Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

You can make a 4 variable

venn diagram by

placing 4 spheres at the

corners of a tetrahedron.

Make the spheres overlap

just like the 3 circle Venn

diagrams you've seen

on flat paper.

**igloo** **myrtilles** **fourmis**

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Here's my drawing for it.

Click image to make big.

**igloo** **myrtilles** **fourmis**

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

So there are 16 places in the 4-ball Venn Diagram.

The places look like the parts of a pyramid, but

not the pyramids with a square base like the Egyptians,

but instead a pyramid with a triangle for the bottom.

1. the four corners called vertices

2. "

3. "

4. "

5. the six edges of the pyramid

6. "

7. "

8. "

9. "

10. "

11. the four triangular sides called faces

12. "

13. "

14. "

15. the space inside the pyramid

16. the space outside the pyramid

These 16 places are like the

16 vertices of a 4-D hypercube,

which is more symmetrical, but

unfortunately we don't live in

4-D, so we can't see the

perfect symmetry of that, but

it would be like the differenence

between a square to a cube, it

gets twice as many corners as

a cube.

But this thread is really about

the Venn diagram, since you

can see it in 3-D, which is nice.

But the 16 places of the tetrahedron

are not uniform between all 16, because

they form groups, such as

sides, edges, corners, inside and outside!!

*Last edited by John E. Franklin (2008-05-12 09:11:28)*

**igloo** **myrtilles** **fourmis**

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Venn diagrams and boolean equations go hand-in-hand.

Another construction is the Karnaugh map, which is

less well known to the mathematician, as it was designed

for digital electronic designers. And don't forget the

hypercubes, as they are actually the same thing as a

Karnaugh map, except even better due to perfect symmetry.

If you would like to see a paper I wrote on this subject,

which is perhaps not very well written yet, follow this

link and X-out the silly ads overlayed on top of my paper.

http://johnericfranklin.250free.com

or same:

http://johnericfranklin.250free.com

This long webpage might give you some insight as to where

I'm coming from, or it might might bring more confusion to

the table!! (quite likely, lol)

**igloo** **myrtilles** **fourmis**

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Here's a 4-D hypercube I just drew that is

unlike others I have seen. It makes use

of the idea that tetrahedrons fit nicely

inside cubes. The green and the red dots

are not really connected. They look like

they are in the picture just because of the

overall cube shape I started with. To travel

from a red to a green dot would require

travelling first through either a yellow,

purple, or blue dot.

*Last edited by John E. Franklin (2009-04-07 08:06:02)*

**igloo** **myrtilles** **fourmis**

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Glad to hear it!!!

**igloo** **myrtilles** **fourmis**

Offline