Geometry
Geometry was actually first used in ancient Egypt and Babylon at around 2000 BC in both cases. In order for the Egyptians to build such massive structures as the pyramids they had to have made plans for them prior to the actually building, in these plans geometry had to be used. On ancient Babylonian tablets there is evidence that they understood the Pythagorean theorem. The so-called "father" of Geometry is Euclid a Greek mathematician. He wrote The Elements, books of postulates and theorems, which paved the way for modern Geometry.
Five occupations that use Geometry in their daily routine are masonry, carpentry, architecture, engineering, and interior design. Two ways that a mason uses Geometry are in finding out how much material is needed for a job by using area formulas and while brick laying a mason must make sure the bricks are being laid at the correct angles. Two ways that a carpenter uses Geometry are in finding out how much material is used and making sure that corners meet at right angles. Two ways an architect uses Geometry are in drawing blue prints with the help of a protractor and it is widely known that when designing something, if it is "Phi" times as long as it is wide, than it is aesthetically pleasing. As an engineer, you must use Geometry in determining how many degrees the increase of a ramp is also, Pythagorean Theorem is used to determine the lengths of the third sides of triangles. Interior designers need to use geometry constantly, they must use area formulas to see what they can fit on walls and in rooms, and they also use "Phi" to make designs.
Geometry has influenced art in many ways, especially in the creation of new forms or art. Cubism, which led to Surrealism, came about early in the 20th century in France. Artists like Picasso and Geoges Bracque used Cubism, which is penetrating the surface of objects and stressing basic abstract geometric forms that presented the object from many angles simultaneously. Op Art, or optical painting, is a movement in art that was started in the 1960's. It is characterized by geometrical forms that create an optical illusion in which the eye is required to blend the colors at a certain distance. With out using geometric shapes, no work of art would have any order.
According to Roland Shearer (1992) the release of non-Euclidean geometries at the end of the 19th Century copied the announcement of art movements occurring at that time, which included Cubism, Constructivism, Orphism, De Stijl, Futurism, Suprematism and Kinetic art. Most of the artists who were involved in these beginnings of Modern art were directly working with the new ideas from non-Euclidean geometry or were at least exposed to it – artists such as Picasso, Braque, Malevich, Mondrian and Duchamp. To explain human-created geometries (Euclidean, non-Euclidean), it is a representation of human-made objects and technology (Shearer
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
In 1907, Picasso created a new type of art, Cubism. For those who don’t know what cubism is, it captured and exaggerated certain features of a subject. “Cubism is renowned as a groundbreaking artistic movement in and of its own right, yet it also influenced generations of artists to follow, shaping the very history of art.” (Unknown 6) This technique changed art all around the world. It helped people express more depths within a painting. To this day, artists look at Picasso’s pieces for inspiration.“There had been no prior artist to Picasso, who had such an impact on the art world, or had a mass following of fans and critics alike, as he did.” (McConell
Cubism began as an intellectual revolt against the artistic expression of previous eras. Analytical Cubism and Synthetic Cubism are the two main terms used to describe paintings from this movement. In Analytical Cubism, the artist broke down, or analyzed, and then reassembled the observed forms in a mixture of ways. Similarly, in Synthetic Cubism, artists attempted to synthesize or combine imaginative elements into new representational structures. Among the specific elements abandoned by the cubists were the sensual appeal of paint texture and color, subject matter with emotional charge or mood, the play of light on form, movement, atmosphere, and the illusionism that proceeded from scientifically based perspective. Instead, Cubists used an analytic system in order to disjoint and reorganize the three-dimensional subject, which they were painting. In a shallow plane or within many interlocking and usually transparent planes the object would be lost and found again. Usually showing the object from different angles on a two dimensional plane.
His work is mostly famous with his Cubism events. As he enters its twenty-fifth year, Picasso changed his style of painting. It breaks down and reproduces objects in simple geometric shapes. Cézanne, African tribal art and Iberian sculpture would be the inspiration the painter when it turned to Cubism. (Picasso, P. (1970) With the Demoiselles d 'Avignon that this new style explodes in 1907. That same year, he met Georges Braque with whom he develops the power of Cubism. The two work closely together. To address the problem of representing what exists in three dimensions on a two dimensional surface, Braque and Picasso bring a new answer. They replace the usual codes of color, volume and perspective through a system of geometric signs. They will add to it, in a subsequent phase (synthetic cubism), the use of pieces of various materials (sand, paper, metal, wood, fabric, cardboard ...) to avoid falling into abstract art. Picasso abandons Cubism in 1915. (p25) It had been demonstrated that his work had given a big importance in our current historical events and how it was also given a big importance in his times such as in the support of the cubism
This source provided a lot of background information on Euclid and his discoveries. This source gave details about the many geometrical theories of Euclid, as well as his practical geometrical uses. This source also explained how geometry helped Greece a long time ago, and how it is used by many people everyday.
