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Thomas Aquinas posed to himself the question (true story), is there anything God can’t do? The Angelic Doctor pondered for a while and came up with a list. God cannot commit a sin. God cannot forget anything. God cannot stop being God…And NOBODY, not even God, can draw a triangle whose angles do not add up to 180 degrees. (God was God, but Euclid was EUCLID!)

As fortune would have it, I own a 1052-acre farm that is shaped like a triangle. One day I measured the three angles and found to my horror that they were

A = 30.000001 degrees, B = 60.000002 degrees, and C = 90.000003 degrees.

What is the radius of the Earth?

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Solution: For a triangle drawn on a sphere of radius R, the three angles of a triangle add up to a little bit more than 180 degrees. The exact formula, with angles measured in radians, is

A + B + C = Pi + (Area of triangle)/R^2

In this problem the three angles add up to 180.000006 degrees, or Pi + .0000001047 radians. The area of the field is 1052 acres, or 1.64375 square miles. Substitute these values into the equation and solve for R to obtain the radius of the Earth, R = 3962 miles.

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