Rib cage

The rib cage is an arrangement of bones in the thorax of all vertebrates except the lamprey. It is formed by the vertebral column, ribs, and sternum and encloses the heart and lungs. In humans, the rib cage, also known as the thoracic cage, is a bony and cartilaginous structure which surrounds the thoracic cavity and supports the pectoral girdle (shoulder girdle), forming a core portion of the human skeleton. A typical human rib cage consists of 24 ribs, the sternum (with xiphoid process), costal cartilages, and the 12 thoracic vertebrae. Together with the skin and associated fascia and muscles, the rib cage makes up the thoracic wall and provides attachments for the muscles of the neck, thorax, upper abdomen, and back.

Structure

Ribs are described based on their location and connection with the sternum. Ribs that articulate directly with the sternum are called true ribs, whereas those that connect indirectly via cartilage are termed false ribs.

Attachment

The terms true and false rib describe rib pairs that are directly or indirectly attached to the sternum. The phrase true rib (Latin: costae verae), or fixed rib, refers to the first seven, or vertebrosternal, rib pairs. The phrase false rib (Latin: costae spuriae), or vertebrochondral ribs refers to the eighth-to-twelfth pairs of ribs. The eighth-to-tenth pairs of ribs connect to the sternum indirectly via the costal cartilages of the ribs above them. Their elasticity allows ribcage movement for respiratory activity.

Axiom

An axiom or postulate as defined in classic philosophy, is a statement (in mathematics often shown in symbolic form) that is so evident or well-established, that it is accepted without controversy or question. Thus, the axiom can be used as the premise or starting point for further reasoning or arguments, usually in logic or in mathematics The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'

As used in modern logic, an axiom is simply a premise or starting point for reasoning. Whether it is meaningful (and, if so, what it means) for an axiom, or any mathematical statement, to be "true" is a central question in the philosophy of mathematics, with modern mathematicians holding a multitude of different opinions.

As used in mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements that are taken to be true within the system of logic they define (e.g., (A and B) implies A), while non-logical axioms (e.g., a + b = b + a) are actually substantive assertions about the elements of the domain of a specific mathematical theory (such as arithmetic). When used in the latter sense, "axiom", "postulate", and "assumption" may be used interchangeably. In general, a non-logical axiom is not a self-evident truth, but rather a formal logical expression used in deduction to build a mathematical theory. As modern mathematics admits multiple, equally "true" systems of logic, precisely the same thing must be said for logical axioms - they both define and are specific to the particular system of logic that is being invoked. To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms). There are typically multiple ways to axiomatize a given mathematical domain.

Axiom (computer algebra system)

Axiom is a free, general-purpose computer algebra system. It consists of an interpreter environment, a compiler and a library, which defines a strongly typed, mathematically (mostly) correct type hierarchy.

History

Two computer algebra systems named Scratchpad were developed by IBM. The first one was started in 1965 by James Greismer at the request of Ralph Gomory, and written in Fortran. The development of this software was stopped before any public release. The second Scratchpad, originally named Scratchpad II, was developed from 1977 on, at Thomas J. Watson Research Center, under the direction of Richard Dimick Jenks. Other key early developers were Barry Trager, Stephen Watt, James Davenport, Robert Sutor, and Scott Morrison.

Scratchpad II was renamed Axiom when IBM decided, circa 1990, to make it a commercial product. A few years later, it was sold to NAG. In 2001, it was withdrawn from the market and re-released under the Modified BSD License. Since then, the project's lead developer has been Tim Daly.

Axiom (disambiguation)

An axiom is a proposition in mathematics and epistemology that is taken to be self-evident.

Axiom may also refer to:

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