rectangles1 - (4) any right triangle has defect=0 (5) there...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math402 Defects and Rectangles Defect of an n -gon is ( n - 2) · 180 minus the sum of interior angles of the n -gon. A rectangle is a quadrilateral with all four angles equal to 90 . In particular the defect of a rectangle is 0. Theorem. The following statements are equivalent in neutral geometry: (1) Playfair (2) any triangle has defect=0 ( i.e. angle sum 180 ). (3) any polygon has defect=0
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (4) any right triangle has defect=0 (5) there is a rectangle of any size (6) there is a rectangle (7) there is a right triangle with defect=0 (8) there is a triangle with defect=0 If any (thus all) of the above is true then we are doing Euclidean Geometry, if any (thus all) is false then we are doing Hyperbolic Geometry....
View Full Document

This note was uploaded on 08/08/2009 for the course MATH 1 taught by Professor Malkin during the Spring '09 term at University of Illinois at Urbana–Champaign.

Ask a homework question - tutors are online