Did it ever occur to you that the mishna ערוגה בת ששה טפחים על ששה טפחים seems a bit strained.
[Five types of vegetables can be planted in a plot of land 6 handbreadths by 6 handbreadths]
Why plant five types of beans or vegetables in a plot of land that is a square foot? Well, the answer is there were three tribes of Indians on the east part of Ohio. (Shawnee, Wyandot, Delaware) Their practice was to plant corn --their main stable. When it sprouted a little they would make a little mound around it and plant beans on that hill. That kept the soil in place [and added nitrogen to the soil afterwards)]. Then planted pumpkins over it--that gave shade and prevented weeds.
So these three crops ["the three sisters"] were in a sort of symbiotic relation. So you can see that planting certain kinds of beans or vegetables in close proximity can be a great help-so one does have to be able to do this without transgressing mixed kinds of vegetables. [So the geometric shapes discussed in that mishna become very practical. --The mishna says 5 types can be planted there but they have to conform to the restriction that each be not actually mixed with the other.