paper, making it by far the most influential paper in high-energy physics. (Symmetry and duality are related but different. Symmetry arises when we rearrange the components of a single equation and it remains the same. Duality arises when we show that two entirely different theories are actually mathematically equivalent. Remarkably, string theory has both of these highly nontrivial features.) As we saw, Maxwell’s equations have a duality between electric and magnetic fields—that is, the equations remain the same if we reverse the two fields, turning electric fields into magnetic fields. (We can see this mathematically, because the EM equations often contain terms like E2 + B2, which remain the same when we rotate the two fields into each other, like in the Pythagorean theorem). Similarly, there are five distinct string theories in ten dimensions, which can be proven to be dual to each other, so they are really a single eleven-dimensional M-theory in disguise. So remarkably, duality shows that two different theories are actually two aspects of the same theory. Maldacena, however, showed that there was yet another duality between strings in ten dimensions and Yang-Mills theory in four dimensions. This was a totally unexpected development but one that has profound implications. It meant that there were deep, unexpected connections between the gravitational force and the nuclear force defined in totally different dimensions. Usually, dualities can be found between strings in the same dimension. By rearranging the terms describing those strings, for example, we can often change one string theory into another. This creates a web of dualities between different string theories, all defined in the same dimension. But a duality between two objects defined in different dimensions was unheard of.

In any event, Socrates’ proof of prenatal immortality is that one of Meno’s uneducated slave boys actually comes up with the Pythagorean theorem without ever having studied geometry! Therefore, he must be remembering it. You recall that theorem: in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Huh? We can barely remember that from tenth grade, let alone from before we were born.

It seemed clear to Wilson that what the rationalists were really doing was generating clever justifications for moral intuitions that were best explained by evolution. Do people believe in human rights because such rights actually exist, like mathematical truths, sitting on a cosmic shelf next to the Pythagorean theorem just waiting to be discovered by Platonic reasoners? Or do people feel revulsion and sympathy when they read accounts of torture, and then invent a story about universal rights to help justify their feelings?

I was a capable boy, intelligent, well-liked, but powerfully afraid. And I felt, vaguely, wordlessly, that for a child to be marked off for such a life, to be forced to live in fear was a great injustice. And what was the source of this fear? What was hiding behind the smoke screen of streets and schools? And what did it mean that number 2 pencils, conjugations without context, Pythagorean theorems, handshakes, and head nods were the difference between life and death, were the curtains drawing down between the world and me?

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.

It is necessary to emphasize this. We begin with a vague concept in our minds, then we create various sets of postulates, and gradually we settle down to one particular set. In the rigorous postulational approach the original concept is now replaced by what the postulates define. This makes further evolution of the concept rather difficult and as a result tends to slow down the evolution of mathematics. It is not that the postulation approach is wrong, only that its arbitrariness should be clearly recognized, and we should be prepared to change postulates when the need becomes apparent. The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way.

A year after I watched the boy with the small eyes pull out a gun, my father beat me for letting another boy steal from me. Two years later, he beat me for threatening my ninth-grade teacher. Not being violent enough could cost me my body. Being too violent could cost me my body. We could not get out. I was a capable boy, intelligent, well-liked, but powerfully afraid. And I felt, vaguely, wordlessly, that for a child to be marked off for such a life, to be forced to live in fear was a great injustice. And what was the source of this fear? What was hiding behind the smoke screen of streets and schools? And what did it mean that number 2 pencils, conjugations without context, Pythagorean theorems, handshakes, and head nods were the difference between life and death, were the curtains drawing down between the world and me?

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.

Gayatri Mantra: 14 words Pythagorean Theorem: 24 words Archimedes’ Principle: 67 words The Ten Commandments: 179 words Jawaharlal Nehru’s inaugural speech: 1,094 words Your recommendations to reduce red tape: 22,913 words

His sense of humor was permanently replaced by the Pythagorean Theorem.

Among mankind’s greatest faults is his a) kindness, b) generosity, c) fortitude, d) contentment, e) vanity. That was debatable. But the Pythagorean theorem was not, and if the civilian Uri was one side and the soldier Uri was the other, the true him was the hypotenuse, slanted opposite, the squared sum of both.

