# Essay, Research Paper: Euclid

## Mathematics

Free Mathematics research papers were donated by our members/visitors and are presented free of charge for informational use only. The essay or term paper you are seeing on this page
was not produced by our company and should not be considered a sample of our research/writing service. We are neither affiliated with the author of this essay nor responsible for its content. If you need high quality, fresh and competent research / writing done on the subject of Mathematics, use the professional writing service offered by our company.

Euclid is one of the most influential and best read mathematician of all time.

His prize work, Elements, was the textbook of elementary geometry and logic up

to the early twentieth century. For his work in the field, he is known as the

father of geometry and is considered one of the great Greek mathematicians. Very

little is known about the life of Euclid. Both the dates and places of his birth

and death are unknown. It is believed that he was educated at Plato's academy in

Athens and stayed there until he was invited by Ptolemy I to teach at his newly

founded university in Alexandria. There, Euclid founded the school of

mathematics and remained there for the rest of his life. As a teacher, he was

probably one of the mentors to Archimedes. Personally, all accounts of Euclid

describe him as a kind, fair, patient man who quickly helped and praised the

works of others. However, this did not stop him from engaging in sarcasm. One

story relates that one of his students complained that he had no use for any of

the mathematics he was learning. Euclid quickly called to his slave to give the

boy a coin because "he must make gain out of what he learns." Another

story relates that Ptolemy asked the mathematician if there was some easier way

to learn geometry than by learning all the theorems. Euclid replied, "There

is no royal road to geometry" and sent the king to study. Euclid's fame

comes from his writings, especially his masterpiece Elements. This 13 volume

work is a compilation of Greek mathematics and geometry. It is unknown how much

if any of the work included in Elements is Euclid's original work; many of the

theorems found can be traced to previous thinkers including Euxodus, Thales,

Hippocrates and Pythagoras. However, the format of Elements belongs to him

alone. Each volume lists a number of definitions and postulates followed by

theorems, which are followed by proofs using those definitions and postulates.

Every statement was proven, no matter how obvious. Euclid chose his postulates

carefully, picking only the most basic and self-evident propositions as the

basis of his work. Before, rival schools each had a different set of postulates,

some of which were very questionable. This format helped standardize Greek

mathematics. As for the subject matter, it ran the gamut of ancient thought. The

subjects include: the transitive property, the Pythagorean theorem, algebraic

identities, circles, tangents, plane geometry, the theory of proportions, prime

numbers, perfect numbers, properties of positive integers, irrational numbers,

3-D figures, inscribed and circumscribed figures, LCD, GCM and the construction

of regular solids. Especially noteworthy subjects include the method of

exhaustion, which would be used by Archimedes in the invention of integral

calculus, and the proof that the set of all prime numbers is infinite. Elements

was translated into both Latin and Arabic and is the earliest similar work to

survive, basically because it is far superior to anything previous. The first

printed copy came out in 1482 and was the geometry textbook and logic primer by

the 1700s. During this period Euclid was highly respected as a mathematician and

Elements was considered one of the greatest mathematical works of all time. The

publication was used in schools up to 1903. Euclid also wrote many other works

including Data, On Division, Phaenomena, Optics and the lost books Conics and

Porisms. Today, Euclid has lost much of the godlike status he once held. In his

time, many of his peers attacked him for being too thorough and including

self-evident proofs, such as one side of a triangle cannot be longer than the

sum of the other two sides. Today, most mathematicians attack Euclid for the

exact opposite reason that he was not thorough enough. In Elements, there are

missing areas which were forced to be filled in by following mathematicians. In

addition, several errors and questionable ideas have been found. The most

glaring one deals with his fifth postulate, also known as the parallel

postulate. The proposition states that for a straight line and a point not on

the line, there is exactly one line that passes through the point parallel to

the original line. Euclid was unable to prove this statement and needing it for

his proofs, so he assumed it as true. Future mathematicians could not accept

such a statement was unproveable and spent centuries looking for an answer. Only

with the onset of non- Euclidean geometry, that replaces the statement with

postulates that assume different numbers of parallel lines, has the statement

been generally accepted as necessary. However, despite these problems, Euclid

holds the distinction of being one of the first persons to attempt to

standardize mathematics and set it upon a foundation of proofs. His work acted

as a springboard for future generations.

0

1

**Good or bad? How would you rate this essay?**

Help other users to find the good and worthy free term papers and trash the bad ones.

Help other users to find the good and worthy free term papers and trash the bad ones.

# Get a Custom Paper on Mathematics:

**Free papers** will not meet the guidelines of your specific project. If you need a custom **essay on
Mathematics: **, we can write you a high quality authentic essay. While **free essays** can be traced by Turnitin (plagiarism detection program),
our **custom written papers** will pass any plagiarism test, guaranteed. Our writing service will save you time and grade.

## Related essays:

2

0

**Mathematics**/ Fractals

The videotape "Fractals" was narrated by a writer of science fiction,
R.C. Clark, who is the creator of 2001 Space Odessy. Individuals interviewed,
experts on the subject included professor...

15

0

**Mathematics**/ Infinity

Most everyone is familiar with the infinity symbol, the one that looks like the
number eight tipped over on its side. Infinity sometimes crops up in everyday
speech as a superlative form of the word ...

2

1

**Mathematics**/ Looks Can Be Deceiving

Paradoxes are sometimes composed of contradictory ideas presented together,
ultimately leading to an unworkable situation. Paradoxes, however, are not
simply ambiguous questions. Paradoxes are the es...

4

1

**Mathematics**/ Modular Arithmetic

Modular arithmetic can be used to compute exactly, at low cost, a set of simple
computations. These include most geometric predicates, that need to be checked
exactly, and especially, the sign of det...

7

4

**Mathematics**/ Pascal`s Triangle

Blasé Pacal was born in France in 1623. He was a child prodigy and was
fascinated by mathematics. When Pascal was 19 he invented the first calculating
machine that actually worked. Many other people ...