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
Venus Equilateral by a low-power source. Powered by batteries, the driver tube enables the multi-G constant-boost spaceships seen throughout the series. At the series opening both Mars and Venus have been colonized. Both are described as having shirt-sleeve environments in at least some regions. Eleven of the thirteen Venus Equilateral stories were published in "Astounding Science Fiction" between 1942 and 1945. They were: Smith wrote a 12th story, "Mad Holiday", for the first book collection "Venus Equilateral" (1947) (which omitted "Lost Art" and "Identity"), and a 13th story, "The External Triangle", for Harry Harrison's 1973 anthology "Astounding". All 13 stories were included