testing header
Math Goodies is a free math help portal for students, teachers, and parents.
Free Math
Newsletter
 
 
Interactive Math Goodies Software

Buy Math Goodies Software
testing left nav
Math Forums @ Math Goodies
Math Forums @ Math Goodies
Home | Profile | Register | Active Topics | Members | Search | FAQ
 All Forums
 Homework Help Forums
 Geometry and Trigonometry
 Hyperbolic geometry

Note: You must be registered in order to post a reply.
To register, click here. Registration is FREE!

Screensize:
UserName:
Password:
Format Mode:
Format: BoldItalicizedUnderlineStrikethrough Align LeftCenteredAlign Right Horizontal Rule Insert HyperlinkInsert EmailInsert Image Insert CodeInsert QuoteInsert List Insert Special Characters Insert Smilie
   
Message:
* HTML is OFF
* Forum Code is ON

Math Symbols
Squared [squared] Cubed [cubed] Square Root [sqrt] Cube Root [cbrt] Pi [pi]
Alpha [alpha] Beta [beta] Gamma [gamma] Theta [theta] Angle [angle]
Degrees [degrees] Times [times] Divide [divide] Less Than or Equal To [less-than] Greater Than or Equal To [greater-than]
Plus Minus [plus-minus] Integral [integral] Sum [sum] Sub 1 [sub-1] Sub 2 [sub-2]
Element Of [element-of] Union [union] Intersect [intersect] Subset [subset] Empty Set [empty-set]

  Check here to subscribe to this topic.
 
   

T O P I C    R E V I E W
the_hill1962 Posted - 11/02/2012 : 13:48:30
Can a right angle be drawn in hyperbolic geometry?
I read a passage in a textbook that stated "there are no right triangles on a hyperbolic plane".
4   L A T E S T    R E P L I E S    (Newest First)
the_hill1962 Posted - 11/14/2012 : 08:56:32
Ahh, thanks! I was wondering about that term.
I still disagree with the text that I read in a lesson somewhere that stated something like "right triangles do not exist in hyperbolic geometry".
It seems like a better statement would be "normal right triangles do not exist in hyperbolic geometry". That would open up the discussion of the terms "defective" and "excess".
This could just be me.
BTW, if "excess" means a triangle with sum of interior angels exceeding 180, then what is the term for the triangles in hyperbolic geometry?
royhaas Posted - 11/13/2012 : 10:26:42
I didn't invent the term "defective" in this context; I don't know who did, but it seems to be in common usage. In the case of Riemannian geometry, I believe the term "excess" is used, since the sum of interior triangle angles exceeds 180. So on a sphere, you can have an equilateral triangle with a total of 270.
the_hill1962 Posted - 11/12/2012 : 13:18:39
"defective" is a very interesting description.
I am not convinced that means it is not a right triangle. It is still a "triangle" with a "90 degree angle".
I am just going to "agree to disagree" with the textbook.
Again, your use of "defective" is interesting.
royhaas Posted - 11/05/2012 : 12:39:29
The (interior) angles of all triagles in hyperbolic geometric sum to less than 180. The plane is really a saddle surface, so you can draw a right angle, but any "right" triangle would be "defective" in the sense that its angles sum less than 180.

Math Forums @ Math Goodies © 2000-2004 Snitz Communications Go To Top Of Page
This page was generated in 0.05 seconds. Snitz Forums 2000
testing footer
About Us | Contact Us | Advertise with Us | Facebook | Blog | Recommend This Page




Copyright © 1998-2014 Mrs. Glosser's Math Goodies. All Rights Reserved.

A Hotchalk/Glam Partner Site - Last Modified 22 Apr 2014