Square foot garden: what is the best way to plant crops that usually are planted in rows?

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Question by SWWIFL: Square foot garden: what is the best way to plant crops that usually are planted in rows?
We just set up our first square foot garden and the instructions I’ve found are a little vague on the pattern to use within the square to take full advantage of the square. Especially for plants like carrots, radishes, beets, lettuces, etc. that are usually in a row.
Lots of good suggestions-thanks! It will be hard to pick a best answer.

A few more details:
Our ground soil is hard clay mixed with rocks, (we live on the side of an extinct volcano-but have none of that lush volcanic soil). We opted to try the method mentioned in the Square Foot Gardening book, rather than try and improve our soil. For now we have a 4 foot by 4 foot square box, and may add a second for warmer crops. We are in the southwestern U.S. so we can start planting now-at least things like peas and radishes.

What do you think? Answer below!