Greek Geometry Importance

The creations of Pythagoras were very powerful during the era in which he lived in. He created a community of followers (known as the Pythagoreans) who believed that mathematics was fundamental and ‘at the heart of reality’ (source 1). The people in the society were all proficient mathematicians took mathematics very seriously, to the extent that it was similar to a religion (source 1).

One of Thales’ most renounced findings include his discovery in geometric studies in the area reading the rules of triangles. He came to the conclusion that if the base angles of an isosceles triangle are equal, the sum of the angles of a triangle are equivalent to two right angles. With the application of “geometric principles to life situations, Thales was able to calculate the height of a pyramid by measuring its shadow, and the distance of a boat to the shore, by using the concept of similar triangles” (pg. 5, Muehlbauer). Realizations such as these helped shape the beginning for the formation of natural law based on observations of the world through explanation.

Mathematics and art have always been closely related: Golden ratio, symmetry, proportion and geometry are elements in the art; not surprisingly, many great artists of history have been great mathematicians; they have been supported in mathematics to express reality with an artistic language. By definition geometry comes from the Greek: Ge = earth and Metron = measure. That is, it is the branch of mathematics that studies the measurement of the Earth that is concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs. (Geometry. (2015).

The Greeks made several inventions, most notably in the subject of math, which are still studied today and taught in school. Mathematician Euclid is often credited as the “Father of Geometry” for all his work and studies in this subject, which are compiled in his books called The Elements. He organized known geometrical statements called theorems and logically proved all of them. He proved the theorem of Pythagoras (another Greek mathematician), which stated that the equation (c2 = a2 + b2) is true for every right triangle.

In this time period the Greeks emperors believed and paid lot of money to have astronomers make new discoveries of the planets and stars. Astronomy was a big mixture of knowing how the planets worked and mathematics. As more and more theories began coming to picture, each of them were built off of eachother. These theories also allowed inventions to come to life, some that we even use still today such as the telescope. Even though these theories and inventions are old, they have influenced today's technologies and space science. Just how Newton's theory of gravity was influenced on other great greek astronomers and their studies.

Even though it’s called Ancient Greece, doesn’t mean that all their ideas and lifestyles are ancient. Greeks have influenced lives today in many ways. They are the base of many different creations. Greeks have influenced the world today through education, architecture, government, and many more things. Many people's ideas are still used today and really affect society and how people live.

The author of Journey through Genius, William Dunham, begins this chapter by depicting how mathematics was spurred and developed in early civilizations. Dunham focuses primarily on the works’ and achievements’ of early Egypt, Mesopotamia, and Greece in this section. These ancient societies, as they developed, produced mathematicians such as; Thales, Pythagoras, and Hippocrates, who turned a basic human intuition for space and quantity into applicable everyday mathematics. The primary influences driving the development of early mathematics were the issues of growing civilizations, most notably counting commodities, taxation, and the division of land equally, rather than a pure desire for understanding that is seen in mathematics today. These influences culminated in the development of early arithmetic and geometry.

Ancient egyptians made some of the earliest forms of technology, mathematics was one of the most important form of technology as it

The world of chaos and disorder has become the world of order and harmony. Ever since the ancient Greek times, chaos has been in existence. This led people to start thinking outside of the box. Many people started questioning why somethings were the way they were. As a result many philosophers emerged in the pre-Socratic times.

For Greek thinkers, math was not simply a way to calculate amounts but a way of testing reality and understanding the true nature of the world around them. One of the first great Greek thinkers, Pythagoras is believed to have coined both philosophy and mathematics into one. Early Greek mathematics was influenced by its neighbors, especially Egypt. When the ports of the Nile were open for the first time, important Greek figures such as Pythagoras and Thales visited Egypt. They brought back new knowledge and skills back with them.

Greeks such as Aristotle, Pythagoras, and Hippocrates have left concepts still used in modern science and mathematics. Their ideas laid a basis for future European thoughts and studies in the fields. Their contributions such as the creating the Pythagorean theory, the writing a comprehensive classification of species and the systematizing of medical knowledge would influence the way Europeans thought and studied the world. Hippocrates’ Oath is still sworn by all medical practitioners. The contributions of the Ancient Greeks in science and math built a foundation upon which future Europeans would build and lead to the development of modern

Learning Greek mythology is a part of having a well-rounded education. Many great works of literature, such as Shakespeare or Dickens, refer back to Greek mythology. Because of this, there is no way to truly understand what the greatest authors of all time were saying, without knowing about this topic. Many current idioms refer back to Greek Myths such as, “You hit his Achilles Heel!” or, “You’ve opened Pandora’s Box.” A myth is a story that has significance to a culture, a story that addresses fundamental and difficult questions that human beings ask; who and what am I, where did I come from, why am I here, how should I live, what is the right thing to do, what is the universe, and how did it all begin? While learning about Greek Myths,

Pythagoras, am Ionian Greek mathematician and philosopher during the naturalist period, is known for the creation of the Pythagoreanism movement. Although very little reliable information about him has been written due to the lack of his own writings, he still served as a major contributor to philosophy, religion, and mathematics. Pythagorean thought emphasized personal salvation, reincarnation, numerology, and focused on a strict religious, philosophical, and mathematical regime. Pythagoras also believed in the value and the power of numbers, believing the elements of numbers could be found in all things. He felt a person should study mathematics in an effort to pursue enlightenment and understanding of the world.

     Euclid's most famous work is his dissertation on mathematics The Elements. The book was a compilation of knowledge that became the center of mathematical teaching for 2000 years. Probably Euclid first proved no results in The Elements but the organization of the material and its exposition are certainly due to him. In fact there is ample evidence that Euclid is using earlier textbooks as he writes the Elements since he introduces quite a number of definitions, which are never used such as that of an oblong, a rhombus, and a rhomboid. This book first began the book by giving the definition of five postulates. The first three are based upon constructions. For example, the first one is that a straight line can be drawn between two points. These three postulates also describe lines, circles, and the existence of points and the possible existence of other geometric objects. The fourth and fifth postulates are written in a different nature. Postulate four states that all right angles are equal. The fifth one is very famous. It is also can be referred to as the parallel, the fifth parallel. It states that one and only one line can be drawn through a point parallel to a given line. His decision to create this

Although Euclid (or the school) may have not been first proved by him, (in fact much of his work may have been based upon earlier writings,) he did manage to insert assumptions and definitions of his own to strengthen the various postulates into the form we know today.