Geometry Art Quotes

Calligraphy is a geometry of the soul which manifests itself physically.

Everything you invent is true: you can be sure of that. Poetry is a subject as precise as geometry.

Mighty is geometry joined with art resistless.

He deals the cards to find the answer The sacred geometry of chance The hidden law of a probable outcome The numbers lead a dance I know that the spades Are the swords of a soldier I know that the clubs are weapons of war I know that diamonds Mean money for this art But that's not the shape of my heart

Geometry is 'number in space', music is 'number in time'.

How physical beauty turns out to be chemistry and geometry and anatomy. Art is really science. Discovering why people like something is so you can replicate it. Copy it. It's a paradox, "creating" a real smile. Rehearsing again and again a spontaneous moment of horror. All the sweat and boring effort that goes into creating what looks easy and instant.

the seven “liberal arts”: Grammar, the foundation of science; Logic, which differentiates the true from the false; Rhetoric, the source of law; Arithmetic, the foundation of order because “without numbers there is nothing”; Geometry, the science of measurement; Astronomy, the most noble of the sciences because it is connected with Divinity and Theology; and lastly Music.

Well then – I see two ways of letting things take their course – Create one’s own sensations with the help of a flamboyant collision of rare words – not often, mind you – or else neatly draw the angles, the squares, the entire geometry of feelings – those of the moment, naturally.

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.

I think all artists struggle to represent the geometry of life in their own way, just like writers deal with archetypes. There are only so many stories that you can tell, but an infinite number of storytellers.

In the various arts, and above all in that of writing, the shortest distance between two points, even if close to each other, has never been and never will be, nor is it now, what is known as a straight line, never, never, to put it strongly and emphatically in response to any doubts, to silence them once and for all.

We see that music, like the world, is formed from unchanging mathematical principles deployed in time, creating complexity, variety and beauty.

Rigid geometry forced in varied curves is "mother," / is "nature," is systematic violation." Muy Bueno. / This device is for you, the mutilated of no art.

Thus nature provides a system for proportioning the growth of plants that satisfies the three canons of architecture. All modules are isotropic and they are related to the whole structure of the plant through self-similar spirals proportioned by the golden mean.

Islamic patterns speak of infinity and the omnipresent center.

sacred knowledge of the cosmos seems to be hidden within our souls and is shown within our artwork and creative expressions.

Art has no immediate future because all art is collective and there is no more collective life(there are only dead collections of people), and also because of this breaking of the true pact between the body and the soul. Greek art coincided with the beginning of geometry and with athleticism, the art of the Middle Ages with the craftsmen's guilds, the art of the Renaissance with the beginning of mechanics, etc....Since 1914 there has been a complete cut. Even comedy is almost impossible. There is only room for satire (when was it easier to understand Juvenal?). Art will never be reborn except from amidst a general anarchy - it will be epic no doubt, because affliction will have simplified a great many things...It is therefore quite useless for you to envy Leonardo or Bach. Greatness in our times must take a different course. Moreover it can only be solitary, obscure and without an echo...(but without an echo, no art).

means of succeeding in the object we set before us. We must make as it were a fresh start, and before going further define what rhetoric is. Rhetoric may be defined as the faculty of observing in any given case the available means of persuasion. This is not a function of any other art. Every other art can instruct or persuade about its own particular subject-matter; for instance, medicine about what is healthy and unhealthy, geometry about the properties of magnitudes, arithmetic about numbers, and the same is true of the other arts and sciences. But rhetoric we look upon as the power of observing the means of persuasion on almost any subject presented to us;

In a way, art is a theory about the way the world looks to human beings. It’s abundantly obvious that one doesn’t know the world around us in detail

When a king asked Euclid, the mathematician, whether he could not explain his art to him in a more compendious manner? he was answered, that there was no royal way to geometry.

Reverence for the natural environment, and experiencing the interconnectedness between all things has long guided me to create watercolor paintings of beauty and spirit. Life's continuing adventure has led me into an exciting exploration into the wisdom and symbolic imagery of Sacred Geometry. These paintings act as a bridge between this reality and a metaphorical world of healing, continuity, and transformation. I use multiple transparent watercolor glazes coupled with image overlapping techniques, and sacred geometry to produce visions of a multi-dimensional reality. It is my intention to create art that embodies the vibration of Universal Love and expresses the joy and gratitude I feel for the honor of being part of this earthwalk." ~Blessings, Francene~

A therapist who fears dependence will tell his patient, sometimes openly, that the urge to rely is pathologic. In doing so he denigrates a cardinal tool. A parent who rejects a child's desire to depend raises a fragile person. Those children, grown to adulthood, are frequently among those who come for help. Shall we tell them again that no one can find an art to lean on, that each alone must work to ease a private sorrow? Then we shall repeat and experiment already conducted; many know its result only too well. If patient and therapist are to proceed together down a curative path, they must allow limbic regulation and its companion moon, dependence, to make the revolutionary magic. Many therapists believe that reliance fosters a detrimental dependency. Instead, they say, patients should be directed to "do it for themselves" - as if they possess everything but the wit to throw that switch and get on with their lives. But people do not learn emotional modulation as they do geometry or the names of state capitals. They absorb the skill from living in the presence of an adept external modulator, and they learn it implicitly. Knowledge leaps the gap from one mind to the other, but the learner does not experience the transferred information as an explicit strategy. Instead, a spontaneous capacity germinates and becomes a natural part of the self, like knowing how to ride a bike or tie one's shoes. The effortful beginnings fade and disappear from memory. (171)

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

In a seven-tone scale the eighth note is the octave, twice the pitch of the first note, and so signals the movement to a new level. This may be why, in religious symbolism, the eighth step is often associated with spiritual evolution or salvation.

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.

In Egypt, construction is male geometry, a glorification of the visible. The first clarity of intelligible form appears in Egypt, the basis of Greek Apollonianism in art and thought. Egypt discovers four-square architecture, a rigid grid laid against mother nature's melting ovals. Social order becomes a visible aesthetic, countering nature's chthonian invisibilities. Pharaonic construction is the perfection of matter in art. Fascist political power, grandiose and self-divinising, creates the hierarchical, categorical superstructure of western mind.

