For this discussion your group must answer the following essential questions:
· How is Spherical Geometry used in the real world?
· How is Hyperbolic Geometry used in the real world?
Your responses must be clear, concise, and must contain explanations that appeal to all learning styles in our classroom. You can create explanations with notes, pictures and links to videos that may enhance the class' understanding of the topic.
Spherical geometry is the geometry of the three
ReplyDelete-dimensional shape which is a sphere
"Hyperbolic geometry is non-euclidean geometry,meaning that the parallel postulate of euclidean geometry is replaced"(http://en.wikipedia.org/wiki/Hyperbolic_geometry)
ReplyDeleteHey Keven Can you write this with your own words, I still don't know what is hyperbolic geometry and Wikipedia is not always a site to trust.
DeleteWait, what does this mean Keven?
DeleteHere is a link to a video that i think will help you understand this better http://www.youtube.com/watch?v=c1hfSYAGmgo
DeleteHyperbolic geometry is basically the study of curved spaces
DeleteKeven can you give example of curved spaces, elaborate more on this....
DeleteKeven can you elaborate more on curved spaces, give example, please explain more I'm still not understanding.....
DeleteWikipedia is not a good site to get information from, can you use another source?
DeleteHyperbolic geometry is a form of non-euclidean geometry that deals with curved spaces or a negative space, triangles in hyperbolic geometry are always less that 180 degrees, straight lines are always curved, and the closer or smaller the curve gets it gets longer also
DeleteThis comment has been removed by the author.
DeleteHere is the link to a website with examples of hyperbolic geometry, http://www.josleys.com/article_show.php?id=83
DeleteIn hyperbolic geometry, the sum of angles of a triangle is less than 180 degrees, and triangles with the same angles have the same areas. Furthermore, not all triangles have the same angle sum (cf. the AAA theorem for triangles in Euclidean two-space). There are no similar triangles in hyperbolic geometry. The best-known example of a hyperbolic space are spheres in Lorentzian four-space. The Poincaré hyperbolic disk is a hyperbolic two-space. Hyperbolic geometry is well understood in two dimensions, but not in three dimensions. (http://mathworld.wolfram.com/HyperbolicGeometry.html)
ReplyDelete-John Walker
What is a Lorentzian four space and Poincare hyperbolic ? Still don't understand
DeleteYes exactly what Sheray said, what do you mean by Lorentizian and Polncare Hyperbolic?
DeleteYou can give the meaning to Lorentzian four-space and Poincare hyperbolic.
DeleteSpherical geometry is used in the real world because people use it to find shortest path to their destination especially pilots and sailors.
ReplyDeleteAlthough its called spherical geometry, can you use it in a shape that has millions of sides, because the shape looks spherical, or does it have to be an exact circular shape?
ReplyDeletehttp://www.learner.org/courses/mathilluminated/units/8/textbook/04.php
ReplyDelete*in the website above the information is further down the page
In Spherical Geometry: - there are no parallel lines
-lines that follow the surface will go around and back to the beginning ppints , doing this creates circles
- the lines length is equal to the circles circumference
also can be called "great circles" an example of this is the Earths equator
-the lines will intersect which is why there will not be any parallel lines
-the lines intersected will create triangles whose angles will equal to more than 180
http://spheresandsuch.wordpress.com/2011/03/11/how-do-people-use-spherical-geometry/
In real world: used as a way to find the shortest distance when traveling
I understand but did you find any picture examples for this ? Where ?
DeleteNice information :)
DeleteThis is an image from the first websie from above I dont know how to post images on here but here is the site for just the picture
Deletehttp://www.learner.org/courses/mathilluminated/images/units/8/1812.png
How is hyperbolic geometry used in the real world? Any examples?
ReplyDeleteHyperbolic geometry in the real world:
Delete-used for predicting the path of
comets
- makes space travel possible
-used to plan the flight patterns of space shuttles and rockets
- astronomy
- used to find the location and distance of
objects all around in space
http://prezi.com/qbbocn0onk5t/hyperbolic-geometry/
And how is hyperbolic geometry used in the real world?
ReplyDeleteHyperbolic geometry in the real world:
Delete-used for predicting the path of
comets
- makes space travel possible
-used to plan the flight patterns of space shuttles and rockets
- astronomy
- used to find the location and distance of
objects all around in space
http://prezi.com/qbbocn0onk5t/hyperbolic-geometry/
So there are triangles that have angles sum to more than 180 degrees?
ReplyDeletehttp://www.learner.org/courses/mathilluminated/images/units/8/1812.png
DeleteThis shows an image of how it would look