
EggMath: The White/Yolk Theorem
Examples of the White/Yolk
Theorem
Each of the four examples on this page shows
two colored regions in the plane. Your job is to
find a straightline cut which simultaneously
divides each region exactly in half. In the left
column, click and drag on the picture to draw a
black line. The bars at the bottom show what
fraction of each region is above the line. Your
job is to drag the line around (drag either
controlling point) until both regions are split
exactly 5050.
If you get stuck, try the applets in the right
column. Here, you simply select (with the slider
at the bottom) the direction of the cut. The
computer calculates and draws for you the lines
(in that direction) that would split each region
in half. As you turn the direction, notice that
those lines are sometimes far apart (meaning that
no single line could do a good job of splitting
both regions) and sometimes closer together. Your
job now is merely to find a direction where the
two lines coincide.








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