I had better say something here about this question of age, since it is particularly important for mathematicians. No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game. To take a simple illustration at a comparatively humble level, the average age of election to the Royal Society is lowest in mathematics. We can naturally find much more striking illustrations. We may consider, for example, the career of a man who was certainly one of the world's three greatest mathematicians. Newton gave up mathematics at fifty, and had lost his enthusiasm long before; he had recognized no doubt by the time he was forty that his greatest creative days were over. His greatest idea of all, fluxions and the law of gravitation, came to him about 1666 , when he was twentyfour—'in those days I was in the prime of my age for invention, and minded mathematics and philosophy more than at any time since'. He made big discoveries until he was nearly forty (the 'elliptic orbit' at thirty-seven), but after that he did little but polish and perfect. Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work a good deal later; Gauss's great memoir on differential geometry was published when he was fifty (though he had had the fundamental ideas ten years before). I do not know an instance of a major mathematical advance initiated by a man past fifty. If a man of mature age loses interest in and abandons mathematics, the loss is not likely to be very serious either for mathematics or for himself.

Long before being artists, we are artisans; and all fabrication, however rudimentary, lives on likeness and repetition, like the natural geometry which serves as its fulcrum. Fabrication works on models which it sets out to reproduce; and even when it invents, it proceeds, or imagines itself to proceed, by a new arrangement of elements already known. Its principle is that “we must have like to produce like.” In short, the strict application of the principle of finality, like that of the principle of mechanical causality, leads to the conclusion that “all is given.” Both principles say the same thing in their respective languages, because they respond to the same need.

How I fevered to study the seven liberal arts: the trivium of grammar, logic, and rhetoric, and the quadrivium of arithmetic, geometry, astronomy, and music.

Fractals, therefore, are also taken as a type of art, denoting the nature of the world around us, as well as the infinity and continuity that are reflected almost evidently in them.

Is Euclidian geometry true or is Riemann geometry true? He answered, The question has no meaning. As well ask whether the metric system is true and the avoirdupois system is false; whether Cartesian coordinates are true and polar coordinates are false. One geometry can not be more true than another; it can only be more convenient. Geometry is not true, it is advantageous.

The abstract, curvilinear motifs of ancient Islamic decorative art found in mosaics and carpet design appear again and again at all scales of magnification on the boundary of the Mandelbrot set.

Sandor Boatly had never guessed that, properly played, baseball consisted of mathematics, geometry, art, philosophy, ballet, and carnival, all intertwined like the mystical ribbons of color in a rainbow.

We therefore find that the triangles and rectangles herein described, enclose a large majority of the temples and cathedrals of the Greek and Gothic masters, for we have seen that the rectangle of the Egyptian triangle is a perfect generative medium, its ratio of five in width to eight in length 'encouraging impressions of contrast between horizontal and vertical lines' or spaces; and the same practically may be said of the Pythagorean triangle

He said to me one day in the second week of July, “Asher Lev, there are two ways of painting the world. In the whole history of art, there are only these two ways. One is the way of Greece and Africa, which sees the world as a geometric design. The other is the way of Persia and India and China, which sees the world as a flower. Ingres, Cézanne, Picasso paint the world as geometry. Van Gogh, Renoir, Kandinsky, Chagall paint the world as a flower.

The Great Pyramid was a fractal resonator for the entire Earth. It is designed according to the proportions of the cosmic temple, the natural pattern that blends the two fundamental principles of creation. The pyramid has golden ratio, pi, the base of natural logarithms, the precise length of the year and the dimensions of the Earth built into its geometry. It demonstrates.... As John Michell has pointed out in his wonderful little book, City of Revelation, 'Above all, the Great Pyramid is a monument to the art of 'squaring the circle''.

I hadn't wanted to explain the lipstick. Or the mascara. Or the skinny jeans I'd snagged from Sienna's laundrey and washed under cover of darkness and paired with a black turtleneck that a jaunt through the dryer had made, to ne honest, a size too small. But this news about the Willing Archive trumped all of that. He gave me a careful once-over. "Well." I sat down next to him, aiming for casual. I should have aimed my butt. I sat on his geometry book. "Well what?" "Don't even.The day you become a good liar is the day I leave you for one of the Hannandas." "I have an appointment at the Willing Archive." I will say this for Frankie: He pays attention. "The utterly-off-limits, place-to-bury-your-face-in-Edward's-old-knickers archive?" "Nice.But yes,that one.Mrs. Evers got me in." "About time someone did." He bumped a shoulder against mine. "I really do hate to burst your bubble, Fiorella, but Edward is a century past appreciating the sight of you in tight jeans. So tell me whassup." I squirmed a little. "What sort of idiot do you think I am?" He sighed. "You look good, but I am concerned about the inspiration." "It's not a big deal. It's some makeup." "When I want a boy to look ta me, it's a day that ends in y. You, it's something else. It's a big deal.

I try to tell the teacher, you know. I don't give a fuck about geometry or English. Like I'm probably going to drive a truck or something when I get out of school. Join the army or something simple. I'm sure in the army they're all going to be wondering what an acute angle is. I'm sure I'll make lots of friends driving my truck because I can diagram some lousy goddamn sentence. And then after school I'm free, right? What's that mean? I go down to the bowling alley or the shopping mall with my friends. We scope the grils, smoke a little doobidge, maybe a tab of acid every now and then. But that's not really living, is it? I mean, if that's living, then excuse me right now. I'll go out and put a bullet in the old brainpan. But if that's not all there is, right, well, maybe there's something I could do a little less radical, like, you know. I don't mind life or anything--I'm perfectly willing to give it a try. So what the hell, I figured. I'm sick of school, drugs, this goddamn oppressive house of Ethel's and all. Maybe it's time I experimented a little more with my life, took a few more chances. So that's when I decided to become a warlock. To master the satanic arts of black magic. Devil worshiping, for you laymen. I want to master what they call the black arts.

