The New Jerusalem

Dusty Wilson
Highline Community College
June 25, 2001

So, you have been reading the book of The Revelation and you are wondering about this glorious city to be - the New Jerusalem.  The city is described at length in chapter 21 and in verse 16 we find that

The city was laid out like a square, as long as it was wide.  He [an angel] measured the city with the rod and found it to be 12,000 stadia in lifgth, and as wide and high as it is long. NIV

We note that 12,000 stadia is approximately 2,200 kilometers.
We further note that the Earth has a polar radius of  and a equitorial radius of 

Thus, if we set the New Jerusalem on the Old Earth, we would be setting a cube with length 2,200 km on a sphere with the approximate radius of 6368 km.

The Question: How much dirt do we have to move to create a flat spot on the earth where the New Jerusalem can stand?

The Solution.

First consider a picture of the solution.  If we just consider the top portion of the spherical Earth and foundation we are trying to build to support the New Jerusalem, it would look something like that portrayed in the picture below.  Notice that this is a mathematicians drawing and not an engineer.  An engineer would have included twelve ramps for people to enter and exit the city.  For the mathematician, this is needless clutter.

For scale, we can note that the square is of length 2,200 km on each side, while the foundation has a maximum height of 192.9 km.  So, this is definately not to scale.

The amount of dirt needed is the volume of rectanguloid with dimensions 2,200 x 2,200 x 192.9  minus the volume of dirt contained inside both the sphere and the rectanguloid.
 

The total amount that must be moved can be represented as  where  is the radius of the Earth and w is half the length of the side of the city.

These solutions are:

Notes: