# Draw a Triangle on Sphere with Interior Angles > Pi & Sum of Angles = 2pi

• UrbanXrisis
In summary, the conversation discusses drawing a triangle on the surface of a sphere with specific conditions for the sum of the interior angles. Suggestions are given for creating a triangle with a slightly greater sum of angles than pi and another with a sum equal to 2pi. The idea of using a meridian and the equator for creating the triangle is also mentioned.
UrbanXrisis
I need to draw a triangle on a surface of a sphere for which the sum of the interior angles is slightly greather than pi and also the sum of angles is equal to 2pi.

I think i have an idea of what to draw for the sum of interior angles slightly greater than pi (http://www.math.hmc.edu/funfacts/ffiles/20001.2.shtml) , but not quite sure how to get the angles greater than 2pi

any ideas?

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well if you want slightly larger than pi, any non-zero area triangle on the surface of the sphere will work. For exactly 2pi, try going from north pole to equator, then around on the equator to direct opposite side, then back up to the north pole. Go farther than direct opposite side if you want more than 2pi. Hope this helps and you can visualize what I'm saying.

it is a bit difficult, could you give another explanation?

what do you mean by "from north pole to equator"?

thanks

it means you dessend along a meridian.

The "triangle" dimachka is talking about is 1/4th of the surface of the sphere.

It has half the equator as one of its side and its other side passes through the north pole.

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## 1. How is it possible to draw a triangle on a sphere with interior angles greater than pi?

This is possible because the surface of a sphere is curved, so the usual rules of Euclidean geometry do not apply. On a flat surface, the interior angles of a triangle always add up to exactly 180 degrees (pi radians), but on a curved surface like a sphere, this is not the case.

## 2. What is the sum of the angles of a triangle on a sphere?

The sum of the angles of a triangle on a sphere is always greater than 180 degrees (pi radians) and can vary depending on the size and shape of the triangle.

## 3. How do you calculate the interior angles of a triangle on a sphere?

The interior angles of a triangle on a sphere can be calculated using spherical trigonometry. This involves using the law of cosines and the law of sines to solve for the angles.

## 4. Are there any real-life examples of triangles on a sphere with interior angles greater than pi?

Yes, one example is a triangle formed by three cities on the surface of the Earth. The shortest distance between these cities is along the surface of the Earth, which is curved, so the angles of the triangle will be greater than 180 degrees.

## 5. How does the sum of the angles of a triangle on a sphere relate to the curvature of the surface?

The sum of the angles of a triangle on a sphere is directly related to the curvature of the surface. On a sphere with positive curvature, the sum of the angles will be greater than 180 degrees, while on a surface with negative curvature, the sum will be less than 180 degrees.

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