Geometry Math Quotes

What's your angle?" I asked, trying to sound more playful than demanding. "Isosceles," Jack quipped.

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.

Philosophy [nature] is written in that great book which ever is before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.

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.

What music is to the heart, mathematics is to the mind.

One might suppose that reality must be held to at all costs. However, though that may be the moral thing to do, it is not necessarily the most useful thing to do. The Greeks themselves chose the ideal over the real in their geometry and demonstrated very well that far more could be achieved by consideration of abstract line and form than by a study of the real lines and forms of the world; the greater understanding achieved through abstraction could be applied most usefully to the very reality that was ignored in the process of gaining knowledge.

Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to? The effect of such a production being made over something so simple is to make people doubt their own intuition. Calling into question the obvious by insisting that it be 'rigorously proved' ... is to say to a student 'Your feelings and ideas are suspect. You need to think and speak our way.

Gosta da música, que é a mesma coisa que ouvir geometria

[As a young teenager] Galois read Legendre]'s geometry from cover to cover as easily as other boys read a pirate yarn.

... I succeeded at math, at least by the usual evaluation criteria: grades. Yet while I might have earned top marks in geometry and algebra, I was merely following memorized rules, plugging in numbers and dutifully crunching out answers by rote, with no real grasp of the significance of what I was doing or its usefulness in solving real-world problems. Worse, I knew the depth of my own ignorance, and I lived in fear that my lack of comprehension would be discovered and I would be exposed as an academic fraud -- psychologists call this "imposter syndrome".

As for methods I have sought to give them all the rigour that one requires in geometry, so as never to have recourse to the reasons drawn from the generality of algebra.

What if Loves are analogous to math? First, arithmetic, then geometry and algebra, then trig and quadratics…

Maths is at only one remove from magic.

a constellation is formed by points of light that are not connected to each other by anything other than the observer

The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.

By degrees, the bitterness at my heart diffused itself to the circumference of the circle in which my life went its cheerless mechanical round.

Even as we sit, we dance – In this cosmic saga of numbers and geometric patterns, continually coming alive.

Believe me, if Archimedes ever had the grand entrance of a girl as pretty as Gloria to look forward to, he would never have spent so much time calculating the value of Pi. He would have been baking her a Pie! If Euclid had ever beheld a vision of loveliness like the one I see walking into my anti-math class, he would have forgotten all the geometry of lines and planes, and concentrated on the sweet simplicity of soft curves. If Pythagoras had ever had a girl look at him the way Gloria's eyes fix in my direction, he would have given up his calculations on the hypotenuse of right triangles and run for the hills to pick a bouquet of wildflowers.

Why did math matter so much? Some reasons were practical: More and more jobs required familiarity with probability, statistics, and geometry. The other reason was that math was not just math. Math is a language of logic. It is a disciplined, organized way of thinking. There is a right answer; there are rules that must be followed. More than any other subject, math is rigor distilled. Mastering the language of logic helps to embed higher-order habits in kids’ minds: the ability to reason, for example, to detect patterns and to make informed guesses. Those kinds of skills had rising value in a

I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my previous researches. Disgusted at my want of success, I went away to spend a few days at the seaside, and thought of entirely different things. One day, as I was walking on the cliff, the idea came to me, again with the same characteristics of conciseness, suddenness, and immediate certainty, that arithmetical transformations of indefinite ternary quadratic forms are identical with those of non-Euclidian geometry.

If our sides were unequal our angles might be unequal. Instead of its being sufficient to feel, or estimate by sight, a single angle in order to determine the form of an individual, it would be necessary to ascertain each angle by the experiment of Feeling. But life would be too short for such a tedious groping. The whole science and art of Sight Recognition would at once perish; Feeling, so far as it is an art, would not long survive; intercourse would become perilous or impossible; there would be an end to all confidence, all forethought; no one would be safe in making the most simple social arrangements; in a word, civilization would relapse into barbarism.

As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid, but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid, but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer...

In physics, theories are made of math. We don’t use math because we want to scare away those not familiar with differential geometry and graded Lie algebras; we use it because we are fools. Math keeps us honest—it prevents us from lying to ourselves and to each other. You can be wrong with math, but you can’t lie.

The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.

