This condition is equivalent to the condition that each side of \(T\) lies within the union of the δ-neighbourhoods of the other two sides, as illustrated in Figure 13, right. There is no constant δ such that all triangles in a Euclidean plane are δ-thin, because for any δ there are triangles large enough that the midpoint of a longest side lies further than δ from all points on the other two sides.