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great circles
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In spherical geometry lines are?
great
In spherical geometry what do they call lines?
Arcs or curves.
Are the rules of parallel and perpendicular lines different in spherical geometry than in Euclidean geometry?
yes
What are applications of spherical geometry?
Pilots and captains of ship use spherical geometry to navigate their working wheel to move it. They can measure their pathway and destiny by using Spherical Geometry.
When Compare and contrast Euclidean geometry and spherical geometry. Be sure to include these points 1. Describe the role of the Parallel Postulate in spherical geometry. 2. How are triangles differen?
Euclidean geometry is based on flat surfaces and includes the Parallel Postulate, which states that through a point not on a line, exactly one parallel line can be drawn. In contrast, spherical geometry operates on a curved surface where the concept of parallel lines does not exist; any two great circles (the equivalent of straight lines on a sphere) will intersect. In spherical geometry, triangles have angles that sum to more than 180 degrees, unlike in Euclidean geometry, where the angles of a triangle always sum to exactly 180 degrees. Thus, the fundamental properties and the behavior of lines and angles differ significantly between the two geometries.
What are lines called in spherical geometry?
great circles
What are lines called in Riemann's spherical geometry?
great circles
What are lunes in spherical geometry?
Lines in spherical geometry are very easy to understand. Lines in spherical geometry are straight looking items that can be found by graphing points in a certain pattern.
In spherical geometry lines are?
great
Can a line segment be extended indefinitely in spherical geometry?
that would be a line and lines do not exist in spherical geometry
In spherical geometry what do they call lines?
Arcs or curves.
Are the rules of parallel and perpendicular lines different in spherical geometry than in Euclidean geometry?
yes
How many right angles are formed by perpendicular lines in spherical geometry?
8
How many times can two great lines intersect is spherical geometry?
Two.
A line in riemann's sperical geometry is called a?
A line in Riemann's spherical geometry is called a great circle, which is the intersection of a sphere with a plane passing through its center. Great circles are the equivalent of straight lines in this non-Euclidean geometry.
Do parallel lines run from the north to south pole?
In plane geometry, the geometry of a flat surface, parallel lines by definition never meet. However in spherical geometry, the geometry of the surface of a sphere (such as the planet Earth) parallel lines meet at the poles.
What are applications of spherical geometry?
Pilots and captains of ship use spherical geometry to navigate their working wheel to move it. They can measure their pathway and destiny by using Spherical Geometry.
