Class 1/27/12 - 3.1 & 3.2

Salut mes amants des maths! 

Aujourd'hui c'est vendredi et nous avons eu un petit test. (Today is Friday and we had a quiz) :( I don't think it went too well, but I'm trying to be optimistic about the results. 

Today, we finally started Chapter 3 which is basically an introduction to the most important mathematical text of Greek times and probably of all time: The Elements (a work of 13 books) of Euclid. This book has been translated into countless languages and has appeared in more editions than any work other than the Bible. The  book simply consists of definitions, axioms, theorems, and proofs. Nevertheless, it has been intensively studied and provides an example of how "pure mathematics" should be written. Below are different elements of Book I of the work. 

Definitions: 

1. A point is that which has no parts
2. A line is a breadthless length. 
3. The ends of a line are points. 
4. A straight line is a line which lies evenly with the points on itself. 
5. A surface is that which has length and breadth only. 
6. ......

Common Notions: 

1. Things which equal the same thing are also equal to one another. (a=x, b=x ==> a =b)
2. If equals are added to equals, then the wholes are equal. 
3. If equals are substracted from equals, then the remainders are equal. 
4. Things which coincide with one another equal one another. 
5. The whole is greater than the part. 

Postulates:

Postulate 5

1. To draw a straight line from any point to any point
2. To produce  a finite straight line continuously in a straight line.
3. To describe a circle with any center and radius. 
4. That all right angles equal one another
5. That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right nagles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. 

Pythagorean Theorem: In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle. 

That's all for now! Until next time!

Bisous

-MB