User:Euclidmathproject-wjhs
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[edit] Notes on Euclid of Alexandria
- there's a crater named after him (suitably named Euclides)
- (taken from article Euclid Biography at [1]):
"Euclid's most famous work is his treatise on mathematics The Elements. The book was a compilation of knowledge that became the centre of mathematical teaching for 2000 years. Probably no results in The Elements were first proved by Euclid but the organisation 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."
- The Elements begins with definitions and 5 postulates
- postulate: a basic assumption that is accepted without proof. It's a starting assumption (considered true) from which other statements logically come from. Some are experimental facts, while others aren't based on anything.
- he based all of his plane geometry on the following 5 postulates:
- A line (segment) can be drawn from any point to any other point. A •-----• B
- A line (segment) can be extended continuously in a straight line. ◄------------►
- A circle may be drawn with any center and distance (radius). - All right angles are equal to one another.
- Through a given point not on a given line exactly one line can be drawn parallel to a given line. (this one's the most complicated)
[edit] Elements
- The first six books deal with plane geometry:
-Books 1 & 2: explain basic properties of triangles, parallels, parallelograms, rectangles, and squares -Book 3: studies properties of the circle - Book 4: deals with problems about circles -Books 5 & 6: (don't really understand)
- Books 7-9 deal with the number theory (which is a branch of math that investigates relationships and properties of numbers):
-Book 7: intro to number theory, contains the Euclidean Algorithm (?) for finding the greatest common divisor of two numbers -Book 8: deals with numbers in geometrical progression (*A geometric progression is a sequence in which each number is the same multiple (the common ratio) of the previous one. As for example: 3, 6, 12, 24, 48, ...)
[edit] When did he live?
[edit] What did he invent/discover?
- he proved that there are infinitely many prime numbers
- developed first set of geometric axioms/postulates
- using deductive reasoning from other already existing axioms/postulates, came up with new theorems. (deductive reasoning: using already existing axioms/postulates, logically coming up with new ideas which are based upon those axioms/postulates)
- introduced notions of axiom and theorem
- one of the best demonstrations of pure logic and reasoning ever
- his vast collection of terms and their definitions are "the solutions to questions that many scholars have been trying to figure out for their whole lives."(Euclid, 1999 Grolier Inc.)
- since he was a very good teacher, his Elements is a book that clearly demonstrates, proves, and perfected ideas introduced before him
- the Elements was very comprehensive
- Euclid considered father of geometry
[edit] Where was he born?
He was probably born in Megara. Some say he was born in Tyre.
[edit] What kind of social life did he have?
- had no wife, no kids, and was totally devoted to his studies
[edit] Did he work alone?
[edit] What was his education
It's very probable that he studied in Plato's Academy in Athens (because he knew so much on the geometry of Eudoxus and Theaetetus, Greek mathematicians who also contributed to the Elements ).
[edit] Influence
- ranked 13 in Michael Halt's Most Influential Persons in History
- Elements used as basis for geometric curriculums for over 2000 years
- most of Euclid's works are used in public schools today
- his works have led to further discoveries and thoughts based on Euclid's works
- more than 1000 editions of his book Elements, which shows how successful the Elements was
