Is the triangle sum theorem true on the surface sphere? Explain why or why not.

Answer: No, the triangle sum theorem is not true for a sphere surface.

Explanation:

Consider 3 cities A,B,C at the following locations

The placement of C is important because this then allows angle ABC to be 90 degrees. Angles BAC and BCA are also 90 degrees each because B is directly north of both A and C (all northerly roads lead to the north pole at point B). This bizarre triangle has all three angles of 90 degrees. The angles here sum to 90+90+90 = 270 degrees.

No, the triangle sum theorem is not true on the surface sphere.

The triangle sum theorem states that, the sum of the three interior angles of any triangle is always 180°.

Given that, is the triangle sum theorem true on the surface sphere or not, so in relation to Euclid's geometry,

A statement that is equivalent to the parallel postulate is that there exists a triangle whose angles add up to 180°. Since spherical geometry violates the parallel postulate, there exists no such triangle on the surface of a sphere. The sum of the angles of a triangle on a sphere is 180°(1 + 4f), where f is the fraction of the sphere's surface that is enclosed by the triangle. For any positive value of f, this exceeds 180°.

Hence, there exists no such triangle on the surface of a sphere.

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Equation:
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What is the width of the yard?
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Answer in full

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A local club team is holding tryouts for six spots on the soccer team. Since there is not much time before a very important tournament they need to select the best players. Which method would be the best to ensure they select the "most talented" soccer players?


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