Geometry, which etymologically means the measurement of the earth in Greek, is a mathematical concept that deals with points, lines, shapes, and space. It has been developed from pre-historic era with ancient Greeks and Egyptians, and is still used in the area of art, architecture, engineering, geology, and astronomy. In ancient societies, while the ancient mathematicians or philosophers such as Plato, Pythagoras, Thales, and Aristotle expanded the different areas of math, philosophy, and science, Euclid, who is also known as ‘the Father of Geometry,’ has greatly influenced the study of geometry over 2000 years.
Euclid of Alexandria (Circa B.C. 300), although the historic information of his life is almost unknown, his contributions to the area of geometry are very significant. He is well-known for the books ‘Stoicheia’, ‘Optics’, and study of catoptrics, conics, geometrical distances and vectors. Especially, his thirteen books of the treatise ‘Elements (Stoicheia)’ has defined the most area of geometry and later divided the geometry as Euclidean and non-Euclidean. The book of Elements discusses plane geometry (books I-IV and VI), number theory (V and VII-X), and solid geometry (XI-XIII). Amongst all thirteen books of the treatise, the most well-known topics are the Euclidean algorithm and the five axioms, or postulates. Regarding the Euclid’s Elements, British mathematician Russell claims “Elements is the one of the greatest books ever written, and one of the most perfect monuments of the Greek intellect” (211) to show the remarkable intellectuality of the book.
The Euclidean algorithm is described in two books of the Elements, VII (7) and X (10), and it discusses the computing of the greatest common factor of two positive intege...
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...he king found it very difficult to learn geometry, he asked Euclid for an easier way to master geometry. According to Robinson, Euclid then answered, “there is no royal road to geometry,” meaning the math can be learned only when the learner voluntarily seeks knowledge and the fact that nothing can change or affect the true nature of mathematics (80). The answer of Euclid becomes popular, and later expands its meaning to “there is no royal road to learning.”
Contributions of Euclid for the various parts of mathematics are numerous, and his knowledge has spread from ancient societies of Egypt to Europe and China. A number of mathematicians or scientists were influenced for millennia. As Euclid is known as ‘the Father of Geometry,’ it is true that his works from pre-historic era has encouraged the human history of mathematics and will still contribute for the future.
Ancient Greece's philosophers and mathematicians have made contributions to western civilizations. Socrates believed that a person must ask questions and seek to understand the world around them. Aristotle, another famous philosopher, is known for believing that if people study the origin of life, they will understand it more. Reasoning is what makes human beings unique. Hippocrates was a mathematician and a doctor. He created the Hippocratic oath. The oath states that Hippocrates will treat his patient to the best of his abilities that he will refuse to give deadly medicine. This oath is still used by doctors today. Another Greek mathematician was Euclid. His ideas were the starting point of geometry, which is still studied around the world today.
Study of Geometry gives students the tools to logical reasoning and deductive thinking to solve abstract equations. Geometry is an important mathematical concept to grasp as we use it in our life every day. Geometry is the study of shape- and there are shapes all around us. Examples of geometry in everyday life are- in sport, nature, games and architecture. The game Jenga involves geometry as it is important to keep the stack of tiles at a 90 degrees angle, otherwise the stack of tiles will fall over. Architects use geometry everyday- it is essential when designing buildings- shape, angles and area and perimeter are some of the geometry concepts architects
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.
Hippocrates taught in Athens and worked on squaring the circle and also worked on duplicating the cube. He grew far in these areas and although his work is not lost, it must have contained much of what Euclid later included in Books One and Two of the Elements.
Margaret Symington was awarded the Trevor Evans Award in 2013 for her article Euclid Makes the Cut. Margaret Symington is an associate professor of mathematics at Mercer University in Macon, Georgia. Her article was one of many issues from Math Horizons vol. 19 on pages six through nine which was published in 2012. “Math Horizons is a vibrant and accessible forum for practitioners, students, educators, and enthusiasts of mathematics, dedicated to exploring the folklore, characters, and current happenings in mathematical culture.” (http://www.maa.org/press/periodicals/math-horizons) Symington tests her readers to study the connection between two unrelated professions fields: geometric topology and dermatologic surgery. The title Euclid Makes the Cut grabbed my attention and the information within in the article was very interesting as well. Even though the title and the information within the article was interesting to me as a Math Major but what about other individuals? I think regardless if you are a Mathematics major or not the subject was worth writing. Symington explains medicine in a mathematical way and it was amazing to read.
Euclidean distance was proposed by Greek mathematician Euclid of Alexandria. In mathematics, the Euclidean distance or Euclidean metric is the distance between two points, which is shown as a length of a line segment and is given by the Pythagorean theorem. The formula of Euclidean distance is a squ...
"The Foundations of Geometry: From Thales to Euclid." Science and Its Times. Ed. Neil Schlager and Josh Lauer. Vol. 1. Detroit: Gale, 2001. Gale Power Search. Web. 20 Dec. 2013.
The concept of impossible constructions in mathematics draws in a unique interest by Mathematicians wanting to find answers that none have found before them. For the Greeks, some impossible constructions weren’t actually proven at the time to be impossible, but merely so far unachieved. For them, there was excitement in the idea that they might be the first one to do so, excitement that lay in discovery. There are a few impossible constructions in Greek mathematics that will be examined in this chapter. They all share the same criteria for constructability: that they are to be made using solely a compass and straightedge, and were referred to as the three “classical problems of antiquity”. The requirements of using only a compass and straightedge were believed to have originated from Plato himself. 1
For the Greeks philosophy wasn’t restricted to the abstract it was also their natural science. In this way their philosophers were also their scientist. Questions such as what is the nature of reality and how do we know what is real are two of the fundamental questions they sought to answer. Pythagoras and Plato were two of the natural philosophers who sought to explain these universal principles. Pythagoras felt that all things could be explained and represented by mathematical formulae. Plato, Socrate’s most important disciple, believed that the world was divided into two realms, the visible and the intelligible. Part of the world, the visible, we could grasp with the five senses, but the intelligible we could only grasp with our minds. In their own way they both sought to explain the nature of reality and how we could know what is real.
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.
Even though Aristotle’s contributions to mathematics are significantly important and lay a strong foundation in the study and view of the science, it is imperative to mention that Aristotle, in actuality, “never devoted a treatise to philosophy of mathematics” [5]. As aforementioned, even his books never truly leaned toward a specific philosophy on mathematics, but rather a form or manner in which to attempt to understand mathematics through certain truths.
Although little is known about him, Diophantus (200AD – 284AD), an ancient Greek mathematician, studied equations with variables, starting the equations of algebra that we know today. Diophantus is often known as the “father of algebra” ("Diophantus"). However, many mathematicians still argue that algebra was actually started in the Arab countries by Al Khwarizmi, also known as the “father of algebra” or the “second father of algebra”. Al Khwarizmi did most of his work in the 9th century. Khwarizmi was a scientist, mathematician, astrologer, and author. The term algorithm used in algebra came from his name. Khwarizmi solved linear and quadratic equations, which paved the way for algebra problems that are now taught in middle school and high school. The word algebra even came from his book titled Al-jabr. In his book, he expanded on the knowledge of Greek and Indian sources of math. His book was the major source of algebra being integrated into European disciplines (“Al-Khwarizmi”). Khwarizmi’s most important development, however, was the Arabic number system, which is the number system that we use today. In the Arabic number system, the symbols 1 – 9 are used in combination to ...
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculator science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry. Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later Abu Abd-Allah ibn Musa al’Khwarizmi, was born abo...