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I have been given the following equation to use to investigate Isoperimetric Quotients:- I will begin by investigating the Isoperimetric Quotients of rectangles:- Using this method I have gathered the following results:- Width (cm) Length (cm) IQ 2 5 0.641* 3 24 0.310 12 17 0.762 2 10 0.436 3 7 0.659 1 4 0.503** 3 3 0.785 2 6 0.589*** 1 3 0.589*** 12 3 0.503** 4 6 0.754 6 15 0.641* At this stage I can observe that IQ's of rectangles are all less than 1. I have marked the shapes that have the same Isoperimetric Quotients as one another with *'s. In each case I observe that the lengths and widths of the shapes are in the same ratio as their partners. To prove this I will investigate 2 more rectangles in ratio with each other:- This proves that rectangles in the same ratio have the same IQ. In the table the rectangle with the largest IQ was a Square, and the lowest IQ was a long, thin rectangle. I will now look further into this, and to keep it fair, both shapes will have the same area:- This is another long,...

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