Euclid is referred to as the father of Geometry. He was a Greek Mathematician who is thought to live in the years 330-260 BC. However, the exact date that he was born is not known. At the same time his place of birth is not certain but his works can be easily traced around Greek. His father Naucrates and his grandfather, Zenarchus was thought to be from Damascus but there is no much proof that Euclid was born in this place. He is also known as Euclid of Alexandria (Barnes-Svarney, p. 12). He developed a lot of books that were used at the time for learning mathematics. He put more emphasis on geometry. It is thought that the reason why he advanced in geometry was the fact that Greek numbers system was difficult to understand. For example the system did not have a Zero. There was thus the need to have a way that people could make sense of various facts that in other countries was explained in mathematical numbers. In this paper I will speak about the mathematician Euclid life, his contributions to the math world, besides I will talk about those people who worked alongside him.
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He lived in the period of Ptolemy 1 (323-283 BC). He was a mathematics teacher at Alexandria, Egypt. Alexandria was also called the museums. This is the place that he got the works of other writers and he developed his first book in geometry that has been in use for over 200years. The influential writers were the likes of Thales, Pythagoras, Plato, Eudoxus, Aristotle, Menaechmus. The above writers were in the ancient Egyptian museum, they contributed to the arts and science in the library. They were also teachers in Alexandria (Egypt Hakim, p. 11).
Available evidence shows that he attended Plato’s Academy in Athens. He moved to Alexandria after Plato Academy training in mathematics. Alexandria supported book trade. It is in the city that had the largest library referred to as museum that kept previous works of art and sciences. Ptolemy was the main character in the library. During his stay, he taught in the place and wrote his first book called The Element, there is also some evidence that he established a school and taught in his place and others. The book has over 1000 editions and it is said to be the second most sold book (second to the bible).
The element is divided into thirteen sections each covering a certain area. The dominant topics were topics in Geometry. Among the topics were; plane geometry, arithmetic and number theory, irrational numbers, and solid geometry. He discussed geometry from the basic point of view and expanded it to more complex issues. He organized Geometry axioms (statements that are proved to be true and correct despite the environment that they are exposed to) and theorems, and logical proofs. From the known point of view he was able to demonstrate logically 467 prepositions in both solid and plane geometry. He used a synthetic approach whereby in his entire theorem, he moved from the known to get the unknown. One of the most used and appreciated theorem is the right angled Pythagoras theorem that gives an equation to look for the measurement of a side of a right angled triangle given the other two sides measurement. It is a theorem that has stood the test of time and it is used even today. He developed five common notions, these are facts that are common and true to both arts and sciences they are:
a) If A is Equal to B, and B is equal to C then A is Equal to c
b) If A is Equal to B, and B is equal to C then the sum of A and B is equal to B and C.
c) If equals are subtracted from equals, the remainders are equal.
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d) Things which coincide with one another are equal to one another.
e) The whole is greater than the part.
There are other axioms that are related to geometry only, they are;
f) Any two points can result into a straight line if joined continuously.
g) A line has no end, it can be extended indefinitely. The length of a line is thus defined by the one drawing it. If extended, it never comes to the original place but keeps going.
h) A circle can be drawn employing any line segment (as the radius). This means that if you fix a point and move another with the same length, you come to the same point after having completed a circle.
i) All right angles make a degree of 90 and are equal. This is the same line that he developed Pythagoras theorem. He tested the theorem with numerous triangles of different sizes and shapes but always ensured that they had a 90 degrees angle.
j) A single line can be drawn parallel to the point that is first line. The same axiom stated that two parallel lines can never meet.
The element was translated to various languages by other mathematicians of the time. One of them is Campanus who translated the book from Arabic to Latin. This was in 1482 in Venice. Later in 1570, the book was first translated to English by John Dee (Francis, p. 23). He was also a mathematician. In 1733, there was an Italian who worked hard to look for a single error in The Element, but he was not successful, he then wrote a book which was similar to The Element and named it as” Euclid Cleared of Every Flaw”. After this it took over a century for another book in geometry to be written. That was done by German mathematician David Hilbert in 1899. He called the book “Foundations of Geometry”. Despite the new book, it was seen as a new version of The Element. Other than in geometry he wrote other books like, Data, this contained 94 propositions and optics which he tried to relate the movement of light and geometry. On the other hand, there are numerous books that at the time of his death, he left incomplete. One of the renowned users of the works of Euclid was Abraham Lincoln, former president of United States of America. It is said that he spent a lot of time reading Euclid’s works and had a copy of Euclid’s Elements in his saddlebag (Anderson and Karen, p. 23).
Euclid is credited “The Father of Geometry”; he brought the sense of testing all axioms that are used in either art or science. He went further and portrayed that we can come from the known to get the unknown. He was the first one who developed the theories that are used in geometry at the time even today. All other books that are written on geography have their connection to his works. Geometry on the other hand is an important unit in the field of mathematics and used in almost all other areas of career. For example it is a major unit in engineering courses. It is used to make sense of angles and using the connections that the unit brings out, it solves various issues. At the time of his death, there were a lot of works that was not completed. These works has been developed by others; he laid foundations to them. The book on optics is seen as mathematics cum physics book. It has been used since its development to give sense to other sectors. At Alexandria, he managed to make and teach in a school. This was at a time that mathematics teachers were few, most of his students also assisted in development of mathematics (Calinger, p. 123). Today, one of the unit that is applicable in almost all areas is mathematics, it is through it that major breakthrough in educations has been attained. Mathematics has been seen as a unit that gives solutions to issues that face human race; Credit is thus given to Euclid and earlier mathematicians.
- Anderson, Margaret J. and Karen F. Stephenson. Scientists of the Ancient World. New York: Enslow Publishers, 1999.
- Barnes-Svarney, Patricia, ed. New York Public Library Science Desk Reference. New York: Macmillan, 1995.
- Calinger, Ronald S. Euclid. London: World Book, 2005.
- Francis, Raymond L. The Illustrated Almanac of Science, Technology and Invention. Plenum Press, 1997.
- Hakim, Joy. The Story of Science: Aristotle Leads the Way. Washington: Smithsonian, 2004.