Euclid Of Alexandria may be the best-known mathematician of the world, he is best known for his work on mathematics The Elements. The fact that his work has survived so long, 2000 years in fact, is a tribute to his mathematical genius, however very little of him is known. Three theories abound as to the true nature of this historical figure. Not all historians agree that Euclid was in fact a historical figure, some argue that the school in Alexandria took up the name Euclid to publish their works. But the more accepted theories are that Euclid was in fact a real historical figure who may have been the leader of a team of mathematicians.
In Euclid’s first postulate he states that it is possible to draw a straight line from any point to any
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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.
The Elements begins with the five postulates and their definitions, these postulates prove or define the existence of points, lines and circles and from there on go to define other aspects of geometry based upon the simpler concepts. The Elements consists of thirteen books. Some assumptions are not totally provable, such that there is only one straight line between two points. Euclid makes some assumptions that make his form of mathematics, Euclidean Geometry, sometimes at odds with other forms. His fifth postulate, states that only one line can be made through a point parallel to a given line, eventually, sometime during the 19th century this postulate was dropped in an attempt to study non-Euclidean geometries.
Euclid’s assumptions about his postulates have set the groundwork for geometry today. He provided society with definitions of a circle, a point, and line, etc and for 2000 was considered “the father of geometry.” His postulates proved to be a framework from which mathematics was able to grow and evolve, from two thousand years ago, till Newton and even to all our classrooms today.
Bibliography
1. Heath, Sir Thomas.
your eyes to see this helped with the creation of geometry.A specific principle that Da
According to Theorem 2, a line and a point not on the line determine a unique plane. As stated in the last paragraph, there are at least two points on a line. In this case, they can act as a segment on the line. The point not on the line will act as a vertex to which the other points connect. These lines will form a plane.
Thus, because these ideals do not exist in the visible world, yet mathematicians still intellectually understand that these concepts exist; objects such as perfect circles must only exist in their true form in the real world (Viera). Concepts such as perfect circles substantiate the claims about reality that Plato illustrates in the “Allegory of the
For example, exact calculation of the Earth boundary “the distance around a circle or sphere”. He calculated this hard mathematic by using his normal and simple trigonometry and geometry knowledge by finding Earth as globe in space. During his time most Greek researcher Aristotle about (384-22 BCB) believed that the Earth is a globe, but none of was not sure that how big the Earth was. The entire Greek researcher observed that liners gone over the horizon while their poles were still noticeable. By this process Greek researcher know that the Earth is sphere. Also they had seen some changing movement position of all the stars in the big sky. He wrote few books that become very popular during that time, one of was named Catasterisms that about the constellation. This book was very helpful to find the story and description about each of the constellation, also it helps to count all the starts was included in it. But there were some confusion about his work which found by some scholars. From the Greek geographer’s books, he was showing his geographical skill and his all mathematical work was from the writing of the Pappus of Alexandria who was Greek geometer. He also wrote some books on geometry and arithmetic. However, he reported that his works was duplicating those were the cube and Sieve of Eratosthenes. It was a method for finding all the prime numbers. He not only wrote some books but also some literary critic, one of most common was “On the Old Comedy” that still available and it
Abstract— Today we use many concepts passed down from generation to generation to solve our physics, mathematics and other general problems. We use concepts that originated in the minds of great mathematicians such as Newton, Leibniz, the Bernoulli family of mathematicians and many others. In the 18th century we find the mathematicians started to structure and format the way we prove solutions. These mathematicians started creating the laws that govern our work and how we go about solving daily problems. During this time we saw the development of calculus and a great deal of progress in the fields where quantities vary such as physics, astronomy, and medicine using these new formats. This paper focuses on the life of Leonhard Euler, a
Pythagoras was a known as many things, a Greek philosopher, mathematician, a man of science, and the Pythagorean theorem. Pythagoras proved the Pythagorean theorem, but did not discover it, Babylonians and Indians discovered it before Pythagoras. It took five centuries after his death before the Pythagoras Theorem associated his name, this was because Plato’s followers said it was a myth two centuries after the death of Pythagoras making people not believe it was a possible theory. It was first published in the writings of Cicero and Plutarch (two well-respected writers of their time).
