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DTMF

Dual-tone multi-frequency signaling (DTMF) is a telecommunication signaling system using the voice-frequency band over telephone lines between telephone equipment and other communications devices and switching centers. DTMF was first developed in the Bell System in the United States, and became known under the trademark Touch-Tone for use in push-button telephones supplied to telephone customers, starting in 1963. DTMF is standardized as ITU-T Recommendation Q.23. It is also known in the UK as MF4.

Touch-Tone dialing with a telephone keypad gradually replaced the use of rotary dials and has become the industry standard in telephony to control automated equipment and signal user intent. Other multi-frequency systems are also used for signaling on trunks in the telephone network.

Multifrequency signaling
Before the development of DTMF, telephone numbers were dialed by users with a loop-disconnect (LD) signaling, more commonly known as pulse dialing (dial pulse, DP) in the United States. It functions by interrupting the current in the local loop between the telephone exchange and the calling party's telephone at a precise rate with a switch in the telephone that is operated by the rotary dial as it spins back to its rest position after having been rotated to each desired number. The exchange equipment responds to the dial pulses either directly by operating relays or by storing the number in a digit register that records the dialed number. The physical distance for which this type of dialing was possible was restricted by electrical distortions and was possible only on direct metallic links between end points of a line. Placing calls over longer distances required either operator assistance or provision of special subscriber trunk dialing equipment. Operators used an earlier type of multi-frequency signaling.

Multi-frequency signaling (MF) is a group of signaling methods that use a mixture of two pure tone (pure sine wave) sounds. Various MF signaling protocols were devised by the Bell System and CCITT. The earliest of these were for in-band signaling between switching centers, where long-distance telephone operators used a 16-digit keypad to input the next portion of the destination telephone number in order to contact the next downstream long-distance telephone operator. This semi-automated signaling and switching proved successful in both speed and cost effectiveness. Based on this prior success with using MF by specialists to establish long-distance telephone calls, dual-tone multi-frequency signaling was developed for end-user signaling without the assistance of operators.

The DTMF system uses a set of eight audio frequencies transmitted in pairs to represent 16 signals, represented by the ten digits, the letters A to D, and the symbols # and *. As the signals are audible tones in the voice frequency range, they can be transmitted through electrical repeaters and amplifiers, and over radio and microwave links, thus eliminating the need for intermediate operators on long-distance circuits.

AT&T described the product as "a method for pushbutton signaling from customer stations using the voice transmission path". In order to prevent consumer telephones from interfering with the MF-based routing and switching between telephone switching centers, DTMF frequencies differ from all of the pre-existing MF signaling protocols between switching centers: MF/R1, R2, CCS4, CCS5, and others that were later replaced by SS7 digital signaling. DTMF was known throughout the Bell System by the trademark Touch-Tone. The term was first used by AT&T in commerce on July 5, 1960, and was introduced to the public on November 18, 1963, when the first push-button telephone was made available to the public. As a parent company of Bell Systems, AT&T held the trademark from September 4, 1962, to March 13, 1984. It is standardized by ITU-T Recommendation Q.23. In the UK, it is also known as MF4.

Other vendors of compatible telephone equipment called the Touch-Tone feature tone dialing or DTMF. Automatic Electric (GTE) referred to it as "Touch-calling" in their marketing. Other trade names such as Digitone were used by the Northern Electric Company in Canada.

As a method of in-band signaling, DTMF signals were also used by cable television broadcasters as cue tones to indicate the start and stop times of local commercial insertion points during station breaks for the benefit of cable companies. Until out-of-band signaling equipment was developed in the 1990s, fast, unacknowledged DTMF tone sequences could be heard during the commercial breaks of cable channels in the United States and elsewhere. Previously, terrestrial television stations used DTMF tones to control remote transmitters. In IP telephony, DTMF signals can also be delivered as either in-band or out-of-band tones, or even as a part of signaling protocols, as long as both endpoints agree on a common approach to adopt.

Keypad
The DTMF telephone keypad is laid out as a matrix of push buttons in which each row represents the low frequency component and each column represents the high frequency component of the DTMF signal. The commonly used keypad has four rows and three columns, but a fourth column is present for some applications. Pressing a key sends a combination of the row and column frequencies. For example, the 1 key produces a superimposition of a 697 Hz low tone and a 1209 Hz high tone. Initial pushbutton designs employed levers, enabling each button to activate one row and one column contact. The tones are decoded by the switching center to determine the keys pressed by the user.

#, *, A, B, C, and D
Engineers had envisioned telephones being used to access computers and automated response systems. They consulted with companies to determine the requirements. This led to the addition of the number sign (#, pound or "diamond" in this context, "hash", "square" or "gate" in the UK, and " octothorpe '' by the original engineers) and asterisk or "star" (*) keys as well as a group of keys for menu selection: A, B, C and D. In the end, the lettered keys were dropped from most keypads and it was many years before the two symbol keys became widely used for vertical service codes such as *67 in the United States and Canada to suppress caller ID.

Public payphones that accept credit cards use these additional codes to send the information from the magnetic strip.

The AUTOVON telephone system of the United States Armed Forces used signals A, B, C, and D to assert certain privilege and priority levels when placing telephone calls. Precedence is still a feature of military telephone networks, but using number combinations. For example, entering 93 before a number is a priority call.

Present-day uses of the signals A, B, C and D are rare in telephone networks, and are exclusive to network control. For example, A is used in some networks for cycling through a list of carriers. The signals are used in radio phone patch and repeater operations to allow, among other uses, control of the repeater while connected to an active telephone line.

The signals *, #, A, B, C and D are still widely used worldwide by amateur radio operators and commercial two-way radio systems for equipment control, repeater control, remote-base operations and some telephone communications systems.

DTMF signaling tones may also be heard at the start or end of some prerecorded VHS videocassettes. Information on the master version of the video tape is encoded in the DTMF tones. The encoded tones provide information to automatic duplication machines, such as format, duration and volume levels in order to replicate the original video as closely as possible.

DTMF tones are used in some caller ID systems to transfer the caller ID information, a function that is performed in the United States by Bell 202 modulated frequency-shift keying (FSK) signaling.

Decoding
DTMF was originally decoded by tuned filter banks. By the end of the 20th century, digital signal processing became the predominant technology for decoding. DTMF decoding algorithms typically use the Goertzel algorithm although application of MUSIC (algorithm) to DTMF decoding has been shown to outperform Goertzel and being the only possibility in cases when number of available samples is limited. As DTMF signaling is often transmitted in-band with voice or other audio signals present simultaneously, the DTMF signal definition includes strict limits for timing (minimum duration and interdigit spacing), frequency deviations, harmonics, and amplitude relation of the two components with respect to each other (twist).

Other multiple frequency signals
National telephone systems define other tones, outside the DTMF specification, that indicate the status of lines, equipment, or the result of calls, and for control of equipment for troubleshooting or service purposes. Such call-progress tones are often also composed of multiple frequencies and are standardized in each country. The Bell System defined them in the Precise Tone Plan. Bell's Multi-frequency signaling was exploited by blue box devices.

Some early modems were based on touch-tone frequencies, such as Bell 400-style modems.

title: DTMF


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Deuterocanonical books

The deuterocanonical books, meaning "Of, pertaining to, or constituting a second canon," collectively known as the Deuterocanon (DC), are certain books and passages considered to be canonical books of the Old Testament by the Catholic Church, the Eastern Orthodox Church, the Oriental Orthodox Churches and the Assyrian Church of the East, but which modern Jews and Protestants regard as apocrypha.

Seven books are accepted as deuterocanonical by all the ancient churches: Tobias, Judith, Baruch, Ecclesiasticus, Wisdom, First and Second Maccabees and also the Greek additions to Esther and Daniel. In addition to these, the Eastern Orthodox Church, the Oriental Orthodox Churches and the Assyrian Church of the East add other books to their canons.

