Geometry was thoroughly organized in about 300 BC, when the Greek mathematician Euclid gathered what was known at the time, added original work of his own, and arranged 465 propositions into 13 books, called 'Elements'. The books covered not only plane and solid geometry but also much of what is now known as algebra, trigonometry, and advanced arithmetic.

Through the ages, the propositions have been rearranged, and many of the proofs are different, but the basic idea presented in the 'Elements' has not changed. In the work facts are not just cataloged but are developed in a fashionable way.

Even in 300 BC, geometry was recognized to be not just for
mathematicians. Anyone can benefit from the basic learning of geometry, which are how to follow lines of reasoning, how to say precisely what is intended, and especially how to prove basic concepts by following these lines of reasoning. Taking a course in geometry is beneficial for all students, who will find that learning to reason and prove convincingly is necessary for every profession. It is true that not everyone must prove things, but everyone is exposed to proof. Politicians, advertisers, and many other people try to offer convincing arguments. Anyone who cannot tell a good proof from a bad one may easily be persuaded in the wrong direction. Geometry provides a simplified universe, where points and lines obey believable rules and where conclusions are easily verified. By first studying how to reason in this simplified universe, people can eventually, through practice and experience, learn how to reason in a complicated world.

Geometry in ancient times was recognized as part of everyone's education. Early Greek philosophers asked that no one come to their schools who had not learned the 'Elements' of Euclid. There were, and still are, many who resisted this kind of education. It is said that Ptolemy I asked Euclid for an easier way to learn the material. Euclid told him there...

...line. His decision to create this postulate enabled him to create what is now called, EuclideanGeometry, taking name after him. Not until the 19th century, was this postulate dropped and non-euclideangeometries were beginning to be studied.
Euclid's elements are divided into 13 books. The first six books are based upon just plane geometry. They give out properties of triangles, parallelograms, parallels, rectangles and squares. They also deal with problems with circles, and circles in general. Books seven through nine explain the number theory. In particular book seven is a self-contained introduction to number theory and contains the Euclidean algorithm for finding the greatest common divisor of two numbers. Book eight talks about geometrical progressions. The tenth book explains the theory of irrational numbers. It is mainly based upon the work of Theaetetus. Euclid had to change many of the proofs written by Eudoxus. From book eleven through thirteen, describes the geometries of three-dimensional shapes. More than one thousand editions of this book have been printed since its first edition in 1482. Euclid also wrote many other books. Data, On Divisions, Optics, and Phenomena are all other books that have survived. The ones that have been lost are Surface Loci, Porisms, Conics, Fallacies and Elements of Music.
Euclid has enabled us today, the ability to create and...

...Euclid “Father of Geometry”
Euclid is a Greek mathematician. He was also known as Euclid of Alexandria, “The Father of Geometry”. Little is known of his life other than the fact that he taught at Alexandria, being associated with the school that grew up there in the late 4th century B.C. It is believed that he taught at Plato's academy in Athens, Greece. Most history states that he was a kind, patient, and fair man. One story that exposes something of his personality, involves a student that has just finished his first geometry lesson. The pupil asked what he would gain from learning geometry. Euclid told his slave to get the student a coin so he would be gaining from his studies. Another story says that Ptomlemy asked Euclid if there was an easier way to learn geometry, the mathematician responded, "there is no royal road to geometry", and sent the king to study. Euclid wrote many books such as Data, On Divisions of Figures, Phaenomena, Optics, the lost books Conics and Porisms. He is famous for his Elements, presented in thirteen books of the geometry and other mathematics known in his day. The first six books involve elementary plane geometry and have served as the basis for most beginning courses on this subject. The other books of the Elements take care of the theory of numbers and certain problems in math (on a geometric basis) and...

...Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of a formal mathematical science emerging in the West as early as Thales (6th Century BC). By the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclideangeometry—set a standard for many centuries to follow.[1] Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially mapping the positions of the stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. Both geometry and astronomy were considered in the classical world to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.
History of geometry
The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the...

...2
1[1
Introduction
segment PQ:
In Euclideangeometry the perpendicular distance between the rays
remains equal to the distance from P to Q as we move to the right.
However, in the early nineteenth century two alternative geometries
were proposed. In hyperbolic geometry (from the Greek hyperballein,
"to exceed") the distance between the rays increases. In elliptic
geometry (from the Greek elleipein, "to fall short") the distance decreases and the rays eventually meet. These non-Euclideangeometries were later incorporated in a much more general geometry developed by C. F. Gauss and G. F. B. Riemann (it is this more general
geometry that is used in Einstein's general theory of relativity).1
We will concentrate on Euclidean and hyperbolic geometries in this
book. Hyperbolic geometry requires a change in only one of Euclid's
axioms, and can be as easily grasped as high school geometry. Elliptic
geometry, on the other hand, involves the new topological notion of
"nonorientability," since all the points of the elliptic plane not on a
given line lie on the same side of that line. This geometry cannot easily
be approached in the spirit of Euclid. I have therefore made only brief
comments about elliptic geometry in the body of the text, with further...

