Geometry: Annotated Bibliography

  M.Lichtheim , Ancient Egyptian Literature, University of California Press,1973,1976. Vol.1.pp.23‐27    J.H.Brested, Ancient Records of Egypt, New York,1962,vol,II,pp.8、9  3   J.H.Brested, Ancient Records of Egypt, New York,1962, vol,II,pp.17、18

Egyptian mathematics began as early as 6000 B.C. One thing the Egyptians are known for is taking measurements with their body parts. For example, a cubit was the length from elbow to fingertips and they often used the palm of their hand to measure land and buildings in early Egyptian times. They also used their hands to develop a decimal numeric system based on our ten fingers. This was thought to be the earliest developed base ten number system as early as 2700 B.C. The Egyptians used hieroglyphic symbols to demonstrate their numbers. For example, a vertical line represented a unit, a heel bone represented ten, a coil of rope represented hundreds, and so forth up to powers of a million. However, they did not have a concept of place value,

The Protogeometric and Geometric periods are good examples of such advanced thinking. The beginnings of the Protogeometric period display a distinct interest in mathematical order. During this period, artists decorated vases with circles and symmetrical patterns. As the dominant style changed from Protogeometric to Geometric, this order and precision was amplified. The popular ?circle and semicircle patterns were replaced by linear designs, zigzags, triangles, diamonds, and meanders? (Cunningham, 40). The increased interest in order seems to have been a reflection of the Greek fascination with nature, and man?s relationship to nature.

To the eyes of the modern person, mathematic may be considered as one of complicated courses, but to the eyes of people who lived during the era of medieval or even earlier era, mathematic was used as a technological tool to build or measure. In the past, most of paintings were very flat and unrealistic, whereas modern art is better realistic and stereoscopic. For instance, a typical painting from ancient Egypt displayed flat look which gives lifeless images. People tend to identify this painting with art before perspective. However, long before the Egyptians, people were making less stylized images but more realistic. During the Revolution era linear perspective by Brunelleschi had large influence on the use of mathematics. For example, the

Venezuela.Awards and Distinctions .Seminar on Art and Science, taught by Prof. Victor.Lucena at the Museum of Contemporary Art of Caracas, Venezuela2008

Descartes - 17th Century Mathematics - The Story of Mathematics. (n.d.). Retrieved June 11, 2016, from

Mathematics has always been very prominent in art since the beginning of time. Mathematical tools such as the Golden Ratio and the De Divina Proportione have helped shape the art we know today. Famous artists and mathematicians such as Piero De Francesca, Polykleitos, and M. C. Escher are the founders of the amazing works of art we are familiar with. Even modern day mathematics has given art a new form, with Fractal Art. Without math, some of the art we have today would not exist.

Art work is not only visual it require other senses other than vision. Visual language involve lines, light, value, color, texture and pattern shape and volume, space and time and motion. In art, line usually has length and width unlike in math which only has length. Art has many types of lines for example they can be straight, broad, thin, jagged, and so on. The direction a line is going in can be meaningful. A horizontal line could mean sleep, quiet or inactivity. Vertical lines may imply aspiration and yearning (Lazzari 23). Diagonal line suggest movement because they occur in the posture of running. To understand any specific lines in an art piece you must look at the whole picture. For example in Shoki the Dmon Queller by Utagawa Kunisada

There are many connections that can be made between math, art and how the concept of both are not as black and white as most people think. Two subjects of which that could be compared to the concept are Gabriel's horn aka, Torricelli's trumpet, and The Spiral of Theodorus , The Great Wave.

Ancient Indian mathematicians were very skilful in geometry. They used the knowledge of geometry in other disciplines also. They derived many of the comprehensive conclusions with the help of geometry.

Proportion is the essence of architecture, and its roots can be traced back to even the ancient Egyptian times. The first recorded information about the theories of proportion comes from Pythagoras’s studies on geometry, ratio and the musical scale. This knowledge has been further explored in relation to proportions of things found in nature, such as the discovery of the golden ratio, and the modulation of the parts that make up the human body. This knowledge is documented in Vitruvius’s treatice, De Architectura, which contains valuable information about how architecture was perceived in these ancient times. His ideas of the ideal proportions of greek temples, and its relationship to the modular system of the human body is most evident in the flawless harmony of parts that make up the Parthenon.

As the Greek empire began to spread its sphere of influence into Asia and beyond, the Greeks were smart enough to adopt and adapt useful elements from the societies they conquered. This was as true of their mathematics as anything else, and they adopted elements of mathematics from both the Babylonians and the Egyptians. But they soon started to make important contributions in their own right and, for the first time, we can acknowledge contributions by individuals. Most of Greek mathematics was based on geometry. Although usually remembered today as a philosopher, Plato was also one of ancient Greece’s most important patrons of mathematics. Inspired by Pythagoras, he founded his Academy in Athens in 387 BCE, where he stressed mathematics as a way of understanding more about reality. In particular, he was convinced that geometry was the key to unlocking the secrets of the universe. By the 3rd Century BCE, in the wake of the conquests of Alexander the Great, mathematical breakthroughs were also beginning to be made on the edges of the Greek Hellenistic empire. Alexandria in Egypt became a great centre of learning under the beneficent rule of the Ptolemy’s, and its famous Library soon gained a reputation to rival that of the Athenian Academy. The patrons of the Library were arguably the first professional scientists, paid for their

Throughout the ages science and art have been two different sides of the very same coin. Initially, these two terms were considered to be completely irrelevant and sometimes even as a contraposition to each other. Along with the progress came the understanding that the connection does exist and even more than that – in some way these

The first discipline, Mathematics, as one of the Natural Sciences, can be traced throughout human history. Formally, Mathematics is defined by Merriam-Webster as, “the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations Algebra, arithmetic, calculus, geometry, and trigonometry are branches of mathematics.” (Merriam-Webster, 2017). Generally, the purpose

Since the invention of numbers and counting systems occurred when people started to live together and formed the first human society, mathematical scenes was the link that helped them to form societies and to develop a type of communication system and in a way help them to establish the first trading system which in turn, was the fundamental factor to establish a communication channel with other societies. For example, the article titled “Mathematics in pre-history” says that there is an archeological evidence which describe that they have used some kind of basic mathematics as early as 30, 000 BCE, the article mentions that “bone artifacts where discovered that had use for reckoning time in sequences of numbers that agree with the number of days included in successive phases of the moon”. So, ancient math is an accepted fact, and maybe the first method of counting was just a simple method like adding tow objects, or dividing food among all the family members. Some scholars agree that they started counting by using their hands and fingers, others say scientist say that the early man started counting by using sticks and stones. However, we can only speculate on the effectiveness of these systems, but it is obvious that despite being so simple it was an effective system for them.