Ludwig Schlafi (1814-1895) proved that there are six regular four-dimensional polytopes (generalisations of polyhedra): the 5-cell made of tetrahedra, the 8-cell or tesseract made of cubes, the 16-cell made of tetrahedra, the 24-cell made of octahedra, the 120-cell made of dodecahedra, and the 600-cell made of tetrahedra.

Classical education was based on the seven liberal arts or sciences: grammar, the formal structures of language; rhetoric, composition and presentation of argument; dialectic, formal logic; arithmetic; geometry; music; astronomy.14 For centuries, the classics dominated the very idea of being educated and attempts at reform were resisted.

Everyone knows that the Arts are Grammar, Dialectic, Rhetoric, Arithmetic, Music, Geometry, and Astronomy. And almost everyone has met the mnemonic couplet Gram loquitur, Dia verba docet, Rhet verba colorat, Mus canit, Ar numerat, Geo ponderat, Ast colit astra. The first three constitute the Trivium or threefold way; the last four, the Quadrivium.

Arthur C. Clarke thinks that it may be just a coincidence, "but", he writes, "the Mandelbrot set does indeed seem to contain an enormous number of mandalas or religious symbols, which are found in ecclesiastical designs-such as stained glass windows, and particularly in Islamic art. We find many forms like the Paisley pattern echoing the Mandelbrot set centuries before it was discovered!

Islamic art in its many forms is of the greatest import for the understanding of the essence of Islam and a central means of transmitting its message to the contemporary world. When one thinks of Islam, one should go beyond the repetitive scenes on television of wars and battles, which unfortunately abound in today’s world, to behold the peace and harmony of Islamic art seen in the great mosques, traditional urban settings and gardens, and the rhythm and geometry of calligraphy and arabesque designs; read in the poems that sing of the love that permeates all of God’s creation and binds creatures to God; and heard in the strains of melodies that echo what we had experienced in that primordial morn preceding creation and our descent into this lowly world. Today more than ever before, the understanding of Islamic art is an indispensable key for the comprehension of Islam itself. Those who are sensitive to the language of traditional art and the beauty of a paradisal order that emanates from it as well as the intellectual principles conveyed through it can learn much from this art.

The Harmony of the World is the continuation of tye Cosmic Mystery, and the climax of his lifelong obsession. What Kepler attempted here is, simply, to bare the ultimate secret of the universe in an all-embracing synthesis of geometry, music, astrology, astronomy, and epistemology. It was the firat attempt of this kind since Plato, and it is the last to our day. After Kepler, fragmentation of experience sets in again, science is divorced from religion, religion from art, substance from form, matter from mind. The work is divided into five books. The first two deal with the concept of harmony in mathematics; the following three with the applications of this concept to music, astrology, and astronomy, in that order.

And barbarians were inventors not only of philosophy, but almost of every art. The Egyptians were the first to introduce astrology among men. Similarly also the Chaldeans. The Egyptians first showed how to burn lamps, and divided the year into twelve months, prohibited intercourse with women in the temples, and enacted that no one should enter the temples from a woman without bathing. Again, they were the inventors of geometry. There are some who say that the Carians invented prognostication by the stars. The Phrygians were the first who attended to the flight of birds. And the Tuscans, neighbours of Italy, were adepts at the art of the Haruspex. The Isaurians and the Arabians invented augury, as the Telmesians divination by dreams. The Etruscans invented the trumpet, and the Phrygians the flute. For Olympus and Marsyas were Phrygians. And Cadmus, the inventor of letters among the Greeks, as Euphorus says, was a Phoenician; whence also Herodotus writes that they were called Phoenician letters. And they say that the Phoenicians and the Syrians first invented letters; and that Apis, an aboriginal inhabitant of Egypt, invented the healing art before Io came into Egypt. But afterwards they say that Asclepius improved the art. Atlas the Libyan was the first who built a ship and navigated the sea. Kelmis and Damnaneus, Idaean Dactyli, first discovered iron in Cyprus. Another Idaean discovered the tempering of brass; according to Hesiod, a Scythian. The Thracians first invented what is called a scimitar (arph), -- it is a curved sword, -- and were the first to use shields on horseback. Similarly also the Illyrians invented the shield (pelth). Besides, they say that the Tuscans invented the art of moulding clay; and that Itanus (he was a Samnite) first fashioned the oblong shield (qureos). Cadmus the Phoenician invented stonecutting, and discovered the gold mines on the Pangaean mountain. Further, another nation, the Cappadocians, first invented the instrument called the nabla, and the Assyrians in the same way the dichord. The Carthaginians were the first that constructed a triterme; and it was built by Bosporus, an aboriginal. Medea, the daughter of Æetas, a Colchian, first invented the dyeing of hair. Besides, the Noropes (they are a Paeonian race, and are now called the Norici) worked copper, and were the first that purified iron. Amycus the king of the Bebryci was the first inventor of boxing-gloves. In music, Olympus the Mysian practised the Lydian harmony; and the people called Troglodytes invented the sambuca, a musical instrument. It is said that the crooked pipe was invented by Satyrus the Phrygian; likewise also diatonic harmony by Hyagnis, a Phrygian too; and notes by Olympus, a Phrygian; as also the Phrygian harmony, and the half-Phrygian and the half-Lydian, by Marsyas, who belonged to the same region as those mentioned above. And the Doric was invented by Thamyris the Thracian. We have heard that the Persians were the first who fashioned the chariot, and bed, and footstool; and the Sidonians the first to construct a trireme. The Sicilians, close to Italy, were the first inventors of the phorminx, which is not much inferior to the lyre. And they invented castanets. In the time of Semiramis queen of the Assyrians, they relate that linen garments were invented. And Hellanicus says that Atossa queen of the Persians was the first who composed a letter. These things are reported by Seame of Mitylene, Theophrastus of Ephesus, Cydippus of Mantinea also Antiphanes, Aristodemus, and Aristotle and besides these, Philostephanus, and also Strato the Peripatetic, in his books Concerning Inventions. I have added a few details from them, in order to confirm the inventive and practically useful genius of the barbarians, by whom the Greeks profited in their studies. And if any one objects to the barbarous language, Anacharsis says, "All the Greeks speak Scythian to me." [...]

