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.
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
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.
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.
In the book Practica Geometriae, geometry problems seemed to be his main focus. The book was arranged into 8 chapters with theorems based on Euclid's Elements and On Divisions. One can say that the authors of the books and him worked togetherbecause of the great influence he received from them. Once people found out about Fibonacci being a ge...
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...
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.
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 this reading concentrates mainly on European mathematicians, it is made obvious that they were building and expanding on earlier works. “These questions
“proposition 15, THEOREM: if two straight lines cut one another, the vertical, or opposite, angles shall be equal.” (DOC5) excerpt from the elements, written by Euclid in about 300 B.C. Euclid is the father of geometry. The elements is his most influential book. It serves as a main textbook for teaching mathamatics. Without Euclid and his teachings The towers in New York, the aqueducts of ancient rome wouldn’t be built, and we wouldn’t know why a ball falls because without a good textbook for mathematicians sir Isaac Newton wouldn’t be able to discover the laws of
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.
The simplest forms of equations in algebra were actually discovered 2,200 years before Mohamed was born. Ahmes wrote the Rhind Papyrus that described the Egyptian mathematic system of division and multiplication. Pythagoras, Euclid, Archimedes, Erasasth, and other great mathematicians followed Ahmes (“Letters”). Although not very important to the development of algebra, Archimedes (212BC – 281BC), a Greek mathematician, worked on calculus equations and used geometric proofs to prove the theories of mathematics (“Archimedes”).
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...