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...Hyperbolic geometry nicholas schroder mat dr vochita mihai introduction euclidean is the study of plane and solid gures which based on a set axioms formulated by greek mathematician euclid in his books elements was born around bce not much known about him other than that he taught at alexandria time ptolemy i soter ruler egypt from formed are basis for most schools today fact up until th century only type there mathematicians found changing euclids last axiom parallel postulate one able to form whole new geometries this what led many dierent forms we have these types called non refer literally any spherical or elliptic will be covered later artmann started with ve undened terms point line distance half angle measure area each term introduced through stated postulates using them constructed rest proving theorem dening euclidian straight segment can drawn joining two points extended indenitely given circle having as radius endpoint center all right angles congruent if lines intersect thi...