# calculate the number of best fit golden rectangles in a given area

• Nov 6th 2011, 01:54 PM
daviskites
calculate the number of best fit golden rectangles in a given area
Hello all :-)

Here's an interesting one that is not as simple as it seems at first.

Lets say my daughter has a piece of paper. It has a height (H) and width (W).

She wants to draw an arial view of a number of farmers fields (N). The thing is she's been learning about the golden ratio in art, and wants all of the fields such that they are Golden Rectangles. All of the fields are the same size and have the width (A) and Length (B). She also wants a gap (G) between the fields so the farmer can walk around them without getting amongst the crops and livestock. She also wants the same gap around the perimeter of the farm plot.

The question is this. For a given number of fields (N), what is the formula to calculate the individual field length (B) and width (A) expressed in terms of the Gap (G), paper height (H) and paper width (W) assuming that all fields are Golden Rectangles, and that there is also a gap equal to (G) all the way round the perimeter of the farm?

Have fun
DK

Approved by CB
• Nov 7th 2011, 07:52 AM
CaptainBlack
Re: calculate the number of best fit golden rectangles in a given area
Quote:

Originally Posted by daviskites
Hello all :-)

Here's an interesting one that is not as simple as it seems at first.

Lets say my daughter has a piece of paper. It has a height (H) and width (W).

She wants to draw an arial view of a number of farmers fields (N). The thing is she's been learning about the golden ratio in art, and wants all of the fields such that they are Golden Rectangles. All of the fields are the same size and have the width (A) and Length (B). She also wants a gap (G) between the fields so the farmer can walk around them without getting amongst the crops and livestock. She also wants the same gap around the perimeter of the farm plot.

The question is this. For a given number of fields (N), what is the formula to calculate the individual field length (B) and width (A) expressed in terms of the Gap (G), paper height (H) and paper width (W) assuming that all fields are Golden Rectangles, and that there is also a gap equal to (G) all the way round the perimeter of the farm?

Have fun
DK

Is this a problem for which you want a solution or a challenge to other members of MHF?

CB
• Nov 7th 2011, 10:55 AM
daviskites
Re: calculate the number of best fit golden rectangles in a given area
It's a problem I was pondering, and came up with a near solution. So I guess it's a challenge. I am new to the forum - are challenges OK?
Thank you
DK
• Nov 7th 2011, 07:23 PM
CaptainBlack
Re: calculate the number of best fit golden rectangles in a given area
Quote:

Originally Posted by daviskites
It's a problem I was pondering, and came up with a near solution. So I guess it's a challenge. I am new to the forum - are challenges OK?
Thank you
DK

They should go in the challenges area, but first you should seek approval from the moderators before posting them there.

CB
• Jul 12th 2012, 03:01 AM
Leraroachs
Re: calculate the number of best fit golden rectangles in a given area
came up with a near solution.

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