Kappa

Encyclopedia

**Kappa**is the 10th letter of the Greek alphabet

Greek alphabet

The Greek alphabet is the script that has been used to write the Greek language since at least 730 BC . The alphabet in its classical and modern form consists of 24 letters ordered in sequence from alpha to omega...

, used to represent the voiceless velar stop, or "k", sound in Ancient

Ancient Greek

Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...

and Modern Greek

Modern Greek

Modern Greek refers to the varieties of the Greek language spoken in the modern era. The beginning of the "modern" period of the language is often symbolically assigned to the fall of the Byzantine Empire in 1453, even though that date marks no clear linguistic boundary and many characteristic...

. In the system of Greek numerals

Greek numerals

Greek numerals are a system of representing numbers using letters of the Greek alphabet. They are also known by the names Ionian numerals, Milesian numerals , Alexandrian numerals, or alphabetic numerals...

it has a value of 20. It was derived from the Phoenician letter Kaph

Kaph

Kaph is the eleventh letter of many Semitic abjads, including Phoenician, Aramaic, Hebrew Kaf , Arabic alphabet , Persian alphabet...

. Letters that arose from kappa include the Roman K

K

K is the eleventh letter of the English and basic modern Latin alphabet.-History and usage:In English, the letter K usually represents the voiceless velar plosive; this sound is also transcribed by in the International Phonetic Alphabet and X-SAMPA....

and Cyrillic К

Ka (Cyrillic)

Ka is a letter of the Cyrillic alphabet.It commonly represents the voiceless velar plosive , like the pronunciation of ⟨k⟩ in "king".-History:...

.

Greek proper names and placenames containing kappa are often written in English with "c" due to contemporary rendering into the Latin alphabet

Latin alphabet

The Latin alphabet, also called the Roman alphabet, is the most recognized alphabet used in the world today. It evolved from a western variety of the Greek alphabet called the Cumaean alphabet, which was adopted and modified by the Etruscans who ruled early Rome...

by ancient Romans. However, modern transliteration of the Greek language invariably use the letter "k". Compare

*Κυνοσκεφαλαι*,

*Cynoscephalae*(ancient placename);

*κυνος κεφαλαι*,

*kunos kephalai*(phrase), meaning "dog

Dog

The domestic dog is a domesticated form of the gray wolf, a member of the Canidae family of the order Carnivora. The term is used for both feral and pet varieties. The dog may have been the first animal to be domesticated, and has been the most widely kept working, hunting, and companion animal in...

's head

Head

In anatomy, the head of an animal is the rostral part that usually comprises the brain, eyes, ears, nose and mouth . Some very simple animals may not have a head, but many bilaterally symmetric forms do....

s".

In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, the kappa curve

Kappa curve

In geometry, the kappa curve or Gutschoven's curve is a two-dimensional algebraic curve resembling the Greek letter κ .Using the Cartesian coordinate system it can be expressed as:x^2=a^2y^2or, using parametric equations:...

is named after this letter; the tangent

Tangent

In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f...

s of this curve

Curve

In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...

were first calculated by Barrow

Isaac Barrow

Isaac Barrow was an English Christian theologian, and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for the discovery of the fundamental theorem of calculus. His work centered on the properties of the tangent; Barrow was...

(17th Century).

## Symbol

In graph theoryGraph theory

In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...

, the connectivity

Connectivity (graph theory)

In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements which need to be removed to disconnect the remaining nodes from each other. It is closely related to the theory of network flow problems...

of a graph

Graph (mathematics)

In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges...

is given by κ.

In differential geometry, the curvature

Curvature

In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...

of a curve is given by κ.

In physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, the torsional constant of an oscillator is given by κ as well as Einstein constant of gravitation.

In structural design, 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

Electrical engineering

Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...

, it 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.

In chemistry

Chemistry

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, the compressibility of a compound is given by κ.

In psychology

Psychology

Psychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...

and psychiatry

Psychiatry

Psychiatry is the medical specialty devoted to the study and treatment of mental disorders. These mental disorders include various affective, behavioural, cognitive and perceptual abnormalities...

, kappa represents a measure of diagnostic reliability.

In biology

Biology

Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

, kappa and kappa prime are important nucleotide

Nucleotide

Nucleotides are molecules that, when joined together, make up the structural units of RNA and DNA. In addition, nucleotides participate in cellular signaling , and are incorporated into important cofactors of enzymatic reactions...

motifs for a tertiary interaction of group II introns.

In biology

Biology

Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

, kappa designates a subtype of an antibody

Antibody

An antibody, also known as an immunoglobulin, is a large Y-shaped protein used by the immune system to identify and neutralize foreign objects such as bacteria and viruses. The antibody recognizes a unique part of the foreign target, termed an antigen...

component.

In pharmacology

Pharmacology

Pharmacology is the branch of medicine and biology concerned with the study of drug action. More specifically, it is the study of the interactions that occur between a living organism and chemicals that affect normal or abnormal biochemical function...

, kappa represents a type of opioid receptors.

Kappa statistics such as Cohen's kappa

Cohen's kappa

Cohen's kappa coefficient is a statistical measure of inter-rater agreement or inter-annotator agreement for qualitative items. It is generally thought to be a more robust measure than simple percent agreement calculation since κ takes into account the agreement occurring by chance. Some...

and Fleiss' kappa

Fleiss' kappa

Fleiss' kappa is a statistical measure for assessing the reliability of agreement between a fixed number of raters when assigning categorical ratings to a number of items or classifying items. This contrasts with other kappas such as Cohen's kappa, which only work when assessing the agreement...

are methods for calculating inter-rater agreement.

Upper-case letter Κ is used as a symbol for:

In textual criticism

Textual criticism

Textual criticism is a branch of literary criticism that is concerned with the identification and removal of transcription errors in the texts of manuscripts...

, the Byzantine text-type

Byzantine text-type

The Byzantine text-type is one of several text-types used in textual criticism to describe the textual character of Greek New Testament manuscripts. It is the form found in the largest number of surviving manuscripts, though not in the oldest...

(from Κοινη,

*Koine*, the common text).

In set theory

Set theory

Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...

, kappa is often used to denote an ordinal which is also a cardinal.