who can explain me a little about the spherical triangles?

Answer 1

A spherical triangle is a triangle on the surface of a spherical surface, the sides of the triangle being the arcs and not straight lines as in a triangle in a plane.

Answer 2

One interesting thing is that the sum of the angles is > 180. The smaller the triangle is the closer to 180 it is. For instance, if you take a really big triangle with sides as 3 perpendicular great circles, the sum of the angles can be 270.

Another is there is no such thing as similar triangles - or more accurately, 2 triangles are similar iff they are congruent, since the sum of the angles is different.

The analog of lines on a sphere are the great circles. Any other circle would be equivalent to a circle in the plane. There is no ideal way to find planar equivalents of spherical triangles. There are maps (conformal) that preserve angles, which do not preserve lines or area, and there are ones that preserve lines and areas, but not angles.

Answer 3

The angles of a spherical triangle don't necessarily add up to 180 degrees. These triangles use what is called Non-Euclidean Geometry

Answer 4

The first reference (.../sphertrig.html) explains just a little.

The second one (Mathworld) explains considerably more.

If both of the references are too involved, you can start with these three basics:

In spherical trigonometry, you consider not just the angle formed by two sides as you do in plane geometry. You also consider the "length" of each side to be an angle.

It is usual to measure all angles in radians. (There are 2π radians in a complete circle; π radians = 180°.)

If we use lowercase a, b, c to denote the "length" of each side (in radians), and uppercase A, B, and C to denote the angle opposite a, b, and c respectively, then two powerful laws emerge:

Law of spherical cosines:
|--: cos a = cos b cos c + sin b sin c cos A

Law of spherical sines:
|--: sin a / sin A = sin b / sin B = sin c / sin C

Answer 5

Spherical Triangles

Click on the URL below for additional information concerning spherical Triangles.

en.wikipedia.org/wiki/Spherical_trigonometry

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