Saccheri

a. Born in San Remo, Italy. He Went to the Jesuit College of Brera to studyphilosophy and theology.Become the student of Tommaso Ceva and directed his studies to mathmatics. In 1694 began teaching philosophy at the University of Turin until 1697. Became the mathematics chair at the University of Ticinese (Jesuit College of Pavia).In 1733 he wrote "Euclid Cleared of Every Flaw" in which he attempted to proved Euclid's Parallel Postulate. b. c. The type of geometry that Saccheri studied was called Hyperbolic geometry, which is a type of non-Euclidean geometry. One of the major differences between this type of geometry and Euclidean, is the plane. In Euclidean, the plane is straight and has no dimension and thickness. In Hyperbolic, mathmaticians use a paraboloid, which is curved, and in the shape of a saddle. Due to the shape, the figures drawn on the planes are much different than their Euclidean counterparts. When a triangle is created on the paraboloid, the lines of the triangle are curved rather than being straight, because of the curved surface of the plane. This also makes the angles of the triangle smaller. This means that the sum of all the interior angles in a triangle on the paraboloid is less than 180 degrees. Also, the parallel postulate does not exist in hyperbolic geometry. The postulate states that through a line and a point not on the line, there is exactly one line through the point that is parallel to the other line. Due to the shape of the paraboloid, this postulate is disproved in this type of geometry. Based on this plane, mathmaticians have found that there are at least two lines through a point that do not intersect another line. http://en.wikipedia/wiki/Hyperbolic_geometry http://mathworld.wolfram.com/HyperbolicGeometry.html d.

Peil, Timothy. "2.6.2 Saccheri Quadrilaterals." 23 Oct 2008 .
 * __Works Cited__**

"Saccheri quadrilateral ." 23 Oct 2008 .

Bowman, Joshua. "Image:Noneuclid.svg." 23 Oct 2008 .
 * __Pictures__**

"Parallel postulate." 23 Oct 2008 .

Dock, Richard. "Image:Saccheri quads.svg." 23 Oct 2008 .