They date from 300 BC to 100 AD, before the separation of the Christian church from Judaism,  and they are regularly found in old manuscripts and cited frequently by the Church Fathers, such as Clement of Rome, Clement of Alexandria, Origen, Irenaeus, Tertullian, among others.

According to the Gelasian Decree written by an anonymous author, the Council of Rome (382 AD) defined a list of books of scripture as canonical. It included most of the deuterocanonical books. Patristic and synodal lists from the 200s, 300s and 400s usually include selections of the deutorocanonical books.

Hebrew Bible canon
Although there is no scholarly consensus as to when the Hebrew Bible canon was fixed, some scholars hold that the Hebrew canon was established well before the 1st century AD – even as early as the 4th century BC, or by the Hasmonean dynasty (140–40 BC).

The canon of modern Rabbinic Judaism excludes the deuterocanonical books. Albert J. Sundberg writes that Judaism did not exclude from their scriptures the deuterocanonicals and the additional Greek texts listed here.

Ancient Christian canons
The Septuagint translation of the Hebrew Bible into Greek, which the early Christian church used as its Old Testament, included all of the deuterocanonical books. The term distinguished these books from both the protocanonical books (the books of the Hebrew canon) and the biblical apocrypha (books of Jewish origin that were sometimes read in Christian churches as scripture but which were not regarded as canonical).

Some commentators see texts from these particular books being paraphrased, referred, or alluded to many times in the New Testament, depending in large measure on what is counted as a reference; other scholars point to a correspondence of thought.

Protestant canon
For churches which espouse sola scriptura independent of ecclesiastical authorities or sacred Tradition, it is necessary and critical to have a clear and complete list of the canonical books.

The early Christian church largely relied upon the Septuagint in the canonization of the Christian Bible. In the 16th century, Martin Luther argued that many of the received texts of the New Testament lacked the authority of the Gospels, and therefore proposed removing a number of books from the New Testament, including Hebrews, James, Jude, and the Book of Revelation. While this proposal was not widely accepted among Protestants, the deuterocanonical books—which had previously been deprecated by Jewish scholars—were moved by Luther into an intertestamental section of the Bible called the apocrypha.

Lutherans and Anglicans do not consider these books to be canonical but do consider them worthy of reverence. As such, readings from the Protestant apocrypha are found in the lectionaries of these churches. Anabaptists use the Luther Bible, which contains the apocrypha as intertestamental books; Amish wedding ceremonies include "the retelling of the marriage of Tobias and Sarah in the Apocrypha".

List of deuterocanonicals
The deuterocanonical texts held as canonical by all the Catholic Church, the Eastern Orthodox Church, the Oriental Orthodox Church and the Church of the East are:
 * Tobit
 * Judith
 * Baruch
 * Sirach (or Ecclesiasticus)
 * 1 Maccabees
 * 2 Maccabees
 * Wisdom
 * Additions to Esther:
 * Fulfillment of Mordecai's Dream (Esther 10:4–13)
 * Interpretation of Mordecai's Dream (Vulgate Esther 11)
 * Conspiracy of the Two Eunuchs (Vulgate Esther 12)
 * Letter of Aman and the Prayer of Mordecai to the Jews (Vulgate Esther 13)
 * The Prayer of Esther (Vulgate Esther 14)
 * Esther Comes into the King's Presence (Vulgate Esther 15)
 * Letter of King Artaxerxes (Vulgate Esther 16)
 * Additions to Daniel:
 * Prayer of Azariah and Song of the Three Holy Children (Septuagint Daniel 3:24–90)
 * Susanna and the Elders (Septuagint prologue, Vulgate Daniel 13)
 * Bel and the Dragon (Septuagint epilogue, Vulgate Daniel 14)
 * Additions to Baruch:
 * Letter of Jeremiah (Baruch chapter 6)

Canonical only for the Eastern Orthodox Church:
 * Prayer of Manasseh
 * 1 Esdras
 * 2 Esdras
 * 3 Maccabees
 * 4 Maccabees as an appendix
 * Additions to Psalms:
 * Psalm 151

Historical background
Deuterocanonical is a term coined in 1566 by the theologian Sixtus of Siena, who had converted to Catholicism from Judaism, to describe scriptural texts considered canonical by the Catholic Church, but which recognition was considered "secondary". For Sixtus, this term included portions of both Old and New Testaments. Sixtus considers the final chapter of the Gospel of Mark to be deuterocanonical. He also applies the term to the Book of Esther from the canon of the Hebrew Bible.

The term was then taken up by other writers to apply specifically to those books of the Old Testament which had been recognised as canonical by the Councils of Rome (382 AD), Hippo (393 AD), Carthage (397 AD and 419 AD), Florence (1442 AD) and Trent (1546 AD), but which were not in the Hebrew canon.

Forms of the term “deuterocanonical” were adopted after the 16th century by the Eastern Orthodox Church to denote canonical books of the Septuagint not in the Hebrew Bible, a wider selection than that adopted by the Council of Trent, and also by the Ethiopian Orthodox Tewahedo Church to apply to works believed to be of Jewish origin translated in the Old Testament of the Ethiopic Bible, a wider selection still.

The acceptance of some of these books among early Christians was widespread, though not universal, and surviving Bibles from the early Church always include, with varying degrees of recognition, books now called deuterocanonical. Some say that their canonicity seems not to have been doubted in the Church until it was challenged by Jews after 100 AD, sometimes postulating a hypothetical Council of Jamnia. Regional councils in the West published official canons that included these books as early as the 4th and 5th centuries.

The Catholic Encyclopedia states: "The official attitude of the Latin Church, always favourable to them, kept the majestic tenor of its way. Two documents of capital importance in the history of the canon constitute the first formal utterance of papal authority on the subject. The first is the so-called 'Decretal of Gelasius', the essential part of which is now generally attributed to a synod convoked by Pope Damasus in the year 382. The other is the Canon of Innocent I, sent in 405 to a Gallican bishop in answer to an inquiry. Both contain all the deuterocanonicals, without any distinction, and are identical with the catalogue of Trent. The African Church, always a staunch supporter of the contested books, found itself in entire accord with Rome on this question. Its ancient version, the Vetus Latina, had admitted all the Old Testament Scriptures. St. Augustine seems to theoretically recognize degrees of inspiration; in practice he employs protos and deuteros without any discrimination whatsoever. Moreover in his 'De Doctrinâ Christianâ' he enumerates the components of the complete Old Testament. The Synod of Hippo (393) and the three of Carthage (393, 397, and 419), in which, doubtless, Augustine was the leading spirit, found it necessary to deal explicitly with the question of the Canon, and drew up identical lists from which no sacred books are excluded. These councils base their canon on tradition and liturgical usage."

Dead Sea scrolls
The Book of Sirach, whose Hebrew text was already known from the Cairo Geniza, has been found in two of the Dead Sea Scrolls (2QSir or 2Q18, 11QPs_a or 11Q5) in Hebrew. Another Hebrew scroll of Sirach has been found in Masada (MasSir). Five fragments from the Book of Tobit have been found in Qumran written in Aramaic and in one written in Hebrew (papyri 4Q, nos. 196–200). The Letter of Jeremiah (or Baruch chapter 6) has been found in cave 7 (papyrus 7Q2) in Greek.

Recent scholars have suggested that the Qumran library of approximately 1,100 manuscripts found in the eleven caves at Qumran was not entirely produced at Qumran, but may have included part of the library of the Jerusalem Temple, that may have been hidden in the caves for safekeeping at the time the Temple was destroyed by Romans in 70 AD.

