# Symmetric Independent Families of Four Isosceles Triangles

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows symmetric independent families of four isosceles triangles with up to 18 regions.

Contributed by: Izidor Hafner (April 2019)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Consider a family of simple (Jordan) curves that intersect pairwise in finitely many points. Let be either the interior or the exterior of . The family is called independent if

for each of the possible choices of the . If, moreover, each of the sets is connected, the independent family is called a Venn diagram. An independent family or Venn diagram is called simple if no three curves have a common point [1, p. 104].

An example with equilateral triangles is from [1, p. 107].

Reference

[1] B. Grünbaum, "The Search for Symmetric Venn Diagrams," *Geombinatorics*, 8(4), 1999 pp. 104–109. (Apr 4, 2019) sites.math.washington.edu/~grunbaum/SymmetricVennDiagrams.pdf.

## Permanent Citation