Pascal's triangle Construct a "d"-dimensional triangle (a 3-dimensional triangle is a tetrahedron) by placing additional dots below an initial dot, corresponding to P(1) = 1. Place these dots in a manner analogous to the placement of numbers in Pascal's triangle. To find P("x"), have a total of "x" dots composing the target shape. P("x") then equals the total number of dots in the shape. A 0-dimensional triangle is a point and a 1-dimensional triangle is simply a line, and therefore P("x") = "1" and P("x") = "x", which is the sequence of natural numbers. The number of dots in each layer corresponds
Grid cell an action potential, then as illustrated in the adjoining figure, these dots build up over time to form a set of small clusters, and the clusters form the vertices of a grid of equilateral triangles. This regular triangle-pattern is what distinguishes grid cells from other types of cells that show spatial firing. By contrast, if a place cell from the rat hippocampus is examined in the same way (i.e., by placing a dot at the location of the rat's head whenever the cell emits an action potential), then the dots build up to form small clusters, but frequently there is