Music is carried by the vibrations of molecules of air, like waves upon an ocean. It perhaps uniquely captures and conveys the interior landscape of one human mind to another, holding our tears and sweat, pain and pleasure, packaged as paeans and preludes and etudes and nocturnes. It is the texturization of the deliquescence of time, the ebb and flow of mood and meaning. It ruminates, vacillates, contemplates, and stimulates. In music we organize and fantasize, arranging the elements of music-melody, rhythm, and harmony-into meaningful shapes and patterns. Its rhythms move our hands, feet and bodies to the pulses of the universe. Its harmonies breathe with the exploratory intricacies and curiosities of relationship and proportion, consonance, dissonance, assonance, and resonance. Its melodies flitter into flights of fancy, weaving woe and wonder.

A pool game mixes ritual with geometry. The slow spaciousness of the green felt mirrors some internal state you get to after a few beers. Back at school, I’d been trying to read the philosophy of art, which I was grotesquely unequipped to do but nonetheless stuck on. I loved the idea that looking at a painting or listening to a concerto could make you somehow “transcend” the day-in, day-out bullshit that grinds you down; how in one instant of pure attention you could draw something inside that made you forever larger. In those days the drug culture was pimping “expanded consciousness,” a lie that partly descended from the old postindustrial lie of progress: any change in how your head normally worked must count as an improvement. Maybe my faith in that lie slid me toward an altered state that day. Or maybe it was just the beer, which I rarely drank. In any case, walking around the pool table, I felt borne forward by some internal force or fire. My first shot sank a ball. Then I made the most unlikely bank shot in history to drop two balls at once after a wild V trajectory. Daddy whistled. The sky through the window had gone the exact blue of the chalk I was digging my cue stick in, a shade solid and luminous at once, like the sheer turquoise used for the Madonna’s robe in Renaissance paintings. Slides from art history class flashed through my head. For a second, I lent that color some credit, as if it meant something that made my mind more buoyant. But that was crazy.

There is an art to the business of making sandwiches which it is given to few ever to find the time to explore in depth. It is a simple task, but the opportunities for satisfaction are many and profound: choosing the right bread for instance. The Sandwich Maker had spent many months in daily consultation and experiment with Grarp the baker and eventually they had between them created a loaf of exactly the consistency that was dense enough to slice thinly and neatly, while still being light, moist and having that fine nutty flavour which best enhanced the savour of roast Perfectly Normal Beast flesh. There was also the geometry of the slice to be refined: the precise relationships between the width and height of the slice and also its thickness which would give the proper sense of bulk and weight to the finished sandwich: here again, lightness was a virtue, but so too were firmness, generosity and that promise of succulence and savour that is the hallmark of a truly intense sandwich experience. The proper tools, of course, were crucial, and many were the days that the Sandwich Maker, when not engaged with the Baker at his oven, would spend with Strinder the Tool Maker, weighing and balancing knives, taking them to the forge and back again. Suppleness, strength, keenness of edge, length and balance were all enthusiastically debated, theories put forward, tested, refined, and many was the evening when the Sandwich Maker and the Tool Maker could be seen silhouetted against the light of the setting sun and the Tool Maker’s forge making slow sweeping movements through the air trying one knife after another, comparing the weight of this one with the balance of another, the suppleness of a third and the handle binding of a fourth. Three knives altogether were required. First there was the knife for the slicing of the bread: a firm, authoritative blade which imposed a clear and defining will on a loaf. Then there was the butter-spreading knife, which was a whippy little number but still with a firm backbone to it. Early versions had been a little too whippy, but now the combination of flexibility with a core of strength was exactly right to achieve the maximum smoothness and grace of spread. The chief amongst the knives, of course, was the carving knife. This was the knife that would not merely impose its will on the medium through which it moved, as did the bread knife; it must work with it, be guided by the grain of the meat, to achieve slices of the most exquisite consistency and translucency, that would slide away in filmy folds from the main hunk of meat. The Sandwich Maker would then flip each sheet with a smooth flick of the wrist on to the beautifully proportioned lower bread slice, trim it with four deft strokes and then at last perform the magic that the children of the village so longed to gather round and watch with rapt attention and wonder. With just four more dexterous flips of the knife he would assemble the trimmings into a perfectly fitting jigsaw of pieces on top of the primary slice. For every sandwich the size and shape of the trimmings were different, but the Sandwich Maker would always effortlessly and without hesitation assemble them into a pattern which fitted perfectly. A second layer of meat and a second layer of trimmings, and the main act of creation would be accomplished.

After Us, the Salamanders!, The Future belongs to the Newts, Newts Mean Cultural Revolution. Even if they don't have their own art (they explained) at least they are not burdened with idiotic ideals, dried up traditions and all the rigid and boring things taught in schools and given the name of poetry, music, architecture, philosophy and culture in any of its forms. The word culture is senile and it makes us sick. Human art has been with us for too long and is worn-out and if the newts have never fallen for it we will make a new art for them. We, the young, will blaze the path for a new world of salamandrism: we wish to be the first newts, we are the salamanders of tomorrow! And so the young poetic movement of salamandrism was born, triton - or tritone - music was composed and pelagic painting, inspired by the shape world of jellyfish, fish and corals, made its appearance. There were also the water regulating structures made by the newts themselves which were discovered as a new source of beauty and dignity. We've had enough of nature, the slogans went; bring on the smooth, concrete shores instead of the old and ragged cliffs! Romanticism is dead; the continents of the future will be outlined with clean straight lines and re-shaped into conic sections and rhombuses; the old geological must be replaced with a world of geometry. In short, there was once again a new trend that was to be the thing of the future, a new aesthetic sensation and new cultural manifestoes; anyone who failed to join in with the rise of salamandrism before it was too late felt bitterly that he had missed his time, and he would take his revenge by making calls for the purity of mankind, a return to the values of the people and nature and other reactionary slogans. A concert of tritone music was booed off the stage in Vienna, at the Salon des Indépendents in Paris a pelagic painting called Capriccio en Bleu was slashed by an unidentified perpetrator; salamandrism was simply victorious, and its rise was unstoppable.

