A Passing Thought: To Gather All Humanity

Let's say that you built your tower of evil and wanted to gather all humanity at it's base to hear your vile decrees. What distance from your great spire would you need to have free of obstruction for your populace?

This problem is just as easy as it sounds. You only need a few things: the total human population, the area needed for an average person, and the shape you want to gather your docile populace in.

The population is easy, just check some website like this one. Currently, the Earth has around 6.77 billion people.

The area per person on average has some flexibility. Clearly, you can't allocate one square centimeter per person, but one square meter per person is not unreasonable. For weddings, I understand that 8 square feet per person is the rule of thumb, but as it's my tower of evil, I don't people to get too comfy. I'll use one square meter per person.

Finally, I need a shape to gather the crowd in. A complete circle would be the smallest radius, but then a fair portion of the people would be stuck behind me where they could make faces at me without fear. Instead, I'll use a fraction of a circle so I can keep an eye on all of them, say 1/4.

Now for the easy bit, the math:
6.77 billion people * 1 square meter per person = 6.77 billion square meters
6.77 bsm = (1/4) * Pi * (radius squared)
radius = square root ( 6.77 bsm * 4 / Pi ) = 92.8 km = 57.7 miles

Hmm, that's a bit far to see...even on a good day, but it's rather reasonable for all humanity. Excellent!