Influence of the Septuagint
Deuterocanonical and Apocryphal books included in the Septuagint are:

The large majority of Old Testament references in the New Testament are taken from the Koine Greek Septuagint (LXX), editions of which include the deuterocanonical books, as well as apocrypha – both of which are called collectively ("readable, worthy of reading"). No two Septuagint codices contain the same apocrypha.

Greek Psalm manuscripts from the fifth century contain three New Testament "psalms": the Magnificat, the Benedictus, the Nunc dimittis from Luke's birth narrative, and the conclusion of the hymn that begins with the "Gloria in Excelsis". Beckwith states that manuscripts of anything like the capacity of Codex Alexandrinus were not used in the first centuries of the Christian era, and believes that the comprehensive codices of the Septuagint, which start appearing in the 4th century AD, are all of Christian origin.

In the New Testament, Hebrews 11:35 is understood by some as referring to an event that was recorded in one of the deuterocanonical books, 2 Maccabees. For instance, the author of Hebrews references oral tradition which spoke of an Old Testament prophet who was sawn in half in Hebrews 11:37, two verses after the 2nd Maccabees reference. Other New Testament authors such as Paul also reference or quote period literature.

Influence of early authors
The Jewish historian Josephus (c. 94 AD) wrote that the Hebrew Bible contained 22 canonical books. The same number of 22 books was reported also by the Christian bishop Athanasius, but they might differ on the exact content (see below for Athanasius), as Josephus did not provide a detailed list.

Origen of Alexandria (c. 240 AD), cited by Eusebius, described the Hebrew Bible as containing 22 canonical books. Among these books he listed the Epistle of Jeremiah and the Maccabees.

"The twenty-two books of the Hebrews are the following: That which is called by us Genesis; Exodus; Leviticus; Numbers; Jesus, the son of Nave (Joshua book); Judges and Ruth in one book; the First and Second of Kings (1 Samuel and 2 Samuel) in one; the Third and Fourth of Kings (1 Kings and 2 Kings) in one; of the Chronicles, the First and Second in one; Esdras, First and Second (Ezra–Nehemiah) in one; the book of Psalms; the Proverbs of Solomon; Ecclesiastes; the Song of Songs; Isaiah; Jeremiah, with Lamentations and the epistle (of Jeremiah) in one; Daniel; Ezekiel; Job; Esther. And besides these there are the Maccabees."

Eusebius wrote in his Church History (c. 324 AD) that Bishop Melito of Sardis in the 2nd century AD considered the deuterocanonical Wisdom of Solomon as part of the Old Testament and that it was considered canonical by Jews and Christians. On the other hand, the contrary claim has been made: "In the catalogue of Melito, presented by Eusebius, after Proverbs, the word Wisdom occurs, which nearly all commentators have been of opinion is only another name for the same book, and not the name of the book now called 'The Wisdom of Solomon'."

Cyril of Jerusalem (c. 350 AD) in his Catechetical Lectures cites as canonical books "Jeremiah one, including Baruch and Lamentations and the Epistle (of Jeremiah)".

In Athanasius's canonical books list (367 AD) the Book of Baruch and the Letter of Jeremiah are included and Esther is omitted. At the same time, he mentioned that the Wisdom of Solomon, the Wisdom of Sirach, Judith and Tobit, the book of Esther and also the Didache and The Shepherd of Hermas, while not being part of the Canon, "were appointed by the Fathers to be read". He excluded what he called "apocryphal writings" entirely.

Epiphanius of Salamis (c. 385 AD) mentions that "there are 27 books given the Jews by God, but they are counted as 22, however, like the letters of their Hebrew alphabet, because ten books are doubled and reckoned as five". He wrote in his that Jews had in their books the deuterocanonical Epistle of Jeremiah and Baruch, both combined with Jeremiah and Lamentations in only one book. While Wisdom of Sirach and the Wisdom of Solomon were books of disputed canonicity.

Augustine of Hippo (c. 397 AD), in his book On Christian Doctrine (Book II Chapter 8), cites a list of the canon of the Old Testament and the New Testament, including the deuterocanonical books as canonical:

"Now the whole canon of Scripture on which we say this judgment is to be exercised, is contained in the following books: – Five books of Moses, that is, Genesis, Exodus, Leviticus, Numbers, Deuteronomy; one book of Joshua the son of Nun; one of Judges; one short book called Ruth; next, four books of Kings (the two books of Samuel and the two books of Kings), and two of Chronicles, Job, and Tobias, and Esther, and Judith, and the two books of Maccabees, and the two of Ezra [Ezra, Nehemiah]; one book of the Psalms of David; and three books of Solomon, that is to say Proverbs, Song of Songs, and Ecclesiastes. For two books, one called Wisdom and the other Ecclesiasticus. Twelve separate books of the prophets which are connected with one another, and having never been disjoined, are reckoned as one book; the names of these prophets are as follows: Hosea, Joel, Amos, Obadiah, Jonah, Micah, Nahum, Habakkuk, Zephaniah, Haggai, Zechariah, Malachi; then there are the four greater prophets, Isaiah, Jeremiah, Daniel, Ezekiel."

According to the monk Rufinus of Aquileia (c. 400 AD) the deuterocanonical books were not called canonical but ecclesiastical books. In this category Rufinus includes the Wisdom of Solomon, Sirach, Judith, Tobit and two books of Maccabees. Baruch is not specified by name in Rufinus's list, but it is in Cyril's, as though a part of Jeremiah, "Jeremiah, with Baruch, and the Lamentations and the Epistle." (Catech. 4, §36.)

Pope Innocent I (405 AD) sent a letter to the bishop of Toulouse citing deuterocanonical books as a part of the Old Testament canon.

"Which books really are received in the canon, this brief addition shows. These therefore are the things of which you desired to be informed. Five books of Moses, that is, Genesis, Exodus, Leviticus, Numbers, and Deuteronomy, and Joshua the son of Nun, and Judges, and the four books of Kings [the two Books of Kings and the two books of Samuel] together with Ruth, sixteen books of the Prophets, five books of Solomon [Proverbs, Ecclesiastes, Song of Songs, Wisdom of Solomon, and Ecclesiasticus], and the Psalms. Also of the historical books, one book of Job, one of Tobit, one of Esther, one of Judith, two of Maccabees, two of Ezra [Ezra, Nehemiah], two of Chronicles."

In the 7th century Latin document the Muratorian fragment, which some scholars actually believe to be a copy of an earlier 170 AD Greek original, the book of the Wisdom of Solomon is counted by the church.

"Moreover, the epistle of Jude and two of the above-mentioned (or, bearing the name of) John are counted (or, used) in the catholic [Church]; and [the book of] Wisdom, written by the friends of Solomon in his honour."

Synods
In later copyings of the canons of the Council of Laodicea (from 364 AD) a canon list became appended to Canon 59, likely before the mid fifth century, which affirmed that Jeremiah, and Baruch, the Lamentations, and the Epistle (of Jeremiah) were canonical, while excluding the other deuterocanonical books.

According to Decretum Gelasianum, which is a work written by an anonymous scholar between 519 and 553, the Council of Rome (382 AD) cites a list of books of scripture presented as having been made canonical. This list mentions all the deuterocanonical books as a part of the Old Testament canon:

"Genesis, Exodus, Leviticus, Numbers, Deuteronomy, Joshua, Judges, Ruth, Kings IV books [1 Samuel, 2 Samuel, 1 Kings, 2 Kings], Chronicles II books, 150 Psalms, three books of Solomon [Proverbs, Ecclesiastes, Song of Songs], Wisdom, Ecclesiasticus, Isaiah, Jeremiah with Cinoth i.e. his lamentations, Ezechiel, Daniel, Hosea, Amos, Micah, Joel, Obadiah, Jonah, Nahum, Habbakuk Zephaniah, Haggai, Zechariah, Malachi, Job, Tobit, Esdras II books [Ezra, Nehemiah], Ester, Judith, Maccabees II books."

