Since (a' neq a), the lines (L_{1}) and (L_{2}) have different slopes and hence intersect at exactly one point, and therefore this point of intersection must be P.
It can be shown that any two blocks of a symmetric (υ, k, λ) design intersect in exactly k treatments.
Steinhaus asked if it were possible to make a set such that no matter how you placed the grid on the plane, the grid and the irregular set always intersect at exactly one point.
Thus, the hypotenuses being diameters meet (intersect) at exactly one point -- the center of the circle!
The blob intersects with exactly one cluster: if the rectangle overlying blob B intersects with the rectangle of a single cluster C, the blob is associated to this cluster, as shown in Figure 15, where I is the intersection rectangle.
Milgrom says experiencing the dioramas is "like peering out of a canvas tent onto bright, enchanted Africa -- an Africa that existed only briefly in the early 1900s, when nature and a man with a prophetic quest to document a vanishing world intersected at exactly the right time".
Let us call an edgeless spacelike surface S a quasi-Cauchy surface if it divides the rest of the manifold into two parts such that a) every point in the manifold can be connected by a timelike curve to S, and b) any timelike curve which connects a point in one region to a point in the other region intersects S exactly once.
We show the necessary conditions are sufficient for the existence of GDD n,2,4; λ2, λ2) with two groups and block size four in which every block intersects each group exactly twice (even GDD's) or in which every block intersects each group in one or three points (odd GDD's).
The selection of five particles from those available (up to 14) also helped us to ensure this center cross-section positioning, as we were able to only select particles where the focal plane exactly intersected with the center of each particle.
