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What curved surface compares to which undefined term in Euclidean geometry?
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∙ 11y ago
a plane
Wiki User
∙ 11y ago
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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.
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.
Infinite flat surface geometry?
a Plane
What is Euclidean geometry mean in math?
Euclidean geometry is the traditional geometry: it is the geometry of a plane surface, as developed by Euclid. Among other things, it is based on Euclid's parallel postulate which said (in effect) that given a line and a point outside that line there could only be one line through that point that was parallel to the given line. It has since been discovered that both alternatives to that postulate - that there are many such lines possible and that there are none - give rise to consistent geometries. These are non-Euclidean geometries.
Do all triangles add up to 180?
The 3 interior angles in any triangle always add up to 180 degrees. This is true for Euclidean geometry (i.e. geometry on a flat surface) which is what most people will always deal with. Non-Euclidean geometry is concerned with geometry that isn't on a flat plane such as the globe and is used mostly in advanced physics and mathematics such as in the general theory of relativity.
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.
What is euclid geometry?
Euclid was a man - a great geometer of the ancient world. Your question should read "What is Euclidean geometry ?" The answer is : Euclidean geometry is that geometry that is based on all Euclid's axioms and postulates, including the one that says "Given a straight line on the plane and a point on the plane that is not on the line, then there can be drawn through the point and on the plane, exactly one line that never intersects the first line." Euclid knew quite well that this last was only a postulate, and that it might be possible to construct a self consistent geometry with this postulate different. It was not until the 19th century that other mathematicians caught on to this, and came up with alternative geometries. When we talk about geometries on a surface then the crucial question is whether the surface is flat - if it is then geometry is Euclidean. If the surface is curved then it isn't. Of course, we amost always do our geometry on a flat surface if we can. We can't if we are trying to navigate on the surface of the earth which is curved. The question becomes really important when we go to three dimensions; what is the geometry of space, is it curved and if so which way. The new geometries were another one of the mathematicians' pretty toys until Einstein showed us that space was in fact curved.
The sum of the measures of the angles of a triangle greater than 180 degrees?
It is not possible in plane Euclidean geometry, but always true on a convex curved surface such as the face of the Earth.
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
Description of the three undefined terms in geometry?
POINT- it has no lenght, no width and no thickness LINE- it has a lenght but no width and thickness. A line in geometry will always mean a straight line, which extends indifinitely in two opposites directions.. PLANE- it is a flat surface in which any two points are joined by a straight line lying entirely on the surface..
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.
What are the 3 undefined terms in geometry and there each examples?
PLANE The Ceiling of a room - PlaneThe Surface of the page - PlaneThe Floor - PlaneLINEThe String on a guitar - LineA Rope - LineA Hair Strand - Line
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.
What is spherical geometry?
It is the geometry of a sphere as well as of shapes on the surface of the sphere.