To a scholar, mathematics is music.

unsolicited advice to adolescent girls with crooked teeth and pink hair When your mother hits you, do not strike back. When the boys call asking your cup size, say A, hang up. When he says you gave him blue balls, say you’re welcome. When a girl with thick black curls who smells like bubble gum stops you in a stairwell to ask if you’re a boy, explain that you keep your hair short so she won’t have anything to grab when you head-butt her. Then head-butt her. When a guidance counselor teases you for handed-down jeans, do not turn red. When you have sex for the second time and there is no condom, do not convince yourself that screwing between layers of underwear will soak up the semen. When your geometry teacher posts a banner reading: “Learn math or go home and learn how to be a Momma,” do not take your first feminist stand by leaving the classroom. When the boy you have a crush on is sent to detention, go home. When your mother hits you, do not strike back. When the boy with the blue mohawk swallows your heart and opens his wrists, hide the knives, bleach the bathtub, pour out the vodka. Every time. When the skinhead girls jump you in a bathroom stall, swing, curse, kick, do not turn red. When a boy you think you love delivers the first black eye, use a screw driver, a beer bottle, your two good hands. When your father locks the door, break the window. When a college professor writes you poetry and whispers about your tight little ass, do not take it as a compliment, do not wait, call the Dean, call his wife. When a boy with good manners and a thirst for Budweiser proposes, say no. When your mother hits you, do not strike back. When the boys tell you how good you smell, do not doubt them, do not turn red. When your brother tells you he is gay, pretend you already know. When the girl on the subway curses you because your tee shirt reads: “I fucked your boyfriend,” assure her that it is not true. When your dog pees the rug, kiss her, apologize for being late. When he refuses to stay the night because you live in Jersey City, do not move. When he refuses to stay the night because you live in Harlem, do not move. When he refuses to stay the night because your air conditioner is broken, leave him. When he refuses to keep a toothbrush at your apartment, leave him. When you find the toothbrush you keep at his apartment hidden in the closet, leave him. Do not regret this. Do not turn red. When your mother hits you, do not strike back.

V geometrickém světě, jehož objev byl umožněn onou pozoruhodnou schopností proniknout skrze čtverec nakreslený v písku ke čtverci geometrickému, nalezla řecká antika místo, v němž se nachází pravda v ničím nezastřené podobě.

So the signs remain incorrect. But at least now I have a framed letter from the UK government saying that they don’t think accurate math is important and they don’t believe street signs should have to follow the laws of geometry.

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.

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.

It is to geometry that we owe in some sort the source of this discovery [of beryllium]; it is that [science] that furnished the first idea of it, and we may say that without it the knowledge of this new earth would not have been acquired for a long time, since according to the analysis of the emerald by M. Klaproth and that of the beryl by M. Bindheim one would not have thought it possible to recommence this work without the strong analogies or even almost perfect identity that Citizen Haüy found for the geometrical properties between these two stony fossils.

But by 1912, Einstein had come to appreciate that math could be a tool for discovering—and not merely describing—nature’s laws. Math was nature’s playbook. “The central idea of general relativity is that gravity arises from the curvature of spacetime,” says physicist James Hartle. “Gravity is geometry.

Ze všeho nejvíce Gausse rozčilovaly stále nové a nové pokusy různých geometrů dokázat pátý postulát. Nyní, když znal nový geometrický svět, když do něj bezpečně nahlížel, odhaloval v těchto domnělých důkazech chybu vždy hned při prvním pohledu. Jasně viděl, jak geometři tápají v tmách, jak plýtvají silami na těchto beznadějných pokusech - a pomoci jim nemohl; nesměl.

... I left Caen, where I was living, to go on a geological excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.

Euclid's Elements has been for nearly twenty-two centuries the encouragement and guide of that scientific thought which is one thing with the progress of man from a worse to a better state. The encouragement; for it contained a body of knowledge that was really known and could be relied on, and that moreover was growing in extent and application. For even at the time this book was written—shortly after the foundation of the Alexandrian Museum—Mathematics was no longer the merely ideal science of the Platonic school, but had started on her career of conquest over the whole world of Phenomena. The guide; for the aim of every scientific student of every subject was to bring his knowledge of that subject into a form as perfect as that which geometry had attained. Far up on the great mountain of Truth, which all the sciences hope to scale, the foremost of that sacred sisterhood was seen, beckoning for the rest to follow her.

