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.

## Making a perfect venn diagram

**Moderators:** gmalivuk, Moderators General, Prelates

- skeptical scientist
- closed-minded spiritualist
**Posts:**6142**Joined:**Tue Nov 28, 2006 6:09 am UTC**Location:**San Francisco

### Re: Making a perfect venn diagram

**Spoiler:**

I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

"With math, all things are possible." —Rebecca Watson

### Re: Making a perfect venn diagram

OK, I don't know how to do the markups to make the pretty math symbols, but I think I can explain it without.

Darn, beaten to it

**Spoiler:**

Darn, beaten to it

### Re: Making a perfect venn diagram

Not to be preachy, but this is a classic example of a problem that people think can't be solved without calculus that requires only one observation to solve with elementary methods. Which is this:

**Spoiler:**

- skeptical scientist
- closed-minded spiritualist
**Posts:**6142**Joined:**Tue Nov 28, 2006 6:09 am UTC**Location:**San Francisco

### Re: Making a perfect venn diagram

Is there something wrong with calculus? I never said I needed it, it's just the first thing I thought of (perhaps because I'm teaching trig substitution right now).

I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

"With math, all things are possible." —Rebecca Watson

### Re: Making a perfect venn diagram

Is the same feat possible with 3 circles?

### Re: Making a perfect venn diagram

Yes. The center of a Venn diagram with three circles is the union of three half-lunes (which are the difference of a sector and a triangle) and a triangle, and once you've got the area of the center you've got the area of the other three intersections.

### Re: Making a perfect venn diagram

You just need to find the area of the center. Damn, old college memories are kicking in x.x

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