(According to the Council of Laodicea, Athanasius, Cyril of Jerusalem, and Epiphanius of Salamis, the Book of Jeremiah forms a single book together with Baruch, Lamentations and the Letter of Jeremiah, also called the Epistle of Jeremiah.)

The Synod of Hippo (in 393 AD), followed by the Council of Carthage (397) and the Council of Carthage (419), may be the first councils that explicitly accepted the first canon which includes a selection of books that did not appear in the Hebrew Bible; the councils were under significant influence of Augustine of Hippo, who regarded the canon as already closed.

Canon XXIV from the Synod of Hippo (in 393 AD) records the scriptures which are considered canonical; the Old Testament books as follows:

"Genesis; Exodus; Leviticus; Numbers; Deuteronomy; Joshua the Son of Nun; The Judges; Ruth; The Kings, iv. books [1 Samuel, 2 Samuel, 1 Kings, 2 Kings]; The Chronicles, ii. books; Job; The Psalter; The Five books of Solomon [Proverbs, Ecclesiastes, Song of Songs, Wisdom of Solomon, and Ecclesiasticus]; The Twelve Books of the Prophets [Hosea, Joel, Amos, Obadiah, Jonah, Micah, Nahum, Habakkuk, Zephaniah, Haggai, Zechariah, Malachi; Isaiah]; Jeremiah; Ezechiel; Daniel; Tobit; Judith; Esther; Ezra, ii. books [Ezra, Nehemiah]; Maccabees, ii. books."

On 28 August 397, the Council of Carthage confirmed the canon issued at Hippo; the recurrence of the Old Testament part is stated:

"Genesis, Exodus, Leviticus, Numbers, Deuteronomy, Joshua the son of Nun, Judges, Ruth, four books of Kings [1 Samuel, 2 Samuel, 1 Kings, 2 Kings], two books of Paraleipomena [1 Chronicles, 2 Chronicles], Job, the Psalter, five books of Solomon [ Proverbs, Ecclesiastes, Song of Songs, Wisdom of Solomon, and Ecclesiasticus ], the books of the twelve prophets, Isaiah, Jeremiah, Ezechiel, Daniel, Tobit, Judith, Esther, two books of Esdras [Ezra, Nehemiah], two Books of the Maccabees."

In 419 AD, the Council of Carthage in its canon 24 lists the deuterocanonical books as canonical scripture:

"The Canonical Scriptures are as follows: Genesis, Exodus, Leviticus, Numbers, Deuteronomy, Joshua the son of Nun, Judges, Ruth, four books of Kings [1 Samuel, 2 Samuel, 1 Kings, 2 Kings], two books of Chronicles, Job, the Psalter, five books of Solomon [Proverbs, Ecclesiastes, Song of Songs, Wisdom of Solomon, and Ecclesiasticus], the books of the twelve prophets, Isaiah, Jeremiah, Ezechiel, Daniel, Tobit, Judith, Esther, two books of Esdras [Ezra, Nehemiah], two Books of the Maccabees."

(According to the Council of Laodicea, Athanasius, Cyril of Jerusalem, and Epiphanius of Salamis, the Book of Jeremiah forms a single book together with Baruch, Lamentations and the Letter of Jeremiah, also called the Epistle of Jeremiah.)

The Apostolic Canons approved by the Eastern Council in Trullo in 692 AD (not recognized by the Catholic Church) states as venerable and sacred the first three books of Maccabees and Wisdom of Sirach.

The Council of Florence (1442) promulgated a list of the books of the Bible, including the books of Judith, Esther, Wisdom, Ecclesiasticus, Baruch and two books of the Maccabees as Canonical books:

"Five books of Moses, namely Genesis, Exodus, Leviticus, Numbers, Deuteronomy; Joshua, Judges, Ruth, four books of Kings [1 Samuel, 2 Samuel, 1 Kings, 2 Kings], two of Paralipomenon [1 Chronicles, 2 Chronicles], Esdras [Ezra], Nehemiah, Tobit, Judith, Esther, Job, Psalms of David, Proverbs, Ecclesiastes, Song of Songs, Wisdom, Ecclesiasticus, Isaiah, Jeremiah, Baruch, Ezechiel, Daniel; the twelve minor prophets, namely Hosea, Joel, Amos, Obadiah, Jonah, Micah, Nahum, Habakkuk, Zephaniah, Haggai, Zechariah, Malachi; two books of the Maccabees."

The Council of Trent (1546) adopted an understanding of the canons of these previous councils as corresponding to its own list of deuterocanonical books:

"Of the Old Testament, the five books of Moses, namely, Genesis, Exodus, Leviticus, Numbers, Deuteronomy; Josue, Judges, Ruth, the four books of Kings [1 Samuel, 2 Samuel, 1 Kings, 2 Kings], two of Paralipomenon [1 Chronicles, 2 Chronicles], the first and second of Esdras [Ezra, Nehemiah], Tobias, Judith, Esther, Job, the Davidic Psalter of 150 Psalms, Proverbs, Ecclesiastes, the Canticle of Canticles [Song of Songs], Wisdom, Ecclesiasticus, Isaias, Jeremias, with Baruch, Ezechiel, Daniel, the twelve minor Prophets, namely, Osee, Joel, Amos, Abdias, Jonas, Micheas, Nahum, Habacuc, Sophonias, Aggeus, Zacharias, Malachias; two books of Machabees, the first and second."

Influence of Jerome
Jerome in one of his Vulgate prologues describes a canon which excludes the deuterocanonical books. In these prologues, Jerome mentions all of the deuterocanonical and apocryphal works by name as being apocryphal or "not in the canon" except for Prayer of Manasses and Baruch. He mentions Baruch by name in his Prologue to Jeremiah and notes that it is neither read nor held among the Hebrews, but does not explicitly call it apocryphal or "not in the canon". The inferior status to which the deuterocanonical books were relegated by authorities like Jerome is seen by some as being due to a rigid conception of canonicity, one demanding that a book, to be entitled to this supreme dignity, must be received by all, must have the sanction of Jewish antiquity, and must moreover be adapted not only to edification, but also to the "confirmation of the doctrine of the Church".

J. N. D. Kelly states that "Jerome, conscious of the difficulty of arguing with Jews on the basis of books they spurned and anyhow regarding the Hebrew original as authoritative, was adamant that anything not found in it was 'to be classed among the apocrypha', not in the canon; later he grudgingly conceded that the Church read some of these books for edification, but not to support doctrine."

Jerome's Vulgate included the deuterocanonical books as well as apocrypha. Jerome referenced and quoted from some as scripture despite describing them as "not in the canon". Michael Barber asserts that, although Jerome was once suspicious of the apocrypha, he later viewed them as scripture. Barber argues that this is clear from Jerome's epistles; he cites Jerome's letter to Eustochium, in which Jerome quotes Sirach 13:2. Elsewhere Jerome apparently also refers to Baruch, the Story of Susannah and Wisdom as scripture. Henry Barker states that Jerome quotes the Apocrypha with marked respect, and even as "Scripture", giving them an ecclesiastical if not a canonical position and use. Luther also wrote introductions to the books of the Apocrypha, and occasionally quoted from some to support an argument.

In his prologue to Judith, without using the word canon, Jerome mentioned that Judith was held to be scriptural by the First Council of Nicaea.

"Among the Hebrews the Book of Judith is found among the Hagiographa. ...But because this book is found by the Nicene Council to have been counted among the number of the Sacred Scriptures, I have acquiesced to your request."

