Kappa

Kappa ('kæpə; uppercase Κ, lowercase κ or cursive ; κάππα, káppa) is the tenth letter of the Greek alphabet, representing the voiceless velar plosive k sound in Ancient and Modern Greek. In the system of Greek numerals, Kʹ has a value of 20. It was derived from the Phoenician letter kaph . Letters that arose from kappa include the Roman K and Cyrillic К. The uppercase form is identical to the Latin K. Greek proper names and placenames containing kappa are often written in English with "c" due to the Romans' transliterations into the Latin alphabet: Constantinople, Corinth, Crete. All formal modern romanizations of Greek now use the letter "k", however. The cursive form is generally a simple font variant of lower-case kappa, but it is encoded separately in Unicode for occasions where it is used as a separate symbol in math and science. In mathematics, the kappa curve is named after this letter; the tangents of this curve were first calculated by Isaac Barrow in the 17th century. Mathematics and statistics In graph theory, the connectivity of a graph is given by κ. In differential geometry, the curvature of a curve is given by κ. In linear algebra, the condition number of a matrix is given by κ. Kappa statistics such as Cohen's kappa and Fleiss' kappa are methods for calculating inter-rater reliability. Physics In cosmology, the Einstein gravitational constant is denoted by κ. In physics, the torsional constant of an oscillator is given by κ. In physics, the coupling coefficient in magnetostatics is represented by κ. In physics, the dielectric coefficient is represented by κ. In fluid dynamics, the von Kármán constant is represented by κ. In thermodynamics, the compressibility of a compound is given by κ. Engineering In structural engineering, κ is the ratio of the smaller factored moment to the larger factored moment and is used to calculate the critical elastic moment of an unbraced steel member. In electrical engineering, κ is the multiplication factor, a function of the R/X ratio of the equivalent power system network, which is used in calculating the peak short-circuit current of a system fault.