On the SB5 Stanford-Binet intelligence test Isaiah’s reasoning scores were near genius levels. His abilities came naturally but were honed in his math classes. He was formally introduced to inductive reasoning in geometry, a tenth-grade subject he took in the eighth. His teacher, Mrs. Washington, was a severe woman who looked to be all gristle underneath her brightly colored pantsuits. Lavender, Kelly green, peach. She talked to the class like somebody had tricked her into it. “All

Let us wonder, Carole, at the genius of hyperbolic geometry, where the sum of the angles adds up to tales than 180 degrees Let us wonder at how the ancient Egyptians worked out how to measure an irregularly-shaped field Let us wonder how X was just a rare letter until algebra came along and made it something special that can be unraveled to reveal its inner value You see, maths is a process of discovery, Carole, it is like the exploration of space, the planets were always there, it just took us a long time to find them

Grossmann went home to think about the question. After consulting the literature, he came back to Einstein and recommended the non-Euclidean geometry that had been devised by Bernhard Riemann.11 Riemann (1826–1866) was a child prodigy who invented a perpetual calendar at age 14 as a gift for his parents and went on to study in the great math center of Göttingen, Germany, under Carl Friedrich Gauss, who had been pioneering the geometry of curved surfaces. This was the topic Gauss assigned to Riemann for a thesis, and the result would transform not only geometry but physics.

Books. More books than I had ever seen in my life. I gasped and crawled to my knees. I couldn’t breathe. Books galore. Music books, philosophy books. Math books. Geometry. Opera scores, logic. I sobbed and cradled the books. I hugged them to my naked chest and I cried. I smelled them and touched their spines. I remember how violently my fingers shook. I buried my nose in their pages and wept. Never had I ever held so many books in my life. And they were mine. All my very own. The orgasm still riddled my body. It had barely begun to fade. One orgasm ended, but the euphoria was just beginning.

Come find us at lunch. We sit at the back table next to the biggest window.” She turns away without waiting for an answer, blond hair sweeping across her shoulders. Ezra watches them leave with a bemused expression, then turns to me. “I have a really strong feeling that on Wednesdays, they wear pink.” Ezra and I have most of the same classes that morning, except for right before lunch, when I head to AP calculus and Ezra goes to geometry. Math isn’t his strong suit. So I end up going to the cafeteria on my own. I make my way through the food line assuming that he’ll join me at any minute, but when I exit with a full tray, he’s still nowhere in sight.

Do you remember that day in Senior Goals when you said it wasn't strange that I wanted to go to the moon?" "I remember." "I think that was the first day I really noticed you." "Took you that long?" Kath teased her. "Maybe I'm a late bloomer," Lily said tartly. "Why, when did you notice me?" Kath shot her a grin. "You really want to know?" "Yes!" "Well . . . last year, you helped me with a geometry proof. You probably don't remember. You do this thing where you . . ." Kath trailed off, looking a little shy. "What? What do I do?" "You chew on your lip when you do a difficult math problem," Kath said. "It's cute." Lily's face went red, and she laughed. "I'd better stop that in college, or no one with take me seriously.

In this book, you will encounter various interesting geometries that have been thought to hold the keys to the universe. Galileo Galilei (1564-1642) suggested that "Nature's great book is written in mathematical symbols." Johannes Kepler (1571-1630) modeled the solar system with Platonic solids such as the dodecahedron. In the 1960s, physicist Eugene Wigner (1902-1995) was impressed with the "unreasonable effectiveness of mathematics in the natural sciences." Large Lie groups, like E8-which is discussed in the entry "The Quest for Lie Group E8 (2007)"- may someday help us create a unified theory of physics. in 2007, Swedish American cosmologist Max Tegmark published both scientific and popular articles on the mathematical universe hypothesis, which states that our physical reality is a mathematical structure-in other words, our universe in not just described by mathematics-it is mathematics.

When they enter the classroom, however, they may well discover that the algorithms have got there first. Companies such as Mindojo are developing interactive algorithms that will not only teach me maths, physics and history, but will also simultaneously study me and get to know exactly who I am. Digital teachers will closely monitor every answer I give, and how long it took me to give it. Over time, they will discern my unique weaknesses as well as my strengths and will identify what gets me excited, and what makes my eyelids droop. They could teach me thermodynamics or geometry in a way that suits my personality type, even if that particular method doesn’t suit 99 per cent of the other pupils. And these digital teachers will never lose their patience, never shout at me, and never go on strike. It remains unclear, however, why on earth I would need to know thermodynamics or geometry in a world containing such intelligent computer programs.