In his reply to Rufinus, Jerome affirmed that he was consistent with the choice of the church regarding which version of the deuterocanonical portions of Daniel to use, which the Jews of his day did not include:

"What sin have I committed in following the judgment of the churches? But when I repeat what the Jews say against the Story of Susanna and the Hymn of the Three Children, and the fables of Bel and the Dragon, which are not contained in the Hebrew Bible, the man who makes this a charge against me proves himself to be a fool and a slanderer; for I explained not what I thought but what they commonly say against us. (Against Rufinus, II:33 [402 AD])"

Thus Jerome acknowledged the principle by which the canon would be settled—the judgment of the Church (at least the local churches in this case) rather than his own judgment or the judgment of Jews; though concerning translation of Daniel to Greek, he wondered why one should use the version of a translator whom he regarded as a heretic and judaizer (Theodotion).

The Vulgate is also important as the touchstone of the canon concerning which parts of books are canonical. When the Council of Trent confirmed the books included in the first canon, it qualified the books as being "entire with all their parts, as they have been used to be read in the Catholic Church, and as they are contained in the old Latin vulgate edition". This decree was clarified somewhat by Pope Pius XI on 2 June 1927, who allowed that the Comma Johanneum was open to dispute.

The Council of Trent also ratified the Vulgate Bible as the official Latin version of the Bible for the Roman Catholic Church.

Deuterocanonical and Apocryphal books included in the Latin Vulgate are:

Masoretic Text
The existence of the Septuagint, Samaritan Pentateuch, and the Peshitta versions of the Hebrew scriptures demonstrate that different versions of Judaism used different texts, and it is debated which is closest to the Urtext (a theoretical "original" text from which all of these emerged). The Dead Sea Scrolls contain some of the deuterocanonical books, while the Masoretic Text excludes them. Since the Enlightenment, it was wrongly believed that the Masoretic Text was the "original" Hebrew Bible when this was in fact a medieval version created by the Masoretes. The oldest nearly-complete manuscripts of the Old Testament include the Codex Vaticanus (4th century) and the Codex Alexandrinus (5th century), while the oldest complete manuscript of the Masoretic text is the Codex Leningradensis from 1008.

The Septuagint was the version of the Hebrew Bible from which the early Christians emerged. The Christian Bible contained these deuterocanonical books until Martin Luther, assuming the Masoretic text to be the original, removed them to match this new Jewish canon. Rabbinic Judaism is a newer form of Judaism that created the Masoretic text in part to deter a Christian reading of the Old Testament.

In the Catholic Church
The Catholic Church considers that in the Council of Rome in 382 AD, under the Papacy of Damasus I, was defined the complete canon of the Bible, accepting 46 books for the Old Testament, including what the Reformed Churches consider as deuterocanonical books, and 27 books for the New Testament. Based in this first canon, Saint Jerome compiled and translated the 73 books of the Bible into Latin, later known as the Vulgate Bible version, which has been considered during many centuries as one of the official Bible translations of the Catholic Church.

The Synod of Hippo (in 393 AD), followed by the Council of Carthage (397) and the Council of Carthage (419), also explicitly accepted the first canon from the Council of Rome. These councils were under significant influence of Augustine of Hippo, who also regarded the Biblical canon as already closed. The Roman Catholic Council of Florence (1442) confirmed the first canon too, while the Council of Trent (1546) elevated the first canon to dogma.

Protestant theologian Philip Schaff states that "the Council of Hippo in 393, and the third (according to another reckoning the sixth) Council of Carthage in 397, under the influence of Augustine, who attended both, fixed the catholic canon of the Holy Scriptures, including the Apocrypha of the Old Testament, ...This decision of the transmarine church, however, was subject to ratification; and the concurrence of the Roman See it received when Innocent I and Gelasius I (AD 414) repeated the same index of biblical books."

Schaff says that this canon remained undisturbed till the 16th century, and was sanctioned by the Council of Trent at its fourth session, although as the Catholic Encyclopedia reports, "in the Latin Church, all through the Middle Ages we find evidence of hesitation about the character of the deuterocanonicals. ... Few are found to unequivocally acknowledge their canonicity," but that the countless manuscript copies of the Vulgate produced by these ages, with a slight, probably accidental, exception, uniformly embrace the complete Roman Catholic Old Testament.

Subsequent research qualifies this latter statement, in that a distinct tradition of large format pandect bibles has been identified as having been promoted by the 11th and 12th century reforming Papacy for presentation to monasteries in Italy; and now commonly termed 'Atlantic Bibles' on account of their very great size. While not all these bibles present a consistent reformed Vulgate text, they generally exclude the deuterocanonical books.

Baruch
According to the canon lists of the Council of Laodicea, Athanasius (367 AD), Cyril of Jerusalem (c. 350 AD), and Epiphanius of Salamis (c. 385 AD), the Book of Jeremiah forms a single book together with Baruch, Lamentations and the Letter of Jeremiah (also called Epistle of Jeremiah).

In the Old Latin version of the Bible, Baruch and the Letter of Jeremiah appear to have been incorporated into the Book of Jeremiah, and Latin Fathers of the 4th century and earlier always cite their texts as being from that book. However, when Jerome translated Jeremiah afresh from the Hebrew text, which is considerably longer than the Greek Septuagint text and with chapters in a different order, he steadfastly refused to incorporate either Baruch or the Letter of Jeremiah from the Greek.

In the 9th century these two works were reintroduced into the Vulgate Bibles produced under the influence of Theodulf of Orleans, originally as additional chapters to the Vulgate book of Jeremiah. Subsequently, and especially in the Paris Bibles of the 13th century, they are found together as a single, combined book after Lamentations.

Esdras
For the Roman Catholic Church and Protestant Churches, Greek Esdras is now considered apocryphal. The Orthodox Church considers it as canonical. The earlier canonical status of this book in the Western church can be less easy to track, as references to Esdras in canon lists and citations may refer either to this book, or to Greek Ezra–Nehemiah, or both together. In the surviving Greek pandect Bibles of the 4th and 5th centuries, Greek Esdras always stands as 'Esdras A' while the Greek translation of the whole of canonical Ezra–Nehemiah stands as 'Esdras B'. The same is found in the surviving witness of the Old Latin Bible.

When Latin fathers of the early church cite quotations from the biblical 'Book of Ezra' it is overwhelmingly 'First Ezra/Esdras A' to which they refer, as in Augustine 'City of God' 18:36. Citations of the 'Nehemiah' sections of Old Latin Second Ezra/'Esdras B' are much rarer. No Old Latin citations from the 'Ezra' sections of Second Ezra/'Esdras B' are known before Bede in the 8th century. Consequently Gallagher and Meade conclude that "when the ancient canon lists, whether Greek or Latin, mention two books of Esdras, they must have in mind the books known in the LXX and Old Latin as Esdras A and Esdras B; i.e. our 1 Esdras and Ezra-Nehemiah."

In his prologue to Ezra Jerome refers to four books of Ezra in the Latin tradition. Jerome's first and second Latin books of Ezra are those of the Old Latin Bible - corresponding to Greek Esdras and Ezra-Nehemiah in the Septuagint. These two books he considers each to be a corrupt version of the single Hebrew book of Ezra, so he claims that his Vulgate version of Ezra from the Hebrew replaces both of them. Jerome condemns the third and fourth Latin books of Ezra as apocrypha. His third book must correspond to the Jewish Apocolypse of Ezra while the fourth book is likely to comprise other material from Latin Ezra.

From the 9th century, occasional Latin Vulgate manuscripts are found in which Jerome's single Ezra text is split to form the separate books of Ezra and Nehemiah. In the Paris Bibles of the 13th century this split has become universal, with Esdras A being reintroduced as '3 Esdras' and Latin Esdras being added as '4 Esdras'. At the Council of Trent neither '3 Esdras' nor '4 Esdras' were accepted as canonical books, but were eventually printed in the section of 'Apocrypha' in the Sixto-Clementine Vulgate, along with the Prayer of Manasses.

