0
Still curious? Ask our experts.
Chat with our AI personalities
Ezra
Fran
Professor
Add your answer:
Earn +20 pts
To what do the internal angles of a triangle add?
In Euclidean geometry, 180. Other answers are possible, depending on the surface on which the triangle is drawn.
What postulate is not of euclidean geometry?
Euclidean Geometry is based on the premise that through any point there is only one line that can be drawn parallel to another line. It is based on the geometry of the Plane. There are basically two answers to your question: (i) Through any point there are NO lines that can be drawn parallel to a given line (e.g. the geometry on the Earth's surface, where a line is defined as a great circle. (Elliptic Geometry) (ii) Through any point, there is an INFINITE number of lines that can be drawn parallel of a given line. (I think this is referred to as Riemannian Geometry, but someone else needs to advise us on this) Both of these are fascinating topics to study.
Curved line in geometry?
In plane, or Euclidean geometry, a line usually means a straight line and a cure often refers to something else. A semicircle would be a curved line for example. But, imagine, and it should not be hard since it is reality, that we DO NOT live on a flat surface. We live on something more like a sphere. The lines are now defined as great circles. Great circles are line that run along the surface of the sphere and cut it into two parts. Imagine a plane that goes through the center of the sphere and cuts it in half. The intersection of the plane and the sphere is a great circle. These lines are not the straight lines we saw in plane of Euclidean geometry. One big difference is that any two or more will intersect. In other geometries, one called hyperbolic geometry, the lines are either traditional vertical lines or semicircles that intersect the x axis. So what I am trying to say is that curved lines depends on the geometry you are talking about and there are many of them. In Euclidean geometry we define a line as a straight curve. So the idea of a curve is more general and a line is a specific case. It has no height or width.
Infinite flat surface geometry?
a Plane
Can a triangle have two right angels?
In normal (Euclidean) geometry, no. However, there are some cases where a triangle can be drawn which does have two right angles.Imagine drawing a great triangle on the earth between three points. The first point is on the equator in Brazil, the second point is at the north pole, and the third point is on the equator in Africa. The two angles drawn from the equator to the north pole are both 90 degrees.This is because the surface of a sphere is not flat, but curved, and it allows the angles of triangles to add up to almost 360 degrees. We call this non-euclidean geometry.
