Amount

Hmm.
I just noticed you posted 2 values for square feet per acre in the OP.
Correct is 43,560. Dividing by 16 gives 2722.5 trees.

From a practical value, if I were the landscaper, I would agree with my supplier for 2700+/- trees. (They probably would estimate) After planting has progressed, I would arrange to fill in with those needed, or return excess.

You need to proof read your posts.

"Randy does the shape of the tract matter or the arrangement"

I will specify:

What if the shape was a rectangle and if the arrangement was in the corner, not in the center ?


" ...and in the case rearrangement matters, are you looking for the range, a min or a max" The min and max.

I will specify.

What if the shape was rectangular ?

The arrangement was in the corner, not in the center.

The range - either min or max.

Sorry for duplicate post for the specification.

Sorry for the typo.

Throwing in planar tiling into the mix...

As there are three platonic shapes that allow uniform tiling in a plane (square/rectangle, triangle and hexagon) and given the problem conditions (4 foot spacing) these three tilings are reduced to two tiling shapes (square and equilateral triangle) with one item in each tiling shape.

As the square area is 16 ft^2/item and the equilateral triangle area is 4*sqrt(3) ft^2/item

To maximize the number of items in a specified area (1 ac= 43560 ft^2) the number if items per acre is determined by the area of the tiling. For a square tiling this is 2722.5 items per acre and 6287.3 items per acre for a equilateral triangle tiling.

So if the tree farm wants to maximize the trees and maintain a 4 foot spacing they should use a triangular tiling.

Rap

Thank you.

Very good q. Presumably each corner planting would constitute only 1/4 of a tree so that all four would be counted as one tree

I suspect your original q might have dozens of not scores of answers depending on details of this sort

I did not think of that. Do you suppose that arrangement was in the mind of the one posing the problem?

The result would have considerable consequences when it comes to managing the plot.

Thanks Neo. You've set me to wondering how many possible answers altogether

Interesting also because Randy's problems are generally intuitive.

I have a question:

How would the number of trees be determined if the acre was circular? The problem did not state the shape. The acre and trees planted 4 feet apart were the only information given in problem.

Just curious.

Draw a picture of the possibilities.
Would trees be planted in parallel chords?
Maybe concentric circles.
I'll bet the number won't be far from the 2700

"Would trees be planted in parallel chords?
Maybe concentric circles."

I know the trees are 4 feet apart. How do I calculate the length and number of rows when I draw the picture ?

I bet there are a kazillion different confiigurations