it is clear that in the study of beings this aim can be fulfilled by us perfectly only through successive examinations of them by one man after another,41 the later ones seeking the help of the earlier in that task, on the model of what has happened in the mathematical sciences. For if we suppose that the art of geometry did not exist in this age of ours, and likewise the art of astronomy, and a single person wanted to ascertain by himself the sizes of the 15 heavenly bodies, their shapes, and their distances from each other, that would not be possible for him—e.g. to know the proportion of the sun to the earth or other facts about the sizes of the stars—even though he were the most intelligent of men by nature, unless by a revelation or something resembling revelation.42 Indeed if he were told that the sun is about 150 or 160 times43 as great as the earth, he would think this statement madness on the part of the speaker, although this is a fact which has been demonstrated in 20 astronomy so surely that no one who has mastered that science doubts it.

Venus draws a fivefold pattern around Earth every eight years allowing us to draw an amazing diagram. In those eight years there are almost exactly 99 full moons, nine elevens, the number of names or reflections of Allah in Islam. Jupiter draws a beautiful elevenfold pattern around Earth.

The ancient Maya were superb stargazers. Their calendar synchronized not just the Sun and Moon, byt also Venus and Mars. They worked out that 81 (or 3X3X3X3) full moons occur exactly every 2,392 (or 8X13X23) days, an astonishingly accurate gearing.

Ten is formed from two pentagons and ten life-invoking pentagons sit perfectly arpund a decagon, and DNA, appropriately as the key to the reproduction of life, has ten steps for each turn of its double helix, so appears in cross-section as a tenfold rosette.

Eleven is important as the first number that allows us to begin to comprehend the measure of a circle. This is because, for practical purposes, a circle measuring seven across will measure eleven halfway around.

The ancients were obsessed with measures, and the number eleven is central in their metrological scheme. Shown opposite is the extraordinary fact that the size of the Moon relates to the size of the Earth as does three to eleven. What this means is that if we draw down the Moon to the Earth, as shown, then a heavenly circle through the moon will have a circumference equal to the perimeter of a square around the Earth. This is called 'squaring the circle'. Quite how the old druids worked this out we may never know, but they clearly did, for the Moon and the Earth are best measured in miles, as shown. A double rainbow also magically squares the circle.

The dodecagon is also made from six squares and six equilateral triangles fitted around a hexagon

When one circle is drawn over another like this so that they pass through each others' centers, then an important almond shape, the vesica piscis, literally 'fish's bladder' is formed. It is one of the first things that circles can do. Christ is often depicted inside a vesica.

Twelve is the number which fits around one in three dimensions in the same way that six fits around one in two dimensions. The New Testament is a story of a teacher surrounded by twelve disciples.

Many familiar objects from cassettes to credit cards and Georgian front doors are Phi (1.618...) rectangles.

As I explain at some length in 'The Crystal Sun' this particular angle, which we can call the 'golden angle,' is the precise value of the acute angle of of a right-angled 'golden triangle' that embodies the golden mean proportion .... The Danish art historian Else Kielland established with conclusive and absolutely overwhelming evidence and analysis that this angle was the basis for all Egyptian art and architecture. She did this in her monumental work 'Geometry in Egyptian Art' ..... The King's Chamber inside the Great Pyramid embodies no fewer than eight occurrences of the golden angle, and the coffer in the chamber embodies yet more.

Merchant Bashir got up and plodded to a pile of rugs. He grabbed a kilim and unrolled it across the floor. A mosaic of black, yellow, and maroon geometries glimmered. “He taught me rug weaving. It’s a nomadic art, he said. Pattern making carries the past into the future.” Bashir pointed to a recurrent cross motif that ran down the kilim’s center. “The four corners of the cross are the four corners of the universe. The scorpion here”—he toed a many-legged symmetric creature woven in yellow—“represents freedom. Sharif taught me this and more. He was a natural at symbols. I asked him why he went to Turkey. He looked at me and said, ‘To learn to weave the best kilim in the world.

BOOKS RECOMMENDED BY KATHLEEN MCGOWAN The Brother of Jesus and the Lost Teachings of Christianity, Jeffrey J. Butz Excellent account of early Christianity and its factions. Rev. Jeff’s understanding of Greek translations was a revelation for me. A rare scholarly work that is entirely readable and entertaining. The Woman with the Alabaster Jar, Margaret Starbird A pioneering book in Magdalene research, Starbird was one of the first to assert the theory of Magdalene as bride. Mary Magdalen, Myth and Metaphor, Susan Haskins The definitive Magdalene reference book. Massacre at Montsegur, Zoé Oldenbourg Classic, scholarly account of the final days of the Cathars. The Perfect Heresy, by Stephen O’Shea A very readable book on Cathar history. Chasing the Heretics, Rion Klawinski A history-filled memoir of traveling through Cathar country. Key to the Sacred Pattern, Henry Lincoln Fascinating theories on the sacred geometry of Rennes-le-Château and the Languedoc by one of the authors of Holy Blood, Holy Grail. Relics of Repentance, James F. Forcucci Contains the letters of Claudia Procula, the wife of Pontius Pilate. The Church of Mary Magdalene, Jean Markale Poet and philosopher Jean Markale’s quest for the sacred feminine in Rennes-le-Château. The Gospel of Mary Magdalene and The Gospel of Philip, Jean-Yves Leloup Highly readable French scholarly analyses of important Gnostic material. Nostradamus and the Lost Templar Legacy, Rudy Cambier Professor Cambier explores the prophecies of the Expected One from another angle. Who Wrote the Gospels?, Randel McCraw Helms Fascinating theories from a noted scholar on the authorship of the Gospels. Jesus and the Lost Goddess, Timothy Freke and Peter Gandy Well-researched alternative theories, also provides excellent resource list. Botticelli, Frank Zollner The ultimate coffee table book, with gorgeous reproductions of the art and great analysis of Sandro’s life and career.

