Euclidean Geometry is a type of geometry created about 2400 years ago by the Greek mathematician, Euclid. Euclid studied points, lines and planes. The discoveries he made were organized into different theorems, postulates, definitions, and axioms. The ideas came up with were all written down in a set of books called Elements. Not only did Euclid state his ideas in Elements, but he proved them as well. Once he had one idea proven, Euclid would prove another idea that would have to be true based on what he had just discovered. Euclid was the first person to create this type of mathematical deduction. Out of all the mathematical discoveries Euclid made, one of the most famous would have to be the parallel postulate. The parallel postulate states that there is only one line that can be drawn through a point so that is parallel to another line not containing that point. To this day, the ideas that Euclid proposed are still relevant and taught in classrooms everywhere.
Non-Euclidean Geometry is any type of geometry that is different from Euclidean Geometry. It contains a postulate (axiom), which is equivalent to the negation of the Euclidean parallel postulate, and usually involves a consistent system of definitions, assumptions, and proofs that describe objects such as points, lines and planes. It can also be defined as the study of shapes and constructions that do not map directly onto any n-dimensional Euclidean system. There are many different forms of it, including spherical geometry and hyperbolic geometry, which are the most common two. The main difference between Euclidean geometry and all non-Euclidean geometries is the nature of parallel lines, as non-Euclidean geometry does not follow the parallel postulate.
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Bogomolny, Alexander. "Euclid's Fifth Postulate." Cut the Knot. N.p., n.d. Web. 21 May 2014. .
Bogomolny, Alexander. "Non-Euclidean Geometrie." Cut the Knot. N.p., n.d. Web. 21 May 2014. .
Castellanos, Joel. "3: What Is Non-Euclidean Geometry." NonEuclid: 1: Non-Euclidean Geometry. N.p., n.d. Web. 21 May 2014. .
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Roberts, Donna. "Euclidean and Non-Euclidean Geometry." Euclidean and Non-Euclidean Geometry. Oswego City School District Regents Exam Prep Center, n.d. Web. 21 May 2014. .
Euclid propositions can be called theorems in common language. In the Book I Euclid main considerations was on geometry. He began with a long list of definitions which followed by the small number of basic statements to take the essential properties of points, lines, angles etc. then he obtained the remaining geometry from these basic statements with proofs. (Berlinghoff, 2015, p.158).
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
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.
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.
By the time Euclid's Elements appeared in about 300 BC, several important results about primes had been proved. In Book IX of the Elements, Euclid proves that there are infinitely many prime numbers. This is one of the first proofs known which uses the method of contradiction to establish a result. Euclid also gives a proof of the Fundamental Theorem of Arithmetic: Every integer can be written as a product of primes in an essentially unique way.
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.
Cheney, Sheldon. The Age of Reason In Greece: Pythagoras and Plato. Baltimore,Md: Kessinger Publishing, 2008.
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
Introduction to online 3 dimensional shapes. In geometry, the three dimensions are known as length, width and height or any three perpendicular directions can act as 3D. The basic three-dimensional shapes are listed below. Online students can get the help about three dimensional shapes.
There is a triangle called the Heronian triangle. It has area and side lengths that are all integers. The Heronian triangle is named after the great hero of Alexandria. The term is sometimes applied more widely to triangles whose sides and area are all rational numbers. An Isosceles triangle is a triangle that has two sides of equal length. Sometimes is specified as having two and only two sides of equal length. Triangles are polygons with the least possible number of sides, which is
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...
Euclid, also known as Euclid of Alexandria, lived from 323-283 BC. He was a famous Greek mathematician, often referred to as the ‘Father of Geometry”. The dates of his existence were so long ago that the date and place of Euclid’s birth and the date and circumstances of his death are unknown, and only is roughly estimated in proximity to figures mentioned in references around the world. Alexandria was a broad teacher that taught lessons across the world. He taught at Alexandria in Egypt. Euclid’s most well-known work is his treatise on geometry: The Elements. His Elements is one of the most influential works in the history of mathematics, serving as the source textbook for teaching mathematics on different grade levels. His geometry work was used especially from the time of publication until the late 19th and early 20th century Euclid reasoned the principles of what is now called Euclidean geometry, which came from a small set of axioms on the Elements. Euclid was also famous for writing books using the topic on perspective, conic sections, spherical geometry, number theory, and rigor.