Pythagorean Proof of Curvature for a Ball with a Radius of 3959 Miles (Using AutoCAD 2015 with 15-Digit Precision)

Micheal Kahnke figured the math and created the chart with Autocad and First Released it in July 2015 on Facebook.  It was shared and modified it into several versions and reshared virally.  


Earth Curvature AutoCAD Chart

The curvature of the earth is an important concept that affects everyday life. The Pythagorean proof of curvature of the earth demonstrates the fact that the earth is curved by calculating the distance between two points equidistant from the middle point on the earth’s circumference. This proof can be quantified by utilizing a computer modeled design program that uses 15 digit precision, such as AutoCAD 2015, and a radius of 3959 miles (which is consistent with the mean radius of the earth).

The Pythagorean proof of curvature of the earth asserts that the circumference of a circle is equal to the sum of its radius squared multiplied by Pi - or C= 2*PI*r^2. With AutoCAD 2015, a rectangle can be drawn, symbolizing the earth, that is 3959 miles in length. Next, a point can be placed equidistant to the center of the rectangle (which represents the center of the earth), and two lines can be drawn from these points to the opposite end of the rectangle to create a triangle, thus demonstrating the Pythagorean theorem.

When the triangle is generated, the length of the hypotenuse (line C) should be longer than the length of line A and B combined, because the earth is curved. This can be demonstrated by measuring the two legs of the triangle are 3959 miles each and then calculating the length of the hypotenuse. 

The Pythagorean proof of curvature of the earth can be demonstrated using a computer modeled design program such as AutoCAD 2015, along with a radius of 3959 miles.