Math;Shapes within a shape?

Question

Math;Shapes within a shape?
Is there a formula in which you can work out how many pieces of an exact shape you can get out of another shape. For example:
I want to get as many squares as possible that measure 270mm x 270mm out of a rectangle that measures 825mm x 1800mm. Answer would be 18.

Anothet example would be i want rectangles that measure 225mm x 300mm out of a rectangle that measures 825mm x 2400mm. Answer would be 28.

Answer

Only in case when smaller shapes are circles, squares, isoscelic triangles and other like those - it would be 'floor (Area of Larger/Area of smaller)'. In case of shapes as rectangles you have an optimisation problem as these can be arranged differently in the bigger shape - you will need a linear programming equation I believe but this is beyound my knowledge

Math;Shapes within a shape?

Answers (1)