Marta's vineyard

At the time of the colony, one of the hard pioneers who had focused on the difficult task of growing the rocky floor of an island near New England, tried to plant a vineyard with the help of his daughter Martha.

To stimulate it, and instead of any other remuneration, it allowed Martha to cultivate a small square whose extension was, exactly, the sixteenth part of an acre.

It is said that she planted her parras according to the custom, in ranks separated from each other by a distance of nine feet, and cultivated them the same as everyone but, according to the story, her small company prospered and grew in such a way that the vineyard Martha became remarkable. From its land it reaped more grapes by acre than any other vineyard of the island and also produced many new and valuable varieties.

There ends the story in regard to the facts. However, without pretending to challenge Martha's expertise, nor question her sweetness, who conferred fragrance to her grapes, I want to propose a practical problem about her vineyard that perhaps explain the reason for her wonderful success.

How many Parra plants, located no less than nine feet away, can be planted in a square terrain that measures the sixteenth part of an acre?

It is a beautiful problem, calculated to demand the ingenuity of our mathematicians, but not to force a return to school books, so forgotten, we take the opportunity to say that an acre is a square of 208 and 710/1000 feet from side, So the sixteenth part of an acre is a square of 52 feet and 2 inches side. Being 1 foot = 12 inches.

Solution

Drawing a bias line, that goes from one corner to another, and then drawing parallel and perpendicular, it will be discovered that 41 parras can be planted, separated by a little more than 9 feet, all of them within the space limited by the fence.