A sphere is the wrong shape in the first place since the majority of Earth is water. Divide the liveable land equally instead.
(And to make it more efficient and objective, charge a (global) land value tax and use the proceeds to finance a (global) basic income. The average person will have a net impact of zero, but anyone using less land by value than the average will be reimbursed for that generosity.)
But let's get back to the math.
Mathematics helps here, too. Game theory to be more precise. Of course, lots of the solutions to fair distribution problems have been discovered before mathematicians got a chance to invent game theory. For two people, the you-cut/I-choose procedure works.
For lots of people introducing money is more efficient: just auction off all the plots to the highest bidders, and distribute the proceeds equally. Auctions are a great way to convert subjective valuations into fair numerical valuations.
See eg things like https://en.wikipedia.org/wiki/Shapley_value or https://en.wikipedia.org/wiki/Fair_division