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

Start the conversation

Send me notifications when other members comment.

By submitting you agree to receive email from TechTarget and its partners. If you reside outside of the United States, you consent to having your personal data transferred to and processed in the United States. Privacy

Please create a username to comment.

-ADS BY GOOGLE

File Extensions and File Formats

Powered by:

SearchCompliance

  • cyborg anthropologist

    A cyborg anthropologist is an individual who studies the interaction between humans and technology, observing how technology can ...

  • RegTech

    RegTech, or regulatory technology, is a term used to describe technology that is used to help streamline the process of ...

  • conduct risk

    Conduct risk is the prospect of financial loss to an organization that is caused by the actions of an organization's ...

SearchSecurity

  • application whitelisting

    Application whitelisting is the practice of identifying applications that have been deemed safe for execution and restricting all...

  • security

    Security, in information technology (IT), is the defense of digital information and IT assets against internal and external, ...

  • insider threat

    An insider threat is a malicious hacker (also called a cracker or a black hat) who is an employee or officer of a business, ...

SearchHealthIT

  • HIPAA Privacy Rule

    The Standards for Privacy of Individually Identifiable Health Information, commonly known as the HIPAA Privacy Rule, establishes ...

  • HIPAA business associate agreement (BAA)

    Under the U.S. Health Insurance Portability and Accountability Act of 1996, a HIPAA business associate agreement (BAA) is a ...

  • telemedicine

    Telemedicine is the remote delivery of healthcare services, such as health assessments or consultations, over the ...

SearchDisasterRecovery

  • data recovery

    Data recovery restores data that has been lost, accidentally deleted, corrupted or made inaccessible. Learn how data recovery ...

  • disaster recovery plan (DRP)

    A company's disaster recovery policy is enhanced with a documented DR plan that formulates strategies, and outlines preparation ...

  • fault-tolerant

    Systems with integrated fault tolerance are designed to withstand multiple hardware failures to ensure continuous availability.

SearchStorage

  • data deduplication

    Deduplication retains one unique data instance to reduce storage and bandwidth consumed by remote backups, replication and ...

  • byte

    In most computer systems, a byte is a unit of data that is eight binary digits long. Bytes are often used to represent a ...

  • Secure Digital card (SD card)

    SD cards use flash memory to provide nonvolatile storage. They are more rugged than traditional storage media and are used in ...

SearchSolidStateStorage

  • flash file system

    Flash file systems are designed specifically for memory devices. A well-designed flash device and flash file system ensure ...

  • IOPS (input/output operations per second)

    IOPS measures the maximum number of reads and writes to non-contiguous storage. It is not an actual benchmark since vendor ...

  • eMMC (embedded MultiMediaCard)

    An embedded MultiMediaCard (eMMC) is a small storage device made up of NAND flash memory and a simple storage controller.

SearchCloudStorage

  • RESTful API

    A RESTful application program interface breaks down a transaction to create a series of small modules, each of which addresses an...

  • cloud storage infrastructure

    Cloud storage infrastructure is the hardware and software framework that supports the computing requirements of a private or ...

  • Zadara VPSA and ZIOS

    Zadara Storage provides block, file or object storage with varying levels of compute and capacity through its ZIOS and VPSA ...

Close