My first proposal was not the best shipping.
I found another, and that would prove your theory to the world.
According to the official map of the world, there are about 100 km of sea between the tip of Russia and the tip of Alaska.
According to the world map of the Flat Earth Society, there is a vast ocean of hundreds (or thousands) of miles away.
So ... a boat expedition could show the world that your theory is true.
OR
this expedition will prove that your theory is wrong. And maybe that's why you will never really want to develop this project.
The area between Alaska and Russia would be no different in FER or RET. The distance between Australia and Africa, on the other hand, would be quite different.
Even if we assume for the sake of this argument that your fantasy formula for distance on the FE is right, then we know that your statement is false. The area between Alaska and Russia would be different in FET and RET (correcting your grammar error and typo).
For example, the distance from Perth to Sydney in RET is 2043 miles according to RET and Google Earth:
...
Distances:
r1 is the first radius (centered at the north pole).
θ1 is the first longitude.
r2 is the second radius.
θ2 is the second longitude.
d is the distance.
~111 km = 69.0 miles
Perth, Australia 31o 57' S 115o 52' E
Sydney, Australia 34o 0' S 151o 0' E
So we have from Perth to Sydney:
r
1 = (31
o 57' S) * 6214 miles = (90+31+57/60) * 69.0 miles = 8,410 miles
r
2 = (34
o 0' S) * 6214 miles = (90+34+0/60) * 69.0 miles = 8,560 miles
theta
1 = 115
o 52' E = 115 + 52/60 degrees = 115.87 degrees
theta
2 = 151
o 0' E = 151.00 degrees
d = sqrt(8,410 miles
2 + 8,560 miles
2 - 2*(8,410 miles)*(8,560 miles)*cos(115.87 degrees - 151.00 degrees)) =
5,120 miles
(I used Google's calculator:
)
So in RET, it's 2,043 miles.
In your fantasy, it's 5,120 miles.
Nope, they aren't the same. Australia's area is greatly overstated by your fantasy formula.