G Guest Guest Jan 12, 2006 #1 I need help explaining why this theorem is not true in elliptic geometry: Through a point outside a line, there is exactly one line perpendicular to the given line. Please help!

I need help explaining why this theorem is not true in elliptic geometry: Through a point outside a line, there is exactly one line perpendicular to the given line. Please help!

pka Elite Member Joined Jan 29, 2005 Messages 7,820 Jan 12, 2006 #2 Elliptical Geometry is also known as Riemannian Geometry. In Riemannain Geometry the following is the case: “Given a line l and a point P not on l there exists possibly more than one line through P perpendicular to l. Please note the qualifier “possibly”!

Elliptical Geometry is also known as Riemannian Geometry. In Riemannain Geometry the following is the case: “Given a line l and a point P not on l there exists possibly more than one line through P perpendicular to l. Please note the qualifier “possibly”!

D Denis Senior Member Joined Feb 17, 2004 Messages 1,470 Jan 13, 2006 #3 Hmmm....what grade are you in, BM ?