Question #766

Let D c R[sup]2[/sup] be the unit disk in the Euclidean plane, and let S c R[sup]2[/sup] be the filled in square of unit side-length. Can you decompose D as the disjoint union of two connected sets, D= D1∪ D2, and S as the disjoint union of two connected sets, S=S1∪S2, such that D1 is similar to S1 and D2 is similar to S2?(here "similar to" means they differ only by scaling;in other words, by th linear transformation L(x)=aXfor some positive number a∈ R.) You can present your proposed solutuion in the form of drwan pictures

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