Browse Definitions :
Definition

transcendental number

A transcendental number is a real number that is not the solution of any single-variable polynomial equation whose coefficients are all integers . All transcendental numbers are irrational numbers . But the converse is not true; there are some irrational numbers that are not transcendental.

Examples of transcendental numbers include pi , the ratio of a circle's circumference to its diameter in a plane, and e , the base of the natural logarithm . The case of pi has historical significance. The fact that pi is transcendental means that it is impossible to draw to perfection, using a compass and straightedge and following the ancient Greek rules for geometric constructions, a square with the same area as a given circle. This ancient puzzle, known as squaring the circle , was, for centuries, one of the most baffling challenges in geometry. Schemes have been devised that provide amazingly close approximations to squaring the circle. But in theoretical mathematics (unlike physics and engineering), approximations are never good enough; a solution, scheme, or method is either valid, or else it is not.

It can be difficult, and perhaps impossible, to determine whether or not a certain irrational number is transcendental. Some numbers defy classification (algebraic, irrational, or transcendental) to this day. Two examples are the product of pi and e (call this quantity P pie ) and the sum of pi and e (call this S pie ). It has been proved that pi and e are both transcendental. It has also been shown that at least one of the two quantities P pie and S pie are transcendental. But as of this writing, no one has rigorously proven that P pie is transcendental, and no one has rigorously proved that S pie is transcendental.

This was last updated in September 2005

SearchCompliance

  • information governance

    Information governance is a holistic approach to managing corporate information by implementing processes, roles, controls and ...

  • enterprise document management (EDM)

    Enterprise document management (EDM) is a strategy for overseeing an organization's paper and electronic documents so they can be...

  • risk assessment

    Risk assessment is the identification of hazards that could negatively impact an organization's ability to conduct business.

SearchSecurity

  • cyber espionage

    Cyber espionage, also called cyber spying, is a form of cyber attack that is carried out against a competitive company or ...

  • virus (computer virus)

    A computer virus is malicious code that replicates by copying itself to another program, computer boot sector or document and ...

  • spam trap

    A spam trap is an email address that is used to identify and monitor spam email.

SearchHealthIT

SearchDisasterRecovery

  • risk mitigation

    Risk mitigation is a strategy to prepare for and lessen the effects of threats faced by a business.

  • call tree

    A call tree is a layered hierarchical communication model that is used to notify specific individuals of an event and coordinate ...

  • Disaster Recovery as a Service (DRaaS)

    Disaster recovery as a service (DRaaS) is the replication and hosting of physical or virtual servers by a third party to provide ...

SearchStorage

  • cloud storage

    Cloud storage is a service model in which data is transmitted and stored on remote storage systems, where it is maintained, ...

  • cloud testing

    Cloud testing is the process of using the cloud computing resources of a third-party service provider to test software ...

  • storage virtualization

    Storage virtualization is the pooling of physical storage from multiple storage devices into what appears to be a single storage ...

Close