When they enter the classroom, however, they may well discover that the algorithms have got there first. Companies such as Mindojo are developing interactive algorithms that will not only teach me maths, physics and history, but will also simultaneously study me and get to know exactly who I am. Digital teachers will closely monitor every answer I give, and how long it took me to give it. Over time, they will discern my unique weaknesses as well as my strengths and will identify what gets me excited, and what makes my eyelids droop. They could teach me thermodynamics or geometry in a way that suits my personality type, even if that particular method doesn’t suit 99 per cent of the other pupils. And these digital teachers will never lose their patience, never shout at me, and never go on strike. It remains unclear, however, why on earth I would need to know thermodynamics or geometry in a world containing such intelligent computer programs.7

When I threw the stick at Jamie, I hadn't intended to hit him with it. But the moment it left my hand, I knew that's what was going to happen. I didn't yet know any calculus or geometry, but I was able to plot, with some degree of certainty, the trajectory of that stick. The initial velocity, the acceleration, the impact. The mathematical likelihood of Jamie's bloody cheek. It had good weight and heft, that stick. It felt nice to throw. And it looked damn fine in the overcast sky, too, flying end over end, spinning like a heavy, two-pronged pinwheel and (finally, indifferently, like math) connecting with Jamie's face. Jamie's older sister took me by the arm and she shook me. Why did you do that? What were you thinking? The anger I saw in her eyes. Heard in her voice. The kid I became to her then, who was not the kid I thought I was. The burdensome regret. I knew the word "accident" was wrong, but I used it anyway. If you throw a baseball at a wall and it goes through a window, that is an accident. If you throw a stick directly at your friend and it hits your friend in the face, that is something else. My throw had been something of a lob and there had been a good distance between us. There had been ample time for Jamie to move, but he hadn't moved. There had been time for him to lift a hand and protect his face from the stick, but he hadn't done that either. He just stood impotent and watched it hit him. And it made me angry: That he hadn't tried harder at a defense. That he hadn't made any effort to protect himself from me. What was I thinking? What was he thinking? I am not a kid who throws sticks at his friends. But sometimes, that's who I've been. And when I've been that kid, it's like I'm watching myself act in a movie, reciting somebody else's damaging lines. Like this morning, over breakfast. Your eyes asking mine to forget last night's exchange. You were holding your favorite tea mug. I don't remember what we were fighting about. It doesn't seem to matter any more. The words that came out of my mouth then, deliberate and measured, temporarily satisfying to throw at the bored space between us. The slow, beautiful arc. The spin and the calculated impact. The downward turn of your face. The heavy drop in my chest. The word "accident" was wrong. I used it anyway.

I BET I CAN guess your favorite math subject in high school. It was geometry.

Mathematics is not just a subject of education system, it is the soul of education system.

As independent as the kid appeared, a twelve-year-old had no business living on her own in an abandoned house. “What are your favorite subjects?” “Math.” “Really? Good for you. I’m terrible at math, though I can do percentages very well.” “Why?” “I’m a bartender. I can calculate tips off the top of my head. I suppose you do much higher math than that.” “Trigonometry and geometry are pretty fun.” Lucy sipped her soda. “Fun? I’m impressed. So do

