Payouts in a tournament paying a certain number of places

Suppose you have a tournament and you have a certain amount of money pooled together and you want to pay a certain number of places. I found this fair way to figure the payouts. Consider the Golden Spiral:

Now consider this payout structure:

See the payouts follow the Golden spiral so you follow the spiral until you have the desired number of rectangles one for each person getting the payout.. 

Then you can use this to figure the actual amounts (this is for 3 places):

For a million dollars paying out to 5 places it looks like:

The general formula is:

Where total is the amount of money pooled and n is the number of places to pay out. Instead of 1.618 you can use more accurate values of the golden ratio but you only need to if the number pooled is quite large. 

Or you can use different ratios, but the golden ratio has the nice property that the amount everyone gets is as much as the next two finishers combined.