Along with George Braque, Picasso was responsible for the invention of cubism. Cubism is one of the most radical restructuring of the way that a work of art constructs its meaning. Cubism is a term that was derived from a reference made to geometric schemes and cubes. Cubism has been known as the first and the most influential of all movements in twentieth century art . Before Picasso did any cubism paintings, there were works exibititing a raw intensity and violence due to his reading of non western art aligned with European primitivism. This contrasting position provided the dynamic for Picasso’s work. In his paintings such as Mother and Child, Picasso showed the fetishistic and simplifying aspects of primitivism. In his paintings Picasso used bright hues and subdued grays and earth colors. Picasso found out that shapes could have meaning and identities by their arrangement .
The ancient Egyptians and ancient Greeks knew about the golden ratio, regarded as a number that can be found when a line or shape is divided into two parts so that the longer part divided by the smaller part is also equal to the whole length or shape divided by the longer part. The Ancient Greeks and Romans incorporated it and other mathematical relationships, such as the triangle with a 3:4:5 ratio, into the design of monuments including the Great Pyramid, the Colosseum, and the Parthenon. Artists who have been inspired by mathematics and studied mathematics include the Greek sculptor Polykleitos, who created a series of mathematical proportions for carving the ‘perfect’ nude male figurine. Renaissance painters such as Piero della Francesca an...
Euclid, who lived from about 330 B.C.E. to 260 B.C.E., is often referred to as the Father of Geometry. Very little is known about his life or exact place of birth, other than the fact that he taught mathematics at the Alexandria library in Alexandria, Egypt during the reign of Ptolemy I. He also wrote many books based on mathematical knowledge, such as Elements, which is regarded as one of the greatest mathematical/geometrical encyclopedias of all time, only being outsold by the Bible.
The construction phase would not be possible without the knowledge of basic geometry. Points, lines, measurements and angles are often used to lay out the building in accordance to the architect drawings.
There are endless styles and themes in which artists can decide to paint in. Surrealism is a well known art movement that started in the 1900s. Surrealism was created to “change life” said Rimbaud or to “transform the world” said Marx and essentially that’s what it did. By eliminating logic, new boundaries were opened and a new focus was demonstrated by some artists. Surrealism was first seen in writing so this movement didn’t necessarily begin in the art field. But, it did help artists enhance their paintings with dream-like features and this was a form of expression. Along the way, the artists used this to create a spiritual orientation in their artwork. According to Cathrin Klingsöhr-Leroy, the definition of surrealism is “a pure psychic automatism by which it is intended to express, either verbally or in writing, or otherwise, the true function of thought. Thought dictated in the absence of all control exerted by reason, and outside all aesthetic or moral preoccupations.” Artists, at this point, were taking the concept of dreams and fantasy and experimenting with it. They applied it to their artwork creating surrealism.
The foundations of mathematics are strongly rooted in the history and way of life of the Egyptian people, dating back to the fourth millennium B.C. in Egypt. Egyptian mathematics was elementary. It was generally arrived at by trial and error as a way to obtain desired results. As such, early Egyptian mathematics were primarily arithmetic, with an emphasis on measurement, surveying, and calculation in geometry. The development of arithmetic and geometry grew out of the need to develop land and agriculture and engage in business and trade. Over time, historians have discovered records of such transactions in the form of Egyptian carvings known as hieroglyphs.
Physics began when man first started to study his surroundings. Early applications of physics include the invention of the wheel and of primitive weapons. The people who built Stone Henge had knowledge of physical mechanics in order to move the rocks and place them on top of each other. It was not until during the period of Greek culture that the first systematic treatment of physics started with the use of mechanics. Thales is often said to have been the first scientist, and the first Greek philosopher. He was an astronomer, merchant and mathematician, and after visiting Egypt he is said to have originated the science of deductive geometry. He also discovered theorems of elementary geometry and is said to have correctly predicted an eclipse of the sun. Many of his studies were in astronomy but he also observed static electricity. Phythogoras was a Greek philosopher. He discovered simple numerical ratios relating the musical tones of major consonances, to the length of the strings used in sounding them. The Pythagorean theorem was named after him, although this fundamental statements of deductive geometry was most likely first an idea from Egyptian methods of measurements. With the help of his followers he discovered that the earth was a sphere, but he did not believe it revolved around the sun.
Fields that use trigonometry or trigonometric functions include astronomy (especially for locating apparent positions of celestial objects, in which spherical trigonometry is essential) and hence navigation (on the oceans, in aircraft, and in space), music theory, audio synthesis, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound),pharmacy, chemistry, number theory (and hence cryptology), seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering, mechanical engineering, civil engineering, computer graphics, cartography, crystallography and game
The basic of mathematics was inherited by the Greeks and independent by the Greeks beg the major Greek progress in mathematics was from 300 BC to 200 AD. After this time progress continued in Islamic countries Unlike the Babylonians, the Egyptians did not develop fully their understanding of mathematics. Instead, they concerned themselves with practical applications of mathematics. Mathematics flourished in particular in Iran, Syria and India from 450B.C. Major progress in mathematics in Europe began again at the beginning of the 16th Century.