Adam: Adam was a young man whose anxiety turned into a monster. Where Shelly had a very mild case of social anxiety, Adam’s case could only be called severe. Over a period of several years, his underlying social fears developed into a full-blown school phobia. A quiet, unassuming person, Adam had never stood out in the classroom. Through elementary school and on into high school, he neither excelled nor failed his subjects. By no means a discipline problem, the “shy” Adam kept to himself and seldom talked in class, whether to answer a teacher’s question or chat with his buddies. In fact, he really had no friends, and the only peers he socialized with were his cousins, whom he saw at weekly family gatherings. Though he watched the other kids working together on projects or playing sports together, Adam never approached them to join in. Maybe they wouldn’t let him, he thought. Maybe he wasn’t good enough. Being rejected was not a chance he was willing to take. Adam never tried hard in school either. If he didn’t understand something, he kept quiet, fearful that raising his hand would bring ridicule. When he did poorly on an exam or paper, it only confirmed to him what he was sure was true: He didn’t measure up. He became so apprehensive about his tests that he began to feel physically ill at the thought of each approaching reminder of his inadequacy. Even though he had studied hard for a math test, for example, he could barely bring himself to get out of bed on the morning it was to take place. His parents, who thought of their child as a reserved but obedient boy who would eventually grow out of this awkward adolescent stage, did not pressure him. Adam was defensive and withdrawn, overwrought by the looming possibility that he would fail. For the two class periods preceding the math test, Adam’s mind was awash with geometry theorems, and his stomach churning. As waves of nausea washed over him, he began to salivate and swallowed hard. His eyes burned and he closed them, wishing he could block the test from his mind. When his head started to feel heavy and he became short of breath, he asked for a hall pass and headed for the bathroom. Alone, he let his anxiety overtake him as he stared into the mirror, letting the cool water flow from the faucet and onto his sweaty palms. He would feel better, he thought, if he could just throw up. But even when he forced his finger down his throat, there was no relief. His dry heaves made him feel even weaker. He slumped to the cold tile and began to cry. Adam never went back to math class that day; instead, he got a pass from the nurse and went straight home. Of course, the pressure Adam was feeling was not just related to the math test. The roots of his anxiety went much deeper. Still, the physical symptoms of anxiety became so debilitating that he eventually quit going to school altogether. Naturally, his parents were extremely concerned but also uncertain what to do. It took almost a year before Adam was sufficiently in control of his symptoms to return to school.

In Ernie’s book I Don’t Want to Live on the Moon, the cover shows stars shining right through a crescent moon. And in a “C in space” segment, the moon looks surprisingly happy, despite the fact that these stars are shining through it. OK, yes, the moon having a face and emotions is not astronomically accurate either, but that is still no excuse for teaching children inaccurate geometry. I expect more from a supposedly “educational” program. The only explanation I can think of is that, in the extended Sesame Street universe, there are Muppet bases on the moon, and those are the dots of light we are seeing.

But it gradually dawned on her that she wasn’t an idiot. Not totally. In math and science, yes. But in the realm of creative thinking, she came to realize she was a sighted person in the kingdom of the blind. Because as much as she seemed unable to process algebra and geometry, she was a savant when it came to pure creativity. And not just in graphic design. In everything. Coming up with ideas for the company picnic. Throwing parties. Wording invitations. Writing poetry. She came to be thought of as a one-woman idea machine. The kind who could take four or five mundane office items and turn them into fifteen different stunning decorations. And she could figure out the most complex fictional mysteries. She was almost always able to see the coming plot twists, even when those who excelled at academics missed them entirely. So maybe she did have a different style of intellect. She thought her self-esteem had become off the charts high, but Hall’s offhanded remark had shown her that the scars of her early struggles in school still remained, as did deep-seated doubts.

The Barmakids were also genuine polymaths and their gaze extended west as well as east. To supplement the translations that they had commissioned from Sanskrit, they began to commission translations from Greek, bringing Euclid’s Elements and Galen’s On the Natural Faculties into Arabic for the first time, as well as works by Hippocrates, Aristotle and Dioscorides.54 In this way they made available to inquisitive scholars in Baghdad the most important western classical works of maths, geometry and astronomy, seeding what would soon turn into a great flowering of scholarship.

