Divide convex polygon into 4 equal areas

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Homework Statement



Show that it is possible to cut any convex polygon into 4 pieces of equal areas by using two cuts perpendicular to each other.

Homework Equations


None, it's just a proof I found on the back of my book. The relevant chapter is Continuity, the maximum principle, and intermediate value theorem for real analysis.


The Attempt at a Solution



I have no idea! Can someone tell me how to approach this please?

Thanks!
 
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Anyone know how to do this?
 
What about considering the centroid of the convex polygon?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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