Night writing visited the National Institute for the Blind in Paris, France, where he met Louis Braille. Braille identified the major failing of the code, which was that the human finger could not encompass the whole symbol without moving and so could not move rapidly from one symbol to another. His modification was to use a six-dot cell, the Braille system that revolutionized written communication for the visually impaired. Night writing Night writing, a.k.a. sonography, was a system of code that used symbols of twelve dots arranged as two columns of six dots embossed on a square of paperboard, and is now
Dot product representation of a graph called the dot product dimension. Dot product representation of a graph A dot product representation of a simple graph is a method of representing a graph using vector spaces and the dot product from linear algebra. Every graph has a dot product representation. Let "G" be a graph with vertex set "V". Let "F" be a field, and "f" a function from "V" to "F" such that "xy" is an edge of "G" if and only if "f"("x")·"f"("y") ≥ "t". This is the dot product representation of "G". The number "t" is called the dot product threshold, and the smallest