Calinger, Ronald (1999). A Contextual History of Mathematics. Prentice-Hall, 150. ISBN 0-02-318285-7. “Shortly after Euclid, compiler of the definitive textbook, came Archimedes of Syracuse (ca. 287–212 B.C.), the most original and profound mathematician of antiquity.”
The most common thing people associate the mathematician Pythagoras with is the Pythagorean Theorem that describes the relationship of the the sides of a right triangle, which is a^2 + b^2 = c^2. Some know him as the first pure mathematician. (Mastin, 2010) His teachings come before other famous philosophers and thinkers, such as Plato and Aristotle. Who is Pythagoras and how did he impact the mathematical world of geometry? In order to answer the previous question, there must be an understanding of who he was, what his teachings were, and how his teachings are applied today.
Ptolemaeus gave credit to those who came before him and laid the foundation for his work. People and geniuses such as Aristole, Hipparchus, Menelaus of Alexandria, and Theon of Smyrna, were some of his inspirations. “Ptolemy’s table of the lengths of chords in a circle is the earliest surviving table of a trigonometric function. He also applied fundamental theorems in spherical trigonometry (apparently discovered half a century earlier by Menelaus of Alexandria) to the solution of many basic astronomical problems”- (Jones 2017). Ptolemy justified the former lie that everything revolved around the earth. He used Aristotle’s earth centered theory to defend this.“In particular he introduces trigonometrical methods based on the chord function Crd (which is related to the sine function by sin a = (Crd 2a)/120). Ptolemy devised new geometrical proofs and theorems. He obtained, using chords of a circle and an inscribed 360-gon, the
The term mathematics was invented by Pythagoras. It means that which is learned. In turn, mathematical theories were applied to building the great architecture of Greece. The great Greek temples are visual representations of the mathematical and aesthetic theories of their day. Today, our modern skyscrapers are designed in the image of the great Greek Columns.
Pythagoras of Samos, son of Mnesarchus and Pythias born 570 BCE in Samos Ionia was a Greek Philosopher, Mathematician and the founder of Pythagorean brotherhood. Although religious in nature , the Pythagorean brotherhood formulated principles that influenced the thought of Plato and Aristotle and contributed to the development of mathematics and Western rational philosophy. Pythagoras was classified as the first “true” mathematician. The contributions he made were noticeably important to the people today. But he also remained a controversial figure. Some historians say that Pythagoras was married to a woman named Theano and had a daughter Damo, and a son named Telauge. Pythagoras as a teacher and taught Empedocles. Others say that Theano was
Ancient Greeks contributed many ideas and methods for calculating mathematical equations, both in Geometry and in Algebra. In the centuries before the birth of Jesus Christ, a man named Euclid made great strides in Geometry, proving what we now know as Euclidean Geometry. This field of Geometry deals solely with flat space, also referred to today as two-dimensional space and the geometrical theorems and proofs associated with such. Euclidean Geometry is now the foundation of most 21st century Geometry curricula. In addition, Greek mathematician Pythagoras created and proved the Pythagorean Theorem, which contributes to both Algebra and Geometry as we now know it. The Pythagorean Theorem states that the two leg
The Greek Philosopher Empedocles is a part of the Pre-Socratic (philosophers before Socrates). He is best recognized for describing the four building blocks that construct the universe. His way of explaining elements were depending on the mixture and the combination of fire, air, earth, and water (page 128) all matter was made from these four building blocks. Aristotle developed the 4 building block theory by comparing the four elements with -hot, moist, cold,
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
Because of the prominent place Greek geometric constructions held in Euclid's Elements, these constructions are sometimes also known as Euclidean