Transcript Euclidean/non-Euclidean Geometry

The study of points,
lines, planes, shapes,
and space
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“Father of Geometry”
Greek mathematician
Discovered the basics of Euclidean geometry as
we know it in the mid 3rd century.
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What we will be learning in this class.
The study of flat space.
Also called “plane geometry”
Important characteristics
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Shortest distance between two points is a straight line
All triangles have exactly 180
The concept of perpendicular to a line can be illustrated as
seen in the picture at the right.
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The study of curved surfaces
There are many different types of non-Euclidean geometry
In curved space, the sum of the angles of any triangle is not
always equal to 180°.
On a sphere, there are no straight lines. As soon as you start
to draw a straight line, it curves on the sphere.
In curved space, the shortest distance between any two points
(called a geodesic) is not unique.
In curved space, (for spherical (riemannian) or hyperbolic
geometry)the concept of perpendicular to a line can be
illustrated as seen in either of these pictures.