Chris Argyris, professor emeritus at Harvard Business School, wrote a lovely article in 1977,191 in which he looked at the performance of Harvard Business School graduates ten years after graduation. By and large, they got stuck in middle management, when they had all hoped to become CEOs and captains of industry. What happened? Argyris found that when they inevitably hit a roadblock, their ability to learn collapsed: What’s more, those members of the organization that many assume to be the best at learning are, in fact, not very good at it. I am talking about the well-educated, high-powered, high-commitment professionals who occupy key leadership positions in the modern corporation.… Put simply, because many professionals are almost always successful at what they do, they rarely experience failure. And because they have rarely failed, they have never learned how to learn from failure.… [T]hey become defensive, screen out criticism, and put the “blame” on anyone and everyone but themselves. In short, their ability to learn shuts down precisely at the moment they need it the most.192 [italics mine] A year or two after Wave, Jeff Huber was running our Ads engineering team. He had a policy that any notable bug or mistake would be discussed at his team meeting in a “What did we learn?” session. He wanted to make sure that bad news was shared as openly as good news, so that he and his leaders were never blind to what was really happening and to reinforce the importance of learning from mistakes. In one session, a mortified engineer confessed, “Jeff, I screwed up a line of code and it cost us a million dollars in revenue.” After leading the team through the postmortem and fixes, Jeff concluded, “Did we get more than a million dollars in learning out of this?” “Yes.” “Then get back to work.”193 And it works in other settings too. A Bay Area public school, the Bullis Charter School in Los Altos, takes this approach to middle school math. If a child misses a question on a math test, they can try the question again for half credit. As their principal, Wanny Hersey, told me, “These are smart kids, but in life they are going to hit walls once in a while. It’s vital they master geometry, algebra one, and algebra two, but it’s just as important that they respond to failure by trying again instead of giving up.” In the 2012–2013 academic year, Bullis was the third-highest-ranked middle school in California.194

Andrew’s kissing Amanda again, her back pinned against the door frame, his hands working through a geometry problem where the goal is to find the point of intersection where two legs bisect. People would like math so much more if it involved real life like that.

Personal measurements provide an opportunity to be wildly creative. If you’re doing a spell for mental clarity, find a way to incorporate your head measurement. If your spellwork is aimed at expressing your feelings more clearly, try incorporating the distance from your heart to your mouth. Talismans, charms, garments, and tools: When we personalize these items, we imbue them with powerful ties to our own imaginations, associations, bodies, and beliefs.

• Little fingers, little Moon (think of that tiny “fingernail clipping” shape). • Thumb joints, Full Moon—either almost, exactly, or just past. • Widdershins means right to left, moon-wise, opposite the Sun’s motion, so: • Right-hand backward-C-shape, the Moon is waxing, growing larger. • Left-hand C-shape, the Moon is waning, shrinking in size.

• Widdershins means right to left, moon-wise, opposite the Sun’s motion, so: • Right-hand backward-C-shape, the Moon is waxing, growing larger. • Left-hand C-shape, the Moon is waning, shrinking in size.

context. Take 5 heel-to-toe steps in each of the four directions from a center point. From one “corner” to the next will be 7 heel-to-toe steps, and when you connect those four corners with straight lines, the resulting square will measure 28 footsteps around the edges.1 (See Figure 3-1.) Whether used as a square or curved outward into a circle, 28 reminds us of the Moon phases, a worthy underpinning to any magical space.

What he found was the geometry of the universe. Looking at the bubbles made by the Wego’s propellers, he recalled his boarding school math teachers, who had taught him to measure a sphere’s volume in terms of pi. He also remembered that pi was an irrational number, a decimal that never ended. He asked himself how nature could ever make bubbles in such circumstances. Did nature approximate? The rules his teachers had taught him must be mistaken. Spheres ought to be understood in terms of the forces that made them. At the age of twenty-one, Bucky determined that the universe had no objects. Geometry described forces. It was an insight bound to shape Bucky’s entire worldview—informing every future invention—but

There! I think it's another zombie." Off in the distance, we could see someone, or something, approaching at the edge of the parking lot. "I can't tell, hold on. I've got a pair of binoculars." I leaned inside, where we'd piled our supplies. "Well?" asked Misty. I adjusted the focus. "It's a zombie." "Are you sure? He doesn't look dead—maybe just a little pale." "Look for yourself, you'll see." I handed them to her and spit in disgust. "I can't see his eyes. He might be alive." "You don't recognize him?" "No, do you?" "It's Mr. Lopez. Teaches—well, taught Math," I said, rubbing my forehead. "Oh my gosh, you're right. How could I have forgotten?" Mr. Lopez had died of a heart attack last week while trying to teach Geometry in summer school—probably enough to kill anyone. It had been in the paper and on the local news. "You had his class last year, didn't you?" "Yeah, Pre-Algebra, hated it. It's just wrong to teach kids algebra. Still, to see him standing there...

geometry is good for the mind; it trains you to think clearly and logically. It’s not the study of triangles, circles, and parallel lines per se that matters. What’s important is the axiomatic method, the process of building a rigorous argument, step by step, until a desired conclusion has been established.

she happens to be daydreaming about some Lovecraft meta that she read on Tumblr, and looking outside, in the moment of the city’s rebirth. The meta wasn’t so much interesting as funny, science-side Tumblr arguing with fantasy-side over the comical notion that non-Euclidean geometry could somehow be sinister, and concluding that Lovecraft was probably just scared of math.

