3
$\begingroup$

You can dissect a circle of radius $3$ into $9$ equal areas by placing within it $5$ unit circles in an orthogonal cross shape. You could then place $5$ of these radius $3$ circles into a circle of radius $9$ in a similar way. Is it then possible to dissect the $4$ irregular shapes each into $9$ equal areas using only circles? Or is there another entirely different way of achieving a similar result?

$\endgroup$
3
$\begingroup$

My first thought was to make 80 concentric circles, all centered at the center of the big circle. Choose radii $r_1, r_2, \cdots, r_{80}$ so that each band of the dart board has the area $1/81$ of the area of the big circle.

$\endgroup$
  • $\begingroup$ Then I guess a natural followup question is how few circles can be used. And another followup question is to generalize to an arbitrary number of pieces. $\endgroup$ – Solomonoff's Secret Aug 9 '17 at 17:28

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.