Early education,” says President Thwing, “occupies itself with description (geometry, space, arithmetic, time, science, the world of nature). Later education with comparison and relations.

Early education,” says President Thwing, “occupies itself with description (geometry, space, arithmetic, time, science, the world of nature). Later education with comparison and relations.” If one asks, “Why not both together? Why learn facts at one time and their relations at another? Is it not the most vital possible way to learn facts to learn them in their relations?”—the answer that would be generally made reveals that most teachers are pessimists, that they have very small faith in what can be expected of the youngest pupils. The theory is that interpretative minds must not be expected of them. Some of us find it very hard to believe as little as this, in any child. Most children have such an incorrigible tendency for putting things together that they even put them together wrong rather than not put them together at all. Under existing educational conditions a child is more of a philosopher at six than he is at twenty-six. The third stage of education for which Dr. Thwing partitions off the human mind is the “stage in which a pupil becomes capable of original research, a discoverer of facts and relations” himself. In theory this means that when a man is thirty years old and all possible habits of originality have been trained out of him, he should be allowed to be original. In practice it means removing a man’s brain for thirty years and then telling him he can think.

Early education,” says President Thwing, “occupies itself with description (geometry, space, arithmetic, time, science, the world of nature). Later education with comparison and relations.” If one asks, “Why not both together? Why learn facts at one time and their relations at another? Is it not the most vital possible way to learn facts to learn them in their relations?”—the answer that would be generally made reveals that most teachers are pessimists, that they have very small faith in what can be expected of the youngest pupils. The theory is that interpretative minds must not be expected of them. Some of us find it very hard to believe as little as this, in any child. Most children have such an incorrigible tendency for putting things together that they even put them together wrong rather than not put them together at all. Under existing educational conditions a child is more of a philosopher at six than he is at twenty-six.

The logical correctness of the arguments that lead from axioms to theorems is not the only thing we have to attend to. Do the rules of perfect logic constitute the whole of mathematics? As well say that the art of the chess-player reduces itself to the rules for the movement of the pieces. A selection must be made out of all the constructions that can be combined with the materials furnished by logic. The true geometrician makes this selection judiciously, because he is guided by a sure instinct, or by some vague consciousness of I know not what profounder and more hidden geometry, which alone gives a value to the constructed edifice.

An architectural curiosity. And a flawed comparison, as the geometry of this chamber is quite different. The great curse of the artistic education, or what you call the liberal arts, is the understanding of the world through metaphor. Understanding things for what they resemble, rather than what they are in themselves. I think that is what draws you to the battle against conspiracy. Am I correct?” “I guess. I call it false narrativization.” Rostam laughed, and the sound echoed back around them “Also it brings in listeners.

Leonardo da Vinci was perhaps the greatest biomimic of all time. Not only did he precisely adhere to nature's proportions in his art but also spent the last ten years of his life studying-even obsessing over-the geometry and motions of natural flow. Based on years of observing birds in flight, Leonardo, the world's first fluid dynamicist, designed flying wings, a helicopter, and numerous other machines. His understanding of how the human heart actually operates-through manipulation of whirlpools-has only been rediscovered in the past decade. Even five hundred years later, the depth of Leonardo's insights into the secrets of nature's form and function cause scientists to marvel.

AN ANSWER TO OUR QUESTION Places of worship embody the aspirations of their architects, and the communities they represent, to ideal beauty. Their chosen means of expression feature color, geometry, and symmetry. Consider, in particular. the magnificent plate HH. Here the local geometry of the ambient surfaces and the local patterns of their color change as our gaze surveys them. It is a vibrant embodiment of anamorphy and anachromy-the very themes that our unveiling of Nature's deep design finds embodied at Nature's core. Does the world embody beautiful ideas? There is our answer, before our eyes: Yes. Color and geometry, symmetry, anachromy, and anamorphy, as ends in themselves, are only one branch of artistic beauty. Islam's injunction against representational art played an important part in bringing these forms of beauty to the fore, as did the physical constraint of structural stability (we need columns to support the weight of ceilings, and the arches and domes to distribute tension). Depictions of human faces, bodies, emotions, landscapes, historic scenes, and the like, when they are allowed, are far more common subjects for art than those austere beauties. The world does not, in its deep design, embody all forms of beauty, nor the ones that people without special study, or very unusual taste, find most appealing. But the world does, in its deep design, embody some forms of beauty that have been highly prized for their own sake, and have been intuitively associated with the divine.

Zooming into the boundary of the M-set, we find smaller and smaller island molecules, surrounded by increasingly intricate circular patterns, evocative of Oriental art, particularly in the meditative designs of Buddhism known as mandalas.

Fractals are beautiful to look at when graphed and, thus, had been used in arts and the sciences.  It first appeared in art in the 19th century, at a painting of Mt. Fuji, which shows a great wave that threatens an open boat, wherein the dimension of the wave is the approximation of a circle’s diameter.  This is an example of a natural fractal, way before Felix Hausdorff first presented the theory of the fractal dimension in 1868.[viii]  They are used to incorporate nature into artistic elements and, thus, had been used to highlight pieces of visual arts.  It became well known when genetic programming entered the world in the 20th century, which optimized parameters of what is called “Mandelbrot sets” that are useful in generating certain biomorphs. 