There was a mailman I loved as a little girl. He would stop at the communal mailbox On the street In the center of the apartment complex And begin sorting mail away Into 150 different little boxes We lived in 1202 I would rush from my house To greet the mailman And he would talk to me as he worked Filing away bills and cards and coupons He would ask me questions Quiz me And give me a piece of Bazooka gum For every question I got right I would spin around and crush my sneakers rocking up and down on my toes I would curl one piece of hair Around my finger while I thought of the answers I would slide my tongue between my teeth and the windows where they were missing And between every mailbox The mailman would look at me and smile He’d pat me on the cheek And tell me That I was as smart as he was. As smart as any man. And I believed him. Because why wouldn’t I? I was 8. I knew that George Bush would win the election. I knew the Pythagorean theorem. I read 300 books from the public library And I could draw every animal by memory. I liked him ’cause he gave me chewing gum And talked to me in his low voice Calm and soft Not the shrill, high-pitched voice They would use on my baby brother. One day the mailman didn’t show up for work I ran out and stopped in my tracks There was a different man there I asked if my friend was sick The imposter ignored me The new mailman showed up a few days in a row The kids in the neighborhood said The old one had a heart attack in a bowl of spaghetti And died with noodles up his nose I cried One Wednesday I ran out to the new mailman And asked if he had any gum He told me to stay away Because he didn’t want to get in trouble like Charlie I didn’t know my friend’s name was Charlie And I didn’t know how I could have gotten him in trouble So I asked my mom How you could give someone a heart attack And she rubbed her head and stretched her feet across the couch and said, “It feels like you’re gonna give me one right now.” I didn’t want my mom to die too. So I hid in my room And I cried Because I was 8 And a murderer.

113. The theorems of philosophy are to be enjoyed as much as possible, as if they were ambrosia and nectar. For the resultant pleasure is genuine, incorruptible and divine. They are also capable of producing magnanimity, and though they cannot make us eternal, yet they enable us to obtain a scientific knowledge of eternal natures.

I’m considering the biological applications of the Pythagorean theorem,

The misery began when I moved beyond the Pythagorean theorem to sine, cosine and tangent. I couldn’t grasp such abstractions. I could feel the logic in them, could sense their power to bestow order and symmetry, but I couldn’t unlock it. They kept their secrets, becoming a kind of gateway beyond which I believed there was a world of law and reason. But I could not pass through the gate.

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.

Long before Alexander, the Babylonians had discovered how to use complex fractions, quadratic equations, and what would come to be known as the Pythagorean theorem.

What if somebody asks what’s on the next math test and I start spouting a prophecy in the middle of geometry class? The Pythagorean theorem shall be problem two…. Gods, that would be embarrassing.

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.

The full treatment of the formal theory of how to make decisions in risky situations—called expected utility theory—was published in 1944 by the mathematician John von Neumann and the economist Oskar Morgenstern. John von Neumann, one of the greatest mathematicians of the twentieth century, was a contemporary of Albert Einstein at the Institute of Advanced Study at Princeton University, and during World War II he decided to devote himself to practical problems. The result was the 600-plus-page opus The Theory of Games and Economic Behavior, in which the development of expected utility theory was just a sideline. The way that von Neumann and Morgenstern created the theory was to begin by writing down a series of axioms of rational choice. They then derived how someone who wanted to follow these axioms would behave. The axioms are mostly uncontroversial notions such as transitivity, a technical term that says if you prefer A over B and B over C then you must prefer A over C. Remarkably, von Neumann and Morgenstern proved that if you want to satisfy these axioms (and you do), then you must make decisions according to their theory. The argument is completely convincing. If I had an important decision to make—whether to refinance my mortgage or invest in a new business—I would aim to make the decision in accordance with expected utility theory, just as I would use the Pythagorean theorem to estimate the altitude of our railroad triangle. Expected utility is the right way to make decisions.

In fact, so detailed was his interest in mathematics, and so acute his understanding, that he had recently written an original proof of the Pythagorean Theorem during a free moment at the capital. The New England Journal of Education had published the proof just the month before, transparently astonished that a member of congress had written it. Despite Garfield's deep admiration for mathematics and the arts, however, he believed that it was science, above all other disciplines that had achieved the greatest good.

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.

Maybe ET will use math to get our attention—a string of prime numbers, perhaps, or the apparently omnipresent, omni-important Pythagorean theorem. High school trig teachers should rebrand it the alien communication formula. That would’ve kept you from daydreaming in class, right?

A meme is simply a unit of memorable cultural information. It can be as small as a tune or a metaphor, as big as a philosophy or religious concept. Hell is a meme; so are the Pythagorean theorem, A Hard Day’s Night, the wheel, Hamlet, pragmatism, harmony, “Where’s the beef?,” and of course the notion of the meme itself.

I began to study trigonometry. There was solace in its strange formulas and equations. I was drawn to the Pythagorean theorem and its promise of a universal--the ability to predict the nature of any three points containing a right angle, anywhere, always. What I knew of physics I had learned in the junkyard, where the physical world often seemed unstable, capricious. But here was a principle through which the dimensions of life could be defined, captured. Perhaps reality was not wholly volatile. Perhaps it could be explained, predicted. Perhaps it could be made to make sense.