mathematics

Telephone number mapping

Telephone number mapping is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Telephone number mapping rather than just read about it. In short: Telephone number mapping is a system of unifying the international telephone number system of the public switched telephone network with the Internet addressing and identification name spaces. Internationally, telephone numbers are systematically organized by the E.164 standard, while the Internet uses the Domain Name System (DNS) for linking domain names to IP addresses and other resource information.

Key takeaways

Telephone number mapping belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Telephone number mapping to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Telephone number mapping from memory before moving on to harder problems.

Reference excerpt

Telephone number mapping is a system of unifying the international telephone number system of the public switched telephone network with the Internet addressing and identification name spaces. Internationally, telephone numbers are systematically organized by the E.164 standard, while the Internet uses the Domain Name System (DNS) for linking domain names to IP addresses and other resource information. Telephone number mapping systems provide facilities to determine applicable Internet communications servers responsible for servicing a given telephone number using DNS queries. The most prominent facility for telephone number mapping is the E.164 number to URI mapping (ENUM) standard. It uses special DNS record types to translate a telephone number into a Uniform Resource Identifier (URI) or IP address that can be used in Internet communications.

Rationale Being able to dial telephone numbers the way customers have come to expect is considered crucial for the convergence of classic telephone service (PSTN) and Internet telephony (Voice over IP, VoIP), and for the development of new IP multimedia services. The problem of a single universal personal identifier for multiple communication services can be solved with different approaches. One simple approach is the Electronic Number Mapping System (ENUM), developed by the IETF, using existing E.164 telephone numbers, protocols and infrastructure to indirectly access different services available under a single personal identifier. ENUM also permits connecting the IP world to the telephone system in a seamless manner.

System details For an ENUM subscriber to be able to activate and use the ENUM service, it needs to obtain three elements from a Registrar:

A personal Uniform Resource Identifier (URI) to be used on the IP part of the network, as explained below. One E.164 regular personal telephone number associated with the personal URI, to be used on the PSTN part of the network. Authority to write their call forwarding/termination preferences in the NAPTR record accessible via the personal URI. This works as follows: (1) the Registrar provides the Subscriber (or Registrant) with a domain name, the URI, that will be used for accessing a DNS server to fetch a NAPTR record, (2) a personal E.164 telephone number (the ENUM number). The URI domain name of (1) is biunivocally associated (one-to-one mapped) to the subscriber E.164 ENUM number of (2). Finally (3) the NAPTR record corresponding to the subscriber URI contains the subscriber call forwarding/termination preferences. Therefore, if a calling party being at the PSTN network dials a called party ENUM number by touch typing the E.164 called party number, the number will be translated at the ENUM gateway into the corresponding URI. This URI will be used for looking-up and fetching the NAPTR record obtaining the called party wishes about how the call should be forwarded or terminated (either on IP or on PSTN terminations) – the so-called access information – which the registrant (the called party) has specified by writing his/her choice at the NAPTR record ("Naming Authority Pointer Resource Records" as defined in RFC 3403), such as e-mail addresses, a fax number, a personal website, a VoIP number, mobile telephone numbers, voice mail systems, IP-telephony addresses, web pages, GPS coordinates, call diversions or instant messaging. Alternatively, when the calling party is at the IP side, the User Agent (UA) piece of software of the dialler will allow to dial a E.164 number, but the dialler UA will convert it into a URI, to be used for looking-up at the ENUM gateway DNS and fetch the NAPTR record obtaining the called party wishes about how the call should be forwarded or terminated (again, either on IP or on PSTN terminations). Calling by using a new personal E.164 number (the ENUM number) to look-up at a database is therefore an indirect calling support service. The ITU ENUM allocates a specific zone, namely "e164.arpa" for use with ENUM E.164 numbers on the IP side of the network. RFC 6116 defines how any E.164 number, such as +1 555 42 42 can be transformed into a URI, by reversing the numbers, separating them with dots and adding the e164.arpa suffix thus: 2.4.2.4.5.5.5.1.e164.arpa The URI can then be used for obtaining the Internet Protocol addresses for services such as the Session Initiation Protocol (SIP) VoIP telephony. In the DNS, NAPTR records are used for setting the subscriber call forwarding/termination preferences. Therefore, the whole system can 'translate' E.164 addresses to SIP addresses. An example NAPTR record is:

This example specifies that if one wants to use the "E2U+sip" service, one should use sip:phoneme@example.net as the address. The regular expression can be used by a telephone company to easily assign addresses to all of its clients. For example, if one's number is +15554242, one's SIP address is sip:4242@555telco.example.net; if the number is +15551234, the SIP address is sip:1234@555telco.example.net. The following Figure illustrates how ENUM works by giving an example: Subscriber A sets out to call Subscriber B.

… excerpt ends here. Continue reading the full article.

Illustrations

Telephone number mapping: Call forwarding with ENUM — Call forwarding with ENUM

Worked examples

Example 1 — a first encounter with Telephone number mapping

Start with the simplest possible case. Write down what Telephone number mapping claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Telephone number mapping before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Telephone number mapping ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Telephone number mapping

In research: Telephone number mapping appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Telephone number mapping in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Telephone number mapping is common in secondary-school and first-year university syllabi. It links to neighbouring topics International telecommunications, Telephone numbers, so understanding it makes those chapters shorter.
In everyday life: Look for Telephone number mapping outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Telephone number mapping in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Telephone number mapping means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Telephone number mapping out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Telephone number mapping in simple terms?

Why does Telephone number mapping matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Telephone number mapping?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Telephone number mapping.