Fractal shapes were being expressed intuitively by artists long before they were recognized in science. Self-similar patterns appear in Celtic artefacts, like the spirals and circles within circles of the exquisitely crafted illuminated pages of the early 9th-century Book of Kells and the Densborough mirror made in the 1st century A.C. Mathematical awareness, particularly fractal awareness, reveals itself in the art of the Romans and the Egyptians, and in the work of the Aztec, Inca and Mayan civilizations of Central and South America. Shapes highly reminiscent of the Koch curve were used to depict waves by the Hellenic artist in a frieze in the ancient Greek town of Akrotiri.

Cutting stone to the optimum basic size for building secure, aesthetically pleasing combinations was tantamount to establishing the smallest prime integer without which there would be no arithmetic or geometry. Working by trial and error with units, Greek mathematical thinking arrived at the idea of beautiful proportions, which in turn formed the basis of all the arts, not just architecture. Masonry as a method led to principles that eventually came to govern the whole of western art.

Père Ubu’s statement to his conscience about discarding old forms of painting by turning to geometry could only have been inspirational to Picasso during his work on Les Demoiselles d’Avignon. Geometry turned out to be the language of the dramatically new art that Picasso sought so passionately beginning in 1907. Before that, however, he required two key periods of transformation.

Is it not fair to say, “The program learned from experience”? Your immediate objection is that there was a program telling the machine how to learn. But when you take a course in Euclidean geometry, is not the teacher putting a similar learning program into you? Poorly, to be sure, but is that not, in a real sense, what a course in geometry is all about? You enter the course and cannot do problems; the teacher puts into you a program and at the end of the course you can solve such problems. Think it over carefully. If you deny the machine learns from experience because you claim the program was told (by the human programmer) how to improve its performance, then is not the situation much the same with you, except you are born with a somewhat larger initial program compared to the machine when it leaves the manufacturer’s hands? Are you sure you are not merely “programmed” in life by what chance events happen to you?

A mandala (Sanskrit for “circle”) is a circular pattern, considered a sacred geometry, that’s been used in spiritual practice since ancient times as an active visual meditation.

The liberal arts are the seven unique skills used to create and justify scientia. how would a scholar justify that his knowledge is true? He would do so through the liberal arts. The arts of the Trivium - grammar, dialectic, and rhetoric - are the tools of language. The arts of the Quadrivium - arithmetic, geometry, astronomy and music - are the tools of mathematics.

Astronomy was born of superstition, eloquence of ambition, hatred, falsehood and flattery; geometry of avarice; physics of an idle curiosity; and even moral philosophy of human pride. Thus the arts and sciences owe their birth to our vices

It has been said that geometry is the art of applying good reasoning to bad diagrams.

A life's journey is like a musical composition, born into the world from nothing, living for a time in form and structure, dancing spontaneously on the edge of chaos and order, and then finally returning. In this respect Western music tends to be more linear, Eastern music more cyclical.

The liberal arts are the prerequisite for any higher education. The three lower ones, also known as the trivium, are grammar, rhetoric, and dialectic. Then follow the four upper arts, called the quadrivium. They include arithmetic, geometry, music, and astronomy.

The important point here is that music for the Greeks and the wider classical tradition was not so much understood as something performed, composed, practiced, or played; rather, music was interpreted as a mathematical discipline that sought to discover and formalize the symmetrical relations between sounds.6 It was an integral component to the mathematical disciplines that comprised the quadrivium: arithmetic, geometry, music, and astronomy. For the classical mind, arithmetic revealed “number in itself,” geometry revealed “number in space,” music revealed “number in time,” and astronomy revealed “number in space and time.” In this sense, music was an integral part of the Greek educational curriculum which functioned as a metaphor for this whole cosmic chain of interrelationships and harmonies. Indeed, Plato could say: “The whole choral art is also in our view the whole of education” (Laws, Bk II). The Greeks understood the nature of reality and its systems of relations in musical terms.

People are like triangles. They differ and match like triangles, and no matter how different their angles are, the sum will always be 180 degrees. While building our personal geometry, the first angle is for science, the second for art, and the third is for expression and communication.

Passyunk Avenue (pronounced pashunk by the locals) cuts a rude swath across an otherwise orderly grid of streets in South Philadelphia. Except for Passyunk (and Moyamensing) Avenue, the neighborhood is composed of a uniform matrix of numbered and named streets—one big street followed by two little streets. Viewed on a map, they form ninety-degree angles and predictable intersections. Passyunk Avenue, or simply Passyunk, is the great disruptor of this comforting geometry. Irregular and meandering, its slashing path intersects with the more obedient byways. Together they form a unique gridwork of inconvenient crossings and odd angles. The cumulative result is one of strangely shaped buildings. Their pointy corners puncture curious cells of dead space—the spaces between. While born of necessity, the resulting architecture created by these acute angles also manages to be strangely beautiful, an exotic visage in a sea of pretty faces. If you’ve ever seen the famous photo of Sophia Loren giving the side-eye to Jayne Mansfield, that’s Passyunk—South Philly’s middle finger to white bread Center City.

Bella inspired this book through a series of questions and conversations that circled around how people live together. Growing up on Maui (and in California), she has observed the challenges of food production, housing, global economies, and environmental losses. She has watched people lose their options, and people fall through the cracks in systems. As a father, it is emotionally cutting to see pain and heartbreak in your daughter's eyes, to witness her start to realize social equations do not calculate toward equity. Her brilliance across these conversations has been the ever-present solutions, her ingenuity and moxie, and the art for creating visions for change. She inspires me to be more present with each choice that circles around her future.

All greek civilization is a search for bridges to relate human misery and divine perfection. Their art, which is incomparable, their poetry, their philosophy, the sciences which they invented (geometry, astronomy, mechanics, physics, biology) are nothing but bridges.