...Willingham
Mr. Warfle
Geometry Honors
26 September 2011
Euclidean & Non-EuclideanGeometry Paper
Isn’t it amazing that we still study the same geometry as people did back nearly twenty-three centuries ago? Euclidean and Non-Euclideangeometry communicates to us through mathematical equations immense amounts of significant information. Without the study ofgeometry, many people would be unemployed. Euclidean and Non-Euclideangeometry have several similarities, however they also have numerous differences, as well as their historical aspects.
To begin with, these mathematical concepts have many similarities. For example, both studies of geometry include perpendicular lines, the drawings for these lines may be different, but they still make 90 degree angles. And both geometries are used in physics by thousands of people daily. Euclideangeometry and Non-Euclideangeometries are both hard to grasp and have a lot of theorems and postulates that say a lot about each individual mathematical study. Both have quite a few similarities, but they have even more differences.
Next, there are several differences between Euclidean and Non-Euclideangeometries, such as those in...

...one thing I focus on is “do I understand the material we covered today?” This will allow the material to build itself up in my head, and I will be less stressed come test time.
Research
For my research topic, I wanted to study Isaac Newton. But Mr. Corby wouldn’t let me do this. So I was given a less cool mathematician, Euclid.
Euclid was a Greek mathematician, and was often considered the “father of geometry.” He was born around 330 BC, and he got his training at Plato’s Academy in Athens. He taught mathematics at the Library of Alexandria in Alexandria, Egypt. His most celebrated accomplishment was his drafting of Elements, a volume of 13 works that compiled general geometric knowledge.
Some of the most basic theorems in Elements are: “a point is that which has no part”, “a line is a breadthless (without width) length”, ”the ends of a line are points”, and “a surface is that which has length and breadth (width) only.” All of these definitions appear in the first of 13 books. There are over 150 definitions in these volumes, dealing with both plane and spatial geometry.
Nearly all of these definitions and propositions are still agreed upon the world over, and they are used as tools to teach students the properties of geometric figures.
One of the most important postulates Euclid drafted was the “Pythagorean Theorem”, a relation between the side lengths of right triangles. This theorem is one of the many definitions and proposals...

...Little is know about Euclid, the father of geometry. Records show that he lived somewhere around 300 B.C. He was a Greek mathematician and is probably best known for his work Elements. Since little is known about the personal life of Euclid, it is difficult to do a biography on him.
His chief work, entitled Elements, is a comprehensive essay on mathematics. It includes 13 volumes that entail such subjects as plane geometry, dealing with the properties of flat surfaces and of planar figures, such as the triangle; proportion in general, a particular kind of relation between groups of numbers or quantities; the properties of numbers; incommensurable magnitudes; and solid geometry, branch of geometry that deals with the properties and measurement of geometric figures in three-dimensional space. Some people say that the geometrical sections of Elements were actually rearrangements of Exodus previous work. However Euclid himself is said to have made several discoveries in his Number Theory, which is a branch of mathematics that deals with the properties and relationships of numbers.
Most historians believe Euclid was educated at Athens. His teachers may have included pupils of Plato, who was a philosopher and one of the most influential thinkers in Western philosophy. Euclid thought geometry in Alexandria and opened a school of mathematics there. He also wrote Data, which was a collection of...

...son of Naucrates. Euclid was named after Euclid of Megara, a philosopher who lived one hundred years before him. Not only was Euclid a mathematician and a scientist, he was an author as well.
Euclid’s most well-known writing was a series of books called “The Elements”. The Elements were on subjects like circles, irrational numbers, 3D geometry, plane geometry and number theory. The Elements consist of five postulates and definitions. These books explained simple theories to detailed explanations of what a line is. Although he did not discover most of these he was the first to publish a series about them.
Euclid also wrote “Data”, “which looked at what properties of figures can be deducted when other properties were given.” He wrote “On Divisions” “which looked at constructions to divide a figure into two parts with area of given ratio.” “Optics” “was the first Greek book on perspective”. “Phaenomena” was about mathematical astronomy. Euclid also wrote many other books that were lost in history such as Surface Loci, Porisms, Elements of Music, Conics, and Book of Fallacies.
He is considered to be the father of geometry because of the theories he discussed in his books. Some of which still have not been proven to be true in this day and age. Although there is very little known about Euclid he is also considered to be the greatest math teacher in the world. In fact after he died in 265 BCE his fellow...