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
Distance from a point to a plane the closest point to the origin may be expressed more succinctly using notation from linear algebra. The expression formula_19 in the definition of a plane is a dot product formula_20, and the expression formula_21 appearing in the solution is the squared norm formula_22. Thus, if formula_23 is a given vector, the plane may be described as the set of vectors formula_24 for which formula_25 and the closest point on this plane is the vector Written in Cartesian form, the closest point is given by formula_27 for formula_28 where and the distance from formula_30 to the hyperplane is Thus in formula_32