Flower of life: A figure composed of evenly-spaced, overlapping circles creating a flower-like pattern. Images of the Platonic solids and other sacred geometrical figures can be discerned within its pattern. FIGURE 3.14 FLOWER OF LIFE The Platonic solids: Five three-dimensional solid shapes, each containing all congruent angles and sides. If circumscribed with a sphere, all vertices would touch the edge of that sphere. Linked by Plato to the four primary elements and heaven. FIGURE 3.15 PENTACHORON The applications of these shapes to music are important to sound healing theory. The ancients have always professed a belief in the “music of the spheres,” a vibrational ordering to the universe. Pythagorus is famous for interconnecting geometry and math to music. He determined that stopping a string halfway along its length created an octave; a ratio of three to two resulted in a fifth; and a ratio of four to three produced a fourth. These ratios were seen as forming harmonics that could restore a disharmonic body—or heal. Hans Jenny furthered this work through the study of cymatics, discussed later in this chapter, and the contemporary sound healer and author Jonathan Goldman considers the proportions of the body to relate to the golden mean, with ratios in relation to the major sixth (3:5) and the minor sixth (5:8).100 Geometry also seems to serve as an “interdimensional glue,” according to a relatively new theory called causal dynamical triangulation (CDT), which portrays the walls of time—and of the different dimensions—as triangulated. According to CDT, time-space is divided into tiny triangulated pieces, with the building block being a pentachoron. A pentachoron is made of five tetrahedral cells and a triangle combined with a tetrahedron. Each simple, triangulated piece is geometrically flat, but they are “glued together” to create curved time-spaces. This theory allows the transfer of energy from one dimension to another, but unlike many other time-space theories, this one makes certain that a cause precedes an event and also showcases the geometric nature of reality.101 The creation of geometry figures at macro- and microlevels can perhaps be explained by the notion called spin, first introduced in Chapter 1. Everything spins, the term spin describing the rotation of an object or particle around its own axis. Orbital spin references the spinning of an object around another object, such as the moon around the earth. Both types of spin are measured by angular momentum, a combination of mass, the distance from the center of travel, and speed. Spinning particles create forms where they “touch” in space.

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.

Understanding develops slowly.

The fact of zero He added nonstop: Did you know that zero was not used throughout human history! Until 781 A.D, when it was first embodied and used in arithmetic equations by the Arab scholar Al-Khwarizmi, the founder of algebra. Algorithms took their name from him, and they are algorithmic arithmetic equations that you have to follow as they are and you will inevitably get the result, the inevitable result. And before that, across tens and perhaps hundreds of thousands of years, humans refused to deal with zero. While the first reference to it was in the Sumerian civilization, where inscriptions were found three thousand years ago in Iraq, in which the Sumerians indicated the existence of something before the one, they refused to deal with it, define it and give it any value or effect, they refused to consider it a number. All these civilizations, some of which we are still unable to decipher many of their codes, such as the Pharaonic civilization that refused to deal with zero! We see them as smart enough to build the pyramids with their miraculous geometry and to calculate the orbits of stars and planets with extreme accuracy, but they are very stupid for not defining zero in a way that they can deal with, and use it in arithmetic operations, how strange this really is! But in fact, they did not ignore it, but gave it its true value, and refused to build their civilizations on an unknown and unknown illusion, and on a wrong arithmetical frame of reference. Throughout their history, humans have looked at zero as the unknown, they refused to define it and include it in their calculations and equations, not because it has no effect, but because its true effect is unknown, and remaining unknown is better than giving it a false effect. Like the wrong frame of reference, if you rely on it, you will inevitably get a wrong result, and you will fall into the inevitability of error, and if you ignore it, your chance of getting it right remains. Throughout their history, humans have preferred to ignore zero, not knowing its true impact, while we simply decided to deal with it, and even rely on it. Today we build all our ideas, our civilization, our software, mathematics, physics, everything, on the basis that 1 + 0 equals one, because we need to find the effect of zero so that our equations succeed, and our lives succeed with, but what if 1 + 0 equals infinity?! Why did we ignore the zero in summation, and did not ignore it in multiplication?! 1×0 equals zero, why not one? What is the reason? He answered himself: There is no inevitable reason, we are not forced. Humans have lived throughout their ages without zero, and it did not mean anything to them. Even when we were unable to devise any result that fits our theorems for the quotient of one by zero, then we admitted and said unknown, and ignored it, but we ignored the logic that a thousand pieces of evidence may not prove me right, and one proof that proves me wrong. Not doing our math tables in the case of division, blowing them up completely, and with that, we decided to go ahead and built everything on that foundation. We have separated the arithmetic tables in detail at our will, to fit our calculations, and somehow separate the whole universe around us to fit these tables, despite their obvious flaws. And if we decide that the result of one multiplied by zero is one instead of zero, and we reconstruct the whole world on this basis, what will happen? He answered himself: Nothing, we will also succeed, the world, our software, our thoughts, our dealings, and everything around us will be reset according to the new arithmetic tables. After a few hundred years, humans will no longer be able to understand that one multiplied by zero equals zero, but that it must be one because everything is built on this basis.