The Council of Trent in 1546 stated the list of books included in the canon as it had been set out in the Council of Florence. In respect to the deuterocanonical books this list conformed with the canon lists of Western synods of the late 4th century, other than including Baruch with the Letter of Jeremiah (Baruch chapter 6) as a single book. While the majority at Trent supported this decision there were participants in the minority who disagreed with accepting any other than the protocanonical books in the canon. Among the minority, at Trent, were Cardinals Seripando and Cajetan, the latter an opponent of Luther at Augsburg.

In Eastern Orthodoxy
The Eastern Orthodox Churches have traditionally included all the books of the Septuagint in their Old Testaments. The Greeks use the word (Ἀναγιγνωσκόμενα, "readable, worthy to be read") to describe the books of the Greek Septuagint that are not present in the Hebrew Bible. When Eastern Orthodox theologians use the term "deuterocanonical", it is important to note that the meaning is not identical to the Roman Catholic usage. In Eastern Orthodox Christianity, deuterocanonical means that a book is part of the corpus of the Old Testament (i.e. is read during the services) but has secondary authority. In other words, deutero (second) applies to authority or witnessing power, whereas in Roman Catholicism, deutero applies to chronology (the fact that these books were confirmed later), not to authority.

The Eastern Orthodox canon includes the deuterocanonical books accepted by Roman Catholics plus Psalm 151, the Prayer of Manasseh, 3 Maccabees and 1 Esdras (also included in the Clementine Vulgate), while Baruch is divided from the Epistle of Jeremiah, making a total of 49 Old Testament books in contrast with the Protestant 39-book canon.

The Eastern Orthodox synod, the Synod of Jerusalem, held in 1672 receive as its canon the books found in the Septuagint, and in the Patristic, Byzantine, and liturgical tradition. The Synod declared the Eastern Orthodox canon as follows:

"specifically, 'The Wisdom of Solomon,' 'Judith,' 'Tobit,' 'The History of the Dragon' [Bel and the Dragon], 'The History of Susanna,' 'The Maccabees,' and 'The Wisdom of Sirach.' For we judge these also to be with the other genuine Books of Divine Scripture genuine parts of Scripture. For ancient custom, or rather the Catholic Church, which has delivered to us as genuine the Sacred Gospels and the other Books of Scripture, has undoubtedly delivered these also as parts of Scripture, and the denial of these is the rejection of those. And if, perhaps, it seems that not always have all of these been considered on the same level as the others, yet nevertheless these also have been counted and reckoned with the rest of Scripture, both by Synods and by many of the most ancient and eminent Theologians of the Universal Church. All of these we also judge to be Canonical Books, and confess them to be Sacred Scripture."

Other texts printed in Eastern Orthodox Bibles are included as an appendix, which is not the same in all churches; the appendix contains 4 Maccabees in Greek-language bibles, while it contains 2 Esdras in Slavonic-language and Russian-language.

In Ethiopian Orthodox Tewahedo Church
In the Bible used by the Eritrean and Ethiopian Orthodox Tewahedo Churches, those books of the Old Testament that are still counted as canonical, but which are not agreed upon by all other Churches, are often set in a separate section titled “deuterocanonical” (ዲዩትሮካኖኒካል). The Ethiopian Orthodox Deuterocanon, in addition to the standard set listed above, and with the books of Esdras and the Prayer of Manasseh, also includes some books that are still held canonical by only the Ethiopian Church, including the Book of Enoch, the Book of Jubilees, and the three books of Meqabyan (which are sometimes wrongly confused with the Books of the Maccabees).

The Book of Enoch is unusual as it was quoted in the New Testament. 1 Enoch 1:9 is directly and explicitly quoted in Jude 1:14-15 and may be alluded to in Galatians 5:19. It is not part of the canon of any other churches.

Anabaptist Churches
Anabaptists use the Luther Bible, which contains the Apocrypha as intertestamental books, which has much overlap with the Catholic deuterocanonical books; Amish wedding ceremonies include "the retelling of the marriage of Tobias and Sarah in the Apocrypha".

The fathers of Anabaptism, such as Menno Simons, quoted "them [the Apocrypha] with the same authority and nearly the same frequency as books of the Hebrew Bible" and the texts regarding the martyrdoms under Antiochus IV in 1 Maccabees and 2 Maccabees are held in high esteem by the Anabaptists, who faced persecution in their history.

Anglican Communion
The Thirty-nine Articles of Religion of the Church of England lists the deuterocanonical books as suitable to be read for "example of life and instruction of manners, but yet doth not apply them to establish any doctrine". The early lectionaries of the Anglican Church (as included in the Book of Common Prayer of 1662) included the deuterocanonical books amongst the cycle of readings, and passages from them were used regularly in services (such as the Kyrie Pantokrator and the Benedicite).

Readings from the deuterocanonical books are now included in many modern lectionaries in the Anglican Communion, based on the Revised Common Lectionary (in turn based on the post-conciliar Roman Catholic lectionary), though alternative readings from protocanonical books are also provided. There is a great deal of overlap between the Apocrypha section of the original 1611 King James Bible and the Catholic deuterocanon, but the two are distinct.

The Apocrypha section of the original 1611 King James Bible includes, in addition to the deuterocanonical books, the following three books, which were not included in the list of the canonical books by the Council of Trent:
 * 1 Esdras (Vulgate 3 Esdras)
 * 2 Esdras (Vulgate 4 Esdras)
 * Prayer of Manasseh

These books make up the Apocrypha section of the Clementine Vulgate: 3 Esdras (a.k.a. 1 Esdras); 4 Esdras (a.k.a. 2 Esdras); and the Prayer of Manasseh, where they are specifically described as "outside of the series of the canon". The 1609 Douai Bible includes them in an appendix, but they have not been included in English Catholic Bibles since the Challoner revision of the Douai Bible in 1750.

Using the word apocrypha (Greek: "hidden away") to describe texts, although not necessarily pejorative, implies that the writings in question should not be included in the canon of the Bible. This classification commingles them with certain non-canonical gospels and New Testament apocrypha. The Society of Biblical Literature recommends the use of the term deuterocanonical books instead of Apocrypha in academic writing.

Lutheran Churches
Luther termed the deuterocanonical books "Apocrypha, that is, books which are not considered equal to the Holy Scriptures, but are useful and good to read." These are included in copies of the Luther Bible as intertestamental books between the Old Testament and New Testament.

Methodist Churches and Moravian Churches
The first Methodist liturgical book, The Sunday Service of the Methodists, employs verses from the biblical apocrypha, such as in the Eucharistic liturgy.

The Revised Common Lectionary, in use by most mainline Protestants including Methodists and Moravians, lists readings from the biblical apocrypha in the liturgical kalendar, although alternate Old Testament scripture lessons are provided.

Presbyterian Churches
The Westminster Confession of Faith, a Calvinist document that serves as a systematic summary of doctrine for the Church of Scotland and other Presbyterian Churches worldwide, recognizes only the sixty-six books of the Protestant canon as authentic scripture. Chapter 1, Article 3 of the Confession reads: "The books commonly called Apocrypha, not being of divine inspiration, are no part of the Canon of Scripture; and therefore are of no authority in the Church of God, nor to be any otherwise approved, or made use of, than other human writings."

Reformed Churches
The Belgic Confession, used in Reformed churches, devotes a section (Article 6) to "the difference between the canonical and apocryphal books" and says of them: "All which the Church may read and take instruction from, so far as they agree with the canonical books; but they are far from having such power and efficacy as that we may from their testimony confirm any point of faith or of the Christian religion; much less to detract from the authority of the other sacred books."

