Unequal circles in a rectangle partition into k equal layers

How can I create circles of different sizes in a rectangle divided into k equal layers. The circles in the first layer are equal and smaller. The circles in the second layers are also equal but bigger than the first layer. This continues in that order. The common radius difference between the two adjacent layer circles is fix

Thank you

[dpb]

I don't know what "a rectangle divided into k equal layers" is????

[Nura Modi]

Rectangle divided into k equal parts, for instance 4 equal parts. Thank you for your response @dpb

[dpb]

Dunno for sure, didn't try the algebrabut otomh I don't know that you can with the constraint given...assuming there has to be an integral number of circles in each section. At least I'd guess it's highly limited choice...

[dpb]

[OP Answer moved to comment--dpb]

The number of circles will be more in first part with smaller radius. That means the number circles is decreasing with respect to the increase in the radius accross the sections with fix interval according to radius difference between the circles in two adjacent parts. Section with small radius more number of circles. Thank you @dpb

[dpb]

Yeah, but if the rectangle is divided into equal parts, then the diameters of the circles have to be able to be divided evenly into each of those parts...if you want whole circles, anyway???

That part is doable if that's the only constraint but when you add in that you want the difference between those diameters to also be fixed you've got a problem...

[dpb]

[OP Answer moved to comment--dpb. Use the comment button for other than actual answer to the question, please]

Thank you Sir. For example if we have ten circles in the first part with smallest radius. Taking the double of the radius of the first layer in the second layer, it is likely to obtain five circles in the second layer. The common radius difference between the circles in the two adjacent layers is likely to be fixed.I am not sure about this. Please Sir, what is the best way to address this in MATLAB. Many thanks @dpb

[dpb]

For two and if you let the ratio be two and pick a first number divisible by two it works, yes.

Try three or pick 25 circles for the first....now what????

We don't have a working definition of what is an allowable solution yet, too soon to worry about code.

[Nura Modi]

If the number of circles can be even it would be better. If number of circles is three,25 or any odd number actually I don't know how to handle this. My thought was that the number of circles could be even. Thank so much Sir.

Answer 1

[Image Analyst]

See previous discussions of circle packing: Click here