EUCLID VS. NON-EUCLIDEAN

Euclid biography
Born325bc - Died265bc
He is Euclid of Alexandria. He was known for his mathematical skill. Not much is known about his life. Except for the fact that he taught in Alexandria in Egypt. We still use his books that he wrote long ago

POSTULATES

• 1. A straight line segment can be drawn joining any two points
• 2. Any straight line segment can be extended indefinitely in a straight line.
• 3. Given any straight line segment a circle can be drawn having the segment a radius and one endpoint as center.

POSTULATES CONTINUED

• 4. All right angles are congruent.
• 5. Parallel postulate. The faith can't be proved even Euclid only used 4 of his postulates.

EUCLIEAN DEFINITIONS

• Lines-a straight path that has no thickness and goes on firever.
• Perpendicular lines-lines that intersect at 90 degrees.
• Triangles-a three sided polygon.

SPHERICAL GEOMETRY DEFINITIONS

• Line- line is a great circle that divides the sphere into equal halves.
• Perpendicular-intersect at 2 points and form 8; 90 degree angles.
• Triangles-a triangle is formed on the surface of a sphere by three great circular arcs. Intersecing at 3 vertices.

HYPERBOLIC GEOMETRY DEFINITIONS

• Line- line intersects at a maximum of one point or it has no points of intersection.
• Perpendicular-the point belongs to line or point that is exterior of the line.
• Triangle- consists of 3 line segments called sides or edges and three points called angles and vertices.

CITATIONS

• HTTP://EULER.SLU.EDU/ESCHER/INDEX.PHP/THE_THREE_GEOMETRIES
• http://www.regentsprep.org/regents/math/geometry/gg1/Euclidean.htm
• http://mathworld.wolfram.com/EuclidsPostulates.html