New Testament deuterocanonicals
The term deuterocanonical is sometimes used to describe the canonical antilegomena, those books of the New Testament which, like the deuterocanonicals of the Old Testament, were not universally accepted by the early Church. Jimmy Akin calls these books "New Testament deuterocanonicals". The antilegomena or "disputed writings" were widely read in the Early Church and include:

 * The Epistle to the Hebrews
 * The Epistle of James
 * The Second Epistle of Peter
 * The Second Epistle of John
 * The Third Epistle of John
 * The Epistle of Jude
 * The Book of Revelation
 * The Apocalypse of Peter
 * The Acts of Paul
 * The Shepherd of Hermas
 * The Epistle of Barnabas
 * The Didache

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Deuterocanonical books


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Discus throw

The discus throw, also known as disc throw, is a track and field sport in which the participant athlete throws an oblate spheroid weight — called a discus — in an attempt to mark a farther distance than other competitors. It is an ancient sport, as demonstrated by the fifth-century-BC Myron statue Discobolus. Although not part of the current pentathlon, it was one of the events of the ancient Greek pentathlon, which can be dated back to at least 708 BC, and it is part of the modern decathlon.

History
The sport of throwing the discus traces back to it being an event in the original Olympic Games of Ancient Greece. The discus as a sport was resurrected in Magdeburg, Germany, by gymnastics teacher Christian Georg Kohlrausch and his students in the 1870s. Organized men's competition was resumed in the late 19th century, and has been a part of the modern Summer Olympic Games since the first modern competition, the 1896 Summer Olympics. Images of discus throwers figured prominently in advertising for early modern Games, such as fundraising stamps for the 1896 Games, and the main posters for the 1920 and 1948 Summer Olympics. Today the sport of discus is a routine part of modern track-and-field meets at all levels, and retains a particularly iconic place in the Olympic Games.

The first modern athlete to throw the discus while rotating the whole body was František Janda-Suk from Bohemia (the present Czech Republic). Janda-Suk invented this technique when studying the position of the famous statue of Discobolus. After only one year of developing the technique, he earned a silver medal in the 1900 Olympics.

Women's competition began in the first decades of the 20th century. Following competition at national and regional levels, it was added to the Olympic program for the 1928 games.

Regulations
The event consists of throwing a heavy disc, with the weight or size depending on the competitor. Men and women throw different sized discs, with varying sizes and weights depending on age. The weight of the discus is either governed by World Athletics for international or USA Track & Field for the United States.

In the United States, Henry Canine advocated for a lighter-weight discus in high school competition. His suggestion was adopted by the National High School Athletic Association in 1938.

Sport discus for men (2 kg) IAAF certified.jpg certified for competitions

]] The typical discus has sides made of plastic, wood, fiberglass, carbon fiber or metal with a metal rim and a metal core to attain the weight. The rim must be smooth, with no roughness or finger holds. A discus with more weight in the rim produces greater angular momentum for any given spin rate, and thus more stability, although it is more difficult to throw. However, a higher rim weight, if thrown correctly, can lead to a longer throw. In some competitions, a solid rubber discus is used (see in the United States).

To make a throw, the competitor starts in a circle of diameter, which is recessed in a concrete pad by 20 mm. The thrower typically takes an initial stance facing away from the direction of the throw. They then spin anticlockwise (for right-handers) $1 1/2$ times while staying within the circle to build momentum before releasing the discus. The discus must land within a 34.92º circular sector that is centered on the throwing circle. The rules of competition for discus are virtually identical to those of shot put, except that the circle is larger, a stop board is not used and there are no form rules concerning how the discus is to be thrown.

The basic motion is a fore-handed sidearm movement. The discus is spun off the index finger or the middle finger of the throwing hand. In flight the disc spins clockwise when viewed from above for a right-handed thrower, and anticlockwise for a left-handed thrower. As well as achieving maximum momentum in the discus on throwing, the discus' distance is also determined by the trajectory the thrower imparts, as well as the aerodynamic behavior of the discus. Generally, throws into a moderate headwind achieve the maximum distance. Also, a faster-spinning discus imparts greater gyroscopic stability. The technique of discus throwing is quite difficult to master and needs much experience to perfect; thus most top throwers are 30 years old or more.

The discus throw is sometimes contested indoors, but it is not included at the World Athletics Indoor Championships. World Athletics used to keep "world indoor best" discus records, but since 2023 they now combine both indoor and outdoor marks.

Phases
The discus technique can be broken down into phases. The purpose is to transfer from the back to the front of the throwing circle while turning through one and a half circles. The speed of delivery is high, and speed is built up during the throw (slow to fast). Correct technique involves the buildup of torque so that maximum force can be applied to the discus on delivery.

Initially, the thrower takes up their position in the throwing circle, distributing their body weight evenly over both feet, which are roughly shoulder width apart. They crouch in order to adopt a more efficient posture to start from whilst also isometrically preloading their muscles; this will allow them to start faster and achieve a more powerful throw. They then begin the wind-up, which sets the tone for the entire throw; the rhythm of the wind-up and throw is very important.

Focusing on rhythm can bring about the consistency to get in the right positions that many throwers lack. Executing a sound discus throw with solid technique requires perfect balance. This is due to the throw being a linear movement combined with a one and a half rotation and an implement at the end of one arm. Thus, a good discus thrower needs to maintain balance within the circle.

For a right handed thrower, the next stage is to move the weight over the left foot. From this position the right foot is raised, and the athlete 'runs' across the circle. There are various techniques for this stage where the leg swings out to a small or great extent, some athletes turn on their left heel (e.g. Ilke Wylluda ) but turning on the ball of the foot is far more common.

The aim is to land in the 'power position', the right foot should be in the center and the heel should not touch the ground at any point. The left foot should land very quickly after the right. Weight should be mostly over the back foot with as much torque as possible in the body—so the right arm is high and far back. This is very hard to achieve.

The critical stage is the delivery of the discus, from this 'power position' the hips drive through hard, and will be facing the direction of the throw on delivery. Athletes employ various techniques to control the end-point and recover from the throw, such as fixing feet (to pretty much stop dead ), or an active reverse spinning onto the left foot (e.g. Virgilijus Alekna ).

Sports scientist Richard Ganslen researched the Aerodynamics of the Discus, reporting the discus will stall at an angle of 29°.

Culture
The discus throw has been the subject of a number of well-known ancient Greek statues and Roman copies such as the Discobolus and Discophoros. The discus throw also appears repeatedly in ancient Greek mythology, featured as a means of manslaughter in the cases of Hyacinth, Crocus, Phocus, and Acrisius, and as a named event in the funeral games of Patroclus.

Discus throwers have been selected as a main motif in numerous collectors' coins. One of the recent samples is the €10 Greek Discus commemorative coin, minted in 2003 to commemorate the 2004 Summer Olympics. On the obverse of the coin a modern athlete is seen in the foreground in a half-turned position, while in the background an ancient discus thrower has been captured in a lively bending motion, with the discus high above his head, creating a vivid representation of the sport.

Men

 * Correct as of May 2024.

Notable series

 * Mykolas Alekna had throws of 72.71, 72.89 and 74.35, initially measured as 74.41, at the Oklahoma Throws Series in Ramona on 14 April 2024, becoming the first man to produce three throws above 72 meters (and six throws above 70 meters) in a single competition.
 * Kristjan Čeh had throws of 71.86, 71.70 and 71.19 in Jõhvi on 16 June 2023 becoming the first man to have three throws above 71 metres in a single competition.
 * At the 2019 Diamond League Meeting in Doha, Qatar, Daniel Ståhl became the first man to produce six throws beyond 69.50 in a single competition.

