Euclid was a famous Greek mathematician known as the Father of Geometry. He wrote a textbook, Elements, which was considered one of the most important textbooks in the history of mathematics. In this textbook the principles of Euclidean Geometry were introduced from a small set of axioms. Euclid understood that building a logical geometry depends on the foundation, this began with Euclid's book. It has 23 definitions (some listed below), five unproved assumptions which Euclid called postulates (now known as axioms), and five further unproved assumptions that he called notions. He then goes on in the book proving elementary theorems about triangles and parallelograms and ends with The Pythagorean Theorem. Below are the basic definitions brought to us by Euclid that are used as the foundation of much of mathematics:
Definition 1. A point is that which has no part.
Definition 2. A line is breadthless length.
Definition 3. The ends of a line are points.
Definition 4. A straight line is a line which lies evenly with the points on itself.
Definition 5. A surface is that which has length and breadth only.
Definition 6. The edges of a surface are lines.
Establishing these terms was a major step in mathematics. Not much is known about Euclid's life except that he taught at Alexandria.
Below is a representation of Euclid's Windmill Proof which we saw in class.
Sources:
http://en.wikipedia.org/wiki/Euclid
http://www.britannica.com/EBchecked/topic/194880/Euclid
clear, coherent +
ReplyDeletecomplete, content: you could flesh out what you've got here with their significance, or the history. Content-wise, it's good to remember that Euclid was an aggregator, and things like the definitions probably weren't original. Nowadays some of these ideas are treated as undefined terms, cf http://www.regentsprep.org/Regents/math/geometry/GG1/undefinedterms.htm.
consolidated: one framwork to use to summarize is answer one or more of: what? (important bits) so what? (why important) or now what? (what's next).