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 identity, also known as "Lagrange's formula" may be remembered as "BAC minus CAB", keeping in mind which vectors are dotted together. This formula finds application in simplifying vector calculations in physics. In physics, vector magnitude is a scalar in the physical sense, i.e. a physical quantity independent of the coordinate system, expressed as the product of a numerical value and a physical unit, not just a number. The dot product is also a scalar in this sense, given by the formula, independent of the coordinate system. Examples include: For vectors with complex entries, using the given definition of the dot