Art is not construction, artifice, meticulous relationship to a space and a worldnexisting outside. It is truly the "inarticulate cry,* as Hermes Trismegistus said, "which seemed to be the voice of the light." And once it is present it awakens powers dormant in ordinary vision, a secret of pre-existence. When through the water's thickness I see the tiling at the bottom of a pool, I do not see it despite the water and the reflections there; I see it through them and because of them. If there were no distortions, no ripples of sunlight, if it were without this flesh that I saw the geometry of the tiles, then I would cease to see it as it is and where it is—which is to say, beyond any identical, specific place. I cannot say that the water itself—the aqueous power, the sirupy and shimmering element—is in space; all this is not somewhere else either, but it is not in the pool. It inhabits it, it materializes itself there, yet it is not contained there; and if I raise my eyes toward the screen of cypresses where the web of reflections is playing, I cannot gainsay the fact that the water visits it, too, or at least sends into it, upon it, its active and living essence. This internal animation, this radiation of the visible is what the painter seeks under the name of depth, of space, of color.

Varro produced an influential encyclopaedia, Nine Books of Disciplines, in which he outlined nine arts: grammar, rhetoric, logic, arithmetic, geometry, astronomy, musical theory, medicine and architecture. Later writers omitted the last two arts.79 In Rome, by the end of the first century AD, education had been more or less standardised and the seven liberal arts identified. In turn, these would become the basis of medieval education,

It's strange. With all this harmonious interplay of numbers you would have expected the whole system to be a precisely coherent whole. It isn't. There are echoes here from the scientific view of a world formed by broken symmetry, subject to quantum uncertainty and (so far) defying a precise comprehensive 'theory of everything'. Is this why the 'near miss' is so often more beautiful than perfection?

If you kept on spiraling you would eventually discover, as the Chinese did long ago, that 53 perfect fifths (or Lu) almost exactly equal 31 octaves. The first five fifths produce the pattern of the black notes on a piano, the Eastern pentatonic scale.

Music shapes and shivers into endless colours, nuanced and diverse, and eternally creative. It is Spirit taking form.

The ordering of knowledge has changed with the centuries. All knowledge was once ordered in relation to the seven liberal arts— grammar, rhetoric, and logic, the trivium; arithmetic, geometry astronomy, and music, the quadrivium. Medieval encyclopedias reflected this arrangement. Since the universities were arranged according to the same system, and students studied according to it also, the arrangement was useful in education. [How to Read a Book (1972), P. 180]

3D Character Modeling & low poly game character by 3D Game Art Studio Low poly game character are three-dimensional models based on a small number of polygons. An important condition is that this amount is enough to understand what the visualizer wanted to demonstrate. Since one of the relevant areas where 3d low-poly character developers are involved in the gaming industry, consider the process of work on the example of creating a Game Character Modeling Services. Work on other low poly character is similar. Each game must be unique in its own way. Character Modeling is the process of creating a character within the 3D space of computer programs. The techniques for character modeling are essential for third - and first - person experiences within film, animation, games, and Virtual Reality. It is important to bear in mind that low poly objects have less definition and are made with fewer polygons, spheres, cylinders, or cubes. By using flat lighting, the models will get the desired flat-shaded blocky look. low poly modeling requires a high degree of creativity, as you need to make the most of limited resources to create complex compositions. It has the power of simplicity. Low poly character also has its uses. The most important use is game engines since a computer can only handle many polygons in real time. Low poly keeps everything as low as possible applying normal mapping everywhere. Other uses of low poly include: • Subdivision modeling • Low-polygon proxy geometry for animating and rigging • Low poly style High poly character are preferable in Movie Character Modeling for the film industry since a large number of polygons are needed there for optimal detail. However, their 3d Rendering & Animation can sometimes take several days. But for games, low-poly character are often used: visualization of 3D characters is carried out directly in the course of the game process. GameYan Studio is a Game Development and Movie Animation company offer an animation 3D Character Modeling Services with a wide range of 3d character design services and animation with a specialized team of highly skilled designers & animators are having a capable to transform any characters to virtually animated characters. GameYan Studio is one stop solution for 3D Character Development - 3D Modeling Company. Whether you have concept or not, our creative team can convert your visualization into Sketches and 3d Character Modeling Design. We can deliver the final model with specific technical requirement like Low Poly, High Polygons and many technical detail will be follow by our 3d artist in realistic game character.

As time passes, what was once an unpredictable step sideways becomes a definitive step forward for art.

Art needs to be imaginatively undressed in order to be appreciated, and so does the world.

Mathematics, after all, lives on unambiguous exactitude, whereas there are types of art that die of it.

At about the same time that St. Augustine lived, the Roman jurists ruled, under the Code of Mathematicians and Evil-Doers, that “to learn the art of geometry and to take part in public exercises, an art as damnable as mathematics, are forbidden.

The art of making pictorial statements in a precise and repeatable form is one that we have long taken for granted in the West. But it is usually forgotten that without prints and blueprints, without maps and geometry, the world of modern sciences and technologies would hardly exist. In the time of Ferdinand and Isabella and other maritime monarchs, maps were top-secret, like new electronic discoveries today. When the captains returned from their voyages, every effort was made by the officers of the crown to obtain both originals and copies of the maps made during the voyage.

The art of making pictorial statements in a precise and repeatable form is one that we have long taken for granted in the West. But it is usually forgotten that without prints and blueprints, without maps and geometry, the world of modern sciences and technologies would hardly exist. In the time of Ferdinand and Isabella and other maritime monarchs, maps were top-secret, like new electronic discoveries today. When the captains returned from their voyages, every effort was made by the officers of the crown to obtain both originals and copies of the maps made during the voyage. The result was a lucrative black-market trade, and secret maps were widely sold. The sort of maps in question had nothing in common with those of later design, being in fact more like diaries of different adventures and experiences.

Collision is when you have one shape crashing into another. Like with Ultra Magnus. With Ultra Magnus we have the original design with these giant shoulders so when he lifts his arm up, that giant shoulder is going to crash to his head and in CG that thing will just go right through it, so we have to figure out ways around that. We had comments from our CG studio on our storyboards where they'll say "Breakdown will fold his arms" and they'll say, "Well he can't do that because his chest comes out this far." So those physics and geometry have to function. -Jose Lopez