Geometry is the cilantro of math.

In 1958, Fortune singled Nash out for his achievements in game theory, algebraic geometry, and nonlinear theory,

हालांकि ज्यादा कुछ नहीं बेनॉय मजुमदार बहुत सी चीजें शुद्ध गणितीय शास्त्र नहीं हैं लिखित व्याख्या गणित में अद्वितीय है ऐसा नहीं है, यह सभी मामलों में उपयुक्त गणितीय सूत्र है सारांश दर्शन के उपयोग का विश्लेषण करें करने का एकमात्र तरीका, गणितीय दर्शन अतिरिक्त अतिरिक्त विचार संभव नहीं हैं। तो देवी, गणित की इकाई देखें पाउंड सेकंड रोकना बंद करो, उनकी नियमित अखंडता और बेईमानी वर्तमान इकाई के रूप में है दुनिया की घटनाओं, विचारशील विषयों पर रोशनी डालना श्रृंखला में कई शब्दों को चित्रित करने के लिए श्रृंखला में वर्ण निर्दिष्ट करता है भविष्य में।

Geometry is knowledge of the eternally existent. Pythagoras Ancient Greek mathematician

Calabi-Yau manifolds, like math itself, are developing stories on a road that undoubtedly holds many twists and turns. It means there's always more to be learned, always more to be done. And for those of us who worry about keeping employed, keeping engaged, and keeping amused, it means there should be plenty of challenges, as well as fun, in the years ahead.

Unit circle is one of the important math concepts that every student must learn and understand. There are numerous concepts related to Trigonometry and geometry that needs to understand basics before solving the problems. Unit circle is known as the foundation of projectile motion, sine, cosine, tangents, degrees and radians. If you are learning the concept of geometry and trigonometry then you must have a unit circle chart as reference sheet. Most of the school teachers us this sheet while teaching the concepts of applied mathematics. This basic circle will be helpful throughout your life. It is necessary to learn this Blank Unit Circle Printable by heart and to practice it regularly for a solid foundation.

It was the math that mattered. And when the math yields a pattern of harmonious proportion, whether it’s the golden section of the Greeks or the Sierpinski gasket and Mandelbrot set of modern fractal geometry, the Platonist knows, as Archimedes did many centuries before, that he is standing at the threshold of the truth.

In geometry, whenever we had to find the area of a circle, pi * radius squared, I would get really hungry for pie. Square pie.

FROM THE AIR there seems to be a system: recognizable designs, networks on the desert floor. Crosshatches of ridge and fissure. Lines that fan out from the source. The shadow of the airplane slips across basin and range. Frost forms between the plane’s double windows, each geometric crystal an argument for the stillborn beauty of pure math. Eventually the cut of a road appears, as deep as a fossil in shale. Unbound by destination, a road simply for the sake of moving, however slowly, through miles of nothing. Through the system. The first grid is the strangest, the geometry of better living etched onto the desert floor: identical houses of a planned community pleated around the nucleus of a swimming pool. One and then another, until the desert is paved under streets and scattered with countless pools like a deck of blue cards.