Dr. Shlomo Libeskind is a professor emeritus at the University of Oregon mathematics department.  He has extensive writing experience (books and articles). In teaching and in writing, Dr. Libeskind uses a heuristic approach to problem solving and proof; in this approach the reasonableness of each step in a solution or proof is emphasized along with a discussion on why one direction might be more promising than another. Dr. Libeskind received his PhD in Mathematics in 1971 at the University of Wisconsin, Madison.Dr. Isa Jubran has nearly 30 years of experience teaching a wide range of undergraduate mathematics courses at SUNY Cortland. He regularly teaches a junior-level geometry course and a first-year elementary geometry course, where he emphasizes the proper use of dynamic geometry software. Occasionally, he teaches a sophomore/junior level fractals and chaos course.

• Preface.- Surprising Results and Basic Notions.- Congruence, Constructions, and the Parallel Postulate.- Circles.- Area and the Pythagorean Theorem.- Similarity.- Isometries and Size Transformations.- Composition of Transformations.- More Recent Discoveries.- Inversion.- Hyperbolic Geometry.- Elliptic Geometries.- Projective Geometry.- Taxicab Geometry.- Fractal Geometry.- Solid Geometry.

Dr. Shlomo Libeskind is a professor emeritus at the University of Oregon mathematics department.  He has extensive writing experience (books and articles). In teaching and in writing, Dr. Libeskind uses a heuristic approach to problem solving and proof; in this approach the reasonableness of each step in a solution or proof is emphasized along with a discussion on why one direction might be more promising than another. Dr. Libeskind received his PhD in Mathematics in 1971 at the University of Wisconsin, Madison.Dr. Isa Jubran has nearly 30 years of experience teaching a wide range of undergraduate mathematics courses at SUNY Cortland. He regularly teaches a junior-level geometry course and a first-year elementary geometry course, where he emphasizes the proper use of dynamic geometry software. Occasionally, he teaches a sophomore/junior level fractals and chaos course.

• Preface.- Surprising Results and Basic Notions.- Congruence, Constructions, and the Parallel Postulate.- Circles.- Area and the Pythagorean Theorem.- Similarity.- Isometries and Size Transformations.- Composition of Transformations.- More Recent Discoveries.- Inversion.- Hyperbolic Geometry.- Elliptic Geometries.- Projective Geometry.- Taxicab Geometry.- Fractal Geometry.- Solid Geometry.

Dr. Shlomo Libeskind is a professor emeritus at the University of Oregon mathematics department.  He has extensive writing experience (books and articles). In teaching and in writing, Dr. Libeskind uses a heuristic approach to problem solving and proof; in this approach the reasonableness of each step in a solution or proof is emphasized along with a discussion on why one direction might be more promising than another. Dr. Libeskind received his PhD in Mathematics in 1971 at the University of Wisconsin, Madison.Dr. Isa Jubran has nearly 30 years of experience teaching a wide range of undergraduate mathematics courses at SUNY Cortland. He regularly teaches a junior-level geometry course and a first-year elementary geometry course, where he emphasizes the proper use of dynamic geometry software. Occasionally, he teaches a sophomore/junior level fractals and chaos course.

• Preface.- Surprising Results and Basic Notions.- Congruence, Constructions, and the Parallel Postulate.- Circles.- Area and the Pythagorean Theorem.- Similarity.- Isometries and Size Transformations.- Composition of Transformations.- More Recent Discoveries.- Inversion.- Hyperbolic Geometry.- Elliptic Geometries.- Projective Geometry.- Taxicab Geometry.- Fractal Geometry.- Solid Geometry.