Michelle Huchette

Block 2

*Euclid and Pythagoras

*Euclid*Greek

*From Alexandria, taught mathematics there

*Worked with prepositions and proofs

*Created the basis for teachings of geometry

*Sometimes called the ‘Father of Geometry”

*Used the “synthetic approach”

*Proved it is impossible to find the largest

prime number

* Wrote the Book Elements

• Divided into 13 books.

• Covers geometry, arithmetic and number theory, and irrational numbers.

• Organized the known know geometrical ideas (definitions, axioms) then created theorems, and created methods for proofs.

• Demonstrated almost 500 propositions in plane and solid geometry.

• Proved the theorem of Pythagoras (proved equation is always true for right triangles).

• Used as a textbook.

* Other books:

• Data- contains 94 propositions.

• Phaenomena- about spherical astronomy.

• Caloptrics- about mirrors.

• Optics- contains the theory of perspective and music theory. Included light rays in geometry as if they’re straight lines.

* Said that we can't be sure of axioms without proofs, divided axioms (postulates) into 2 groups of five, common notations, and postulates related to geometry

1. Things equal to the same thing are equal

2. Equals added together equal an equal

3. When an equal is subtracted from an equal it equals an equal

4. Things that coincide with each other are equal

5. A whole is greater than a part

6. A straight line can be between two points

7. A line can be extended indefinitely

8. A circle can be drawn using a line segment as the radius and an end point as the center

9. Right angles are equal

10. With a line and a point, only one line can be draw through the point parallel to the first line

*Euclid

*Greek

*Sometimes called the first pure mathematician

*Created a school, The Semicircle

*Studied types of numbers- odd, even, triangular, perfect

*Related music to mathematics

*Founded a philosophical and religious

school in Crotona

*Pythagoras

*Credited with:

• Angles in a triangle equal two right angles

• For a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

• Construction of figures of certain are and geometrical algebra

• Five regular solids

• Earth is a sphere in the center of the universe. Planets stars and universe are spherical because a sphere is the most perfect solid figure

*Believed:

• Everything is numbers, math is the basis of everything. Geometry is the highest form of mathematics. The physical world can be taught through mathematics.

• The soul is present in the brain and is immortal. The soul can move through beings through reincarnations. Math and Music can purify.

• Numbers have personalities, characteristics, strengths and weaknesses.

• World depends on interactions between opposites.

• Some symbols have mystical significance.

• Members of society should be loyal and secretive.

*Pythagoras

*Bibliography

*"Euclid - Math Word Definition - Math Open Reference." Table of Contents. Web. 25 Mar. 2012. <http://www.mathopenref.com/euclid.html>.

*"Biography of Pythagoras - Math Word Definition - Math Open Reference." Table of Contents. Web. 25 Mar. 2012. <http://www.mathopenref.com/pythagoras.html>.

* "Pythagoras." : , Social Studies, Social Studies. Web. 25 Mar. 2012. <http://sc5gz8e.edu.glogster.com/false/>.

*"2010/2011 Math Euro Section." : Euclid: A Greek Mathematician !! Web. 25 Mar. 2012. <http://pondicherry-mathseurosection.blogspot.com/2011/02/euclid-greek-mathematician.html>.