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27. General relativity by Benjamin Crowell, Light and Matter licensed under the Creative Commons Attribution-ShareAlike license.

a / Noneuclidean effects, such as the discrepancy from `180°` in the sum of the angles of a triangle, are expected to be proportional to area. Here, a noneuclidean equilateral triangle is cut up into four smaller equilateral triangles, each with 1/4 the area. As proved in problem 1, the discrepancy is quadrupled when the area is quadrupled.

What you've learned so far about relativity is known as the special theory of relativity, which is compatible with three of the four known forces of nature: electromagnetism, the strong nuclear force, and the weak nuclear force. Gravity, however, can't be shoehorned into the special theory. In order to make gravity work, Einstein had to generalize relativity. The resulting theory is known as the general theory of relativity.^{1}

*Postulates of Euclidean geometry:*

1. Two points determine a line.

2. Line segments can be extended.

3. A unique circle can be constructed given any point as its center and any line segment as its radius.

4. All right angles are equal to one another.

5. Given a line and a point not on the line, no more than one line can be drawn through the point and parallel to the given line.

27. General relativity by Benjamin Crowell, Light and Matter licensed under the Creative Commons Attribution-ShareAlike license.