### Making a perfect venn diagram

Posted:

**Sun Jan 11, 2009 3:56 am UTC**This problem has been bugging me over the last 2 days. My math-fu is lacking so hopefully someone can help me out.

In a nutshell, what is the ratio (red line:blue line) of the perfect venn diagram (ie each portion has an equal area).

The green area would have to be equal to half of either of circles. It doesn't strike me as a very difficult problem but I can't seem to find any equations for lunes/lenses/vesica piscis.

In other related questions:

What about if the area of the green is equal to the total of the yellow.

Is it possible to do this with three circles and have 7 equal areas?

If not, what about 6 equal portions ignoring the centre.

In a nutshell, what is the ratio (red line:blue line) of the perfect venn diagram (ie each portion has an equal area).

The green area would have to be equal to half of either of circles. It doesn't strike me as a very difficult problem but I can't seem to find any equations for lunes/lenses/vesica piscis.

In other related questions:

What about if the area of the green is equal to the total of the yellow.

Is it possible to do this with three circles and have 7 equal areas?

If not, what about 6 equal portions ignoring the centre.