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In non-Euclidean geometry triangles on a sphere have 180 degrees?
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In non-Euclidean geometry triangles on a sphere have exactly 180 degrees?
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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.
Does a right triangle have three right angles?
Not in traditional, 2 dimensional, euclidean geometry, because a triangles angles always equal 180º .However, there is a branch of Geometry that deals with a coordinate system on a sphere, instead of a plane, and in spherical geometry a triangle with three right angles is very much possible. Consider, for example, the triangle bounded by the Prime Meridian, 90o west longitude, and the equator.
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.
In non-Euclidean geometry triangles on a sphere have 180 degrees?
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In non-Euclidean geometry triangles on a sphere have 180 degrees.?
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In non-Euclidean geometry triangles on a sphere have exactly 180 degrees?
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In non-Euclidean geometry triangles on a sphere have more than 180 degrees true or false?
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In non-Euclidean geometry, triangles on a sphere have 180 degree?
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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.
Do all angles of a triangle add up to 270 degrees?
It depends on whether the triangle is in euclidean geometry or not (flat plane). IN Euclidean Geometry they always add up to 180 degrees. On the surface area of a sphere it can be 270, 230, 360 etc. it depends on which type of triangle you are talking about
Can a triangle have two right angles yes or no?
No. A triangle's angles must add up to 180 degrees so it cannot have two right angles. However, the answer is yes if you are talking about a triangle on the surface of a sphere. In this case the geometry is non-Euclidean. If you are staying with standard Euclidean geometry, then the answer no above is correct.
Did Lobachevsky negation created spherical geometry?
Lobachevsky's work did not create spherical geometry; rather, he is known for developing hyperbolic geometry, which deviates from Euclidean principles. Spherical geometry, on the other hand, is based on the properties of figures on the surface of a sphere and includes concepts such as great circles and the sum of angles in a triangle exceeding 180 degrees. Both geometries are non-Euclidean, but they arise from different fundamental assumptions about space. Lobachevsky's contributions helped to expand the understanding of non-Euclidean geometries, including both hyperbolic and spherical forms.
What does non Euclidean apply to in real life?
Non-Euclidean geometry is most practical when used for calculations in three dimensions, as opposed to only two. For example, planning the fastest route for an airplane or a ship to travel across the world requires non-Euclidean geometry, because the Earth is a sphere.
How are euclidean and non-euclidean geometry alike?
They are not alike euclidean is based on a plane. non-euclidean is based on a sphere, similar to earth. Both forms are correct based on the proof the formulas provide. However neither are 100 percent accurate since, although it looks like earth a sphere it is not. The gravitational pole contributes to earth being misshaped and is more of an oval. True geometry would have to take this in consideration when calculating something as simple as the angles of a triangle.
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.
