euclid's 5th postulate

A detailed Summary of euclid's 5th postulate

One of the most fascinating aspects of Mathematics is that there exist statements that are both true and false. Perhaps the most famous of these is Euclid's controversial fifth postulate. Throughout history, almost from the postulate conception, mathematics have tried to prove or disprove it. Actually, it seems that even Euclid himself did not entirely trust the postulate, for he avoided using it as long as he could in his great work, The Elements.

From the beginning, Euclid's fifth postulate, also called the parallel postulate stood out from among Euclid's other postulates. The first four postulates are short, brief, and to the point, whereas the fifth is longer and rather strange sounding. The postulates are listed in The Elements as such:

1. To draw a straight line from any point to another.

2. To produce a finite straight line continuously in a straight line.

3. To describe a circle with any center and distance.

4. That all right angles are equal to each oth

Clearly there are dissimilarities between the last and the first four, as Euclid must have been aware, mainly in the length of the postulate. In any case, mathematicians of the time, seeing that there was something strange about this parallel postulate set out to prove it by using only the first four postulates.

At the same time, in Russia, Lobaschevsky published a work on this alternate geometry in 1829. His work did not receive wide recognition, though, and he developed his theory a great deal more before it did so. In the Bolyai-Lobaschevian model, there are two lines which pass through a point not on a line parallel to that line. Similarly, Riemann, who studied under Gauss, mentioned a theory of spherical geometry in a lecture which was not published until after his death. In this geometry, no parallels are possible. It was at this time that mathematicians realized that the mystery of parallel lines would never be solved satisfactorily. Today, there are two main classes of geometry: Euclide

Some common words found in the essay are:
Actually Euclid, Needless Greek, Similarly Riemann, Fifth Postulate, Russia Lobaschevsky, Euclidean Gauss, Bolyai-Lobaschevsky Reimann, Euclidean Geometry, Janos Bolyai, fifth postulate, parallel postulate, straight line, Euclidean Non-Euclidean, euclid's fifth postulate, euclid's fifth, geometrical world, true false, geometry euclidean, parallel lines, angles angles,

Approximate Word count = 680
Approximate Pages = 3 (250 words per page double spaced)

Category: Miscellaneous

join now Save Paper

Saved Paper

Save your papers so you can locate them quickly!

Newest Essays

Testimonials

"Thank You So Much!!! You have saved me once again!!!"
Jack M.
"With so many papers to chose from, I was able to get ideas to help me with all of my classes. Thank You!"
Brian P.
"I've used this site for the last 3 years to help me come up with ideas for my papers."
Sara J.
"I use this site every week to help me write my own papers!"
Rachel W.
"I love this site!!!"
Marie N.