• University of Toronto, Scarborough

• STAB 23

University of Toronto Scarborough Department of Computer & Mathematical Sciences Final Exam MATD02 – Classical Plane Geometries and their Transformations Examiner: Z. Shahbazi December 13, 2016 Time: 3 Hours FAMILY NAME: GIVEN NAME(S): STUDENT NUMBER: SIGNATURE: DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED TO DO SO NOTES: • There are 15 numbered pages in the test including the blank pages 13, 14 and 15. It is your responsibility to ensure that, at the start of the exam, this booklet has all its pages and that all pages are handed in. • Justify your answers. FOR MARKERS ONLY Question Marks 1 / 25 2 / 25 3 / 25 4 / 25 TOTAL /100 MATD02 page 1 1. (a) (10 marks) Describe two bounded models and two unbounded models of hyperbolic plane with the interpretation of lines for each model. Provide appropriate images for each model. MATD02 page 2 1. (b) (10 marks) Prove that Semi-circles centred at x-axis are lines in the upper half pla