Annulled marks

 * Ben Plucknett also threw a world record of 72.34 in Stockholm on 7 July 1981. This performance was annulled due to doping offences.
 * Kamy Keshmiri threw 70.84 in Salinas on 27 May 1992. This performance was annulled due to doping offences.

Non-legal marks

 * Rickard Bruch also threw 72.18 at an exhibition meeting in Piteå on 23 July 1974.
 * John Powell also threw 72.08 in Klagshamn on 11 September 1987, but the throw was made onto a sloping/downhill sector.

Women

 * Correct as of April 2024.

Annulled marks

 * Daniela Costian of Romania threw a best of 73.48 in Bucharest on 30 April 1988. This performance was annulled due to doping offences.
 * Darya Pishchalnikova of Russia threw a best of 70.69 in Cheboksary on 5 July 2012. This performance was annulled due to doping offences.

Non-legal marks

 * Martina Hellmann also threw 78.14 at an unofficial meeting in Berlin on 6 September 1988.
 * Ilke Wyludda also threw 75.36 at an unofficial meeting in Berlin on 6 September 1988.

title: Discus throw


text:
Discrete mathematics

Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (finite sets or sets with the same cardinality as the natural numbers). However, there is no exact definition of the term "discrete mathematics".

The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business.

Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in "discrete" steps and store data in "discrete" bits. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems.

Although the main objects of study in discrete mathematics are discrete objects, analytic methods from "continuous" mathematics are often employed as well.

In university curricula, discrete mathematics appeared in the 1980s, initially as a computer science support course; its contents were somewhat haphazard at the time. The curriculum has thereafter developed in conjunction with efforts by ACM and MAA into a course that is basically intended to develop mathematical maturity in first-year students; therefore, it is nowadays a prerequisite for mathematics majors in some universities as well. Some high-school-level discrete mathematics textbooks have appeared as well. At this level, discrete mathematics is sometimes seen as a preparatory course, like precalculus in this respect.

The Fulkerson Prize is awarded for outstanding papers in discrete mathematics.

Theoretical computer science

Theoretical computer science includes areas of discrete mathematics relevant to computing. It draws heavily on graph theory and mathematical logic. Included within theoretical computer science is the study of algorithms and data structures. Computability studies what can be computed in principle, and has close ties to logic, while complexity studies the time, space, and other resources taken by computations. Automata theory and formal language theory are closely related to computability. Petri nets and process algebras are used to model computer systems, and methods from discrete mathematics are used in analyzing VLSI electronic circuits. Computational geometry applies algorithms to geometrical problems and representations of geometrical objects, while computer image analysis applies them to representations of images. Theoretical computer science also includes the study of various continuous computational topics.

Information theory
Information theory involves the quantification of information. Closely related is coding theory which is used to design efficient and reliable data transmission and storage methods. Information theory also includes continuous topics such as: analog signals, analog coding, analog encryption.

Logic
Logic is the study of the principles of valid reasoning and inference, as well as of consistency, soundness, and completeness. For example, in most systems of logic (but not in intuitionistic logic) Peirce's law (((P→Q)→P)→P) is a theorem. For classical logic, it can be easily verified with a truth table. The study of mathematical proof is particularly important in logic, and has accumulated to automated theorem proving and formal verification of software.

Logical formulas are discrete structures, as are proofs, which form finite trees or, more generally, directed acyclic graph structures (with each inference step combining one or more premise branches to give a single conclusion). The truth values of logical formulas usually form a finite set, generally restricted to two values: true and false, but logic can also be continuous-valued, e.g., fuzzy logic. Concepts such as infinite proof trees or infinite derivation trees have also been studied, e.g. infinitary logic.

Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects, such as {blue, white, red} or the (infinite) set of all prime numbers. Partially ordered sets and sets with other relations have applications in several areas.

In discrete mathematics, countable sets (including finite sets) are the main focus. The beginning of set theory as a branch of mathematics is usually marked by Georg Cantor's work distinguishing between different kinds of infinite set, motivated by the study of trigonometric series, and further development of the theory of infinite sets is outside the scope of discrete mathematics. Indeed, contemporary work in descriptive set theory makes extensive use of traditional continuous mathematics.

Combinatorics
Combinatorics studies the way in which discrete structures can be combined or arranged. Enumerative combinatorics concentrates on counting the number of certain combinatorial objects - e.g. the twelvefold way provides a unified framework for counting permutations, combinations and partitions. Analytic combinatorics concerns the enumeration (i.e., determining the number) of combinatorial structures using tools from complex analysis and probability theory. In contrast with enumerative combinatorics which uses explicit combinatorial formulae and generating functions to describe the results, analytic combinatorics aims at obtaining asymptotic formulae. Topological combinatorics concerns the use of techniques from topology and algebraic topology/combinatorial topology in combinatorics. Design theory is a study of combinatorial designs, which are collections of subsets with certain intersection properties. Partition theory studies various enumeration and asymptotic problems related to integer partitions, and is closely related to q-series, special functions and orthogonal polynomials. Originally a part of number theory and analysis, partition theory is now considered a part of combinatorics or an independent field. Order theory is the study of partially ordered sets, both finite and infinite.

Graph theory
Graph theory, the study of graphs and networks, is often considered part of combinatorics, but has grown large enough and distinct enough, with its own kind of problems, to be regarded as a subject in its own right. Graphs are one of the prime objects of study in discrete mathematics. They are among the most ubiquitous models of both natural and human-made structures. They can model many types of relations and process dynamics in physical, biological and social systems. In computer science, they can represent networks of communication, data organization, computational devices, the flow of computation, etc. In mathematics, they are useful in geometry and certain parts of topology, e.g. knot theory. Algebraic graph theory has close links with group theory and topological graph theory has close links to topology. There are also continuous graphs; however, for the most part, research in graph theory falls within the domain of discrete mathematics.

Number theory

Number theory is concerned with the properties of numbers in general, particularly integers. It has applications to cryptography and cryptanalysis, particularly with regard to modular arithmetic, diophantine equations, linear and quadratic congruences, prime numbers and primality testing. Other discrete aspects of number theory include geometry of numbers. In analytic number theory, techniques from continuous mathematics are also used. Topics that go beyond discrete objects include transcendental numbers, diophantine approximation, p-adic analysis and function fields.

Algebraic structures
Algebraic structures occur as both discrete examples and continuous examples. Discrete algebras include: Boolean algebra used in logic gates and programming; relational algebra used in databases; discrete and finite versions of groups, rings and fields are important in algebraic coding theory; discrete semigroups and monoids appear in the theory of formal languages.

Discrete analogues of continuous mathematics
There are many concepts and theories in continuous mathematics which have discrete versions, such as discrete calculus, discrete Fourier transforms, discrete geometry, discrete logarithms, discrete differential geometry, discrete exterior calculus, discrete Morse theory, discrete optimization, discrete probability theory, discrete probability distribution, difference equations, discrete dynamical systems, and discrete vector measures.

Calculus of finite differences, discrete analysis, and discrete calculus
In discrete calculus and the calculus of finite differences, a function defined on an interval of the integers is usually called a sequence. A sequence could be a finite sequence from a data source or an infinite sequence from a discrete dynamical system. Such a discrete function could be defined explicitly by a list (if its domain is finite), or by a formula for its general term, or it could be given implicitly by a recurrence relation or difference equation. Difference equations are similar to differential equations, but replace differentiation by taking the difference between adjacent terms; they can be used to approximate differential equations or (more often) studied in their own right. Many questions and methods concerning differential equations have counterparts for difference equations. For instance, where there are integral transforms in harmonic analysis for studying continuous functions or analogue signals, there are discrete transforms for discrete functions or digital signals. As well as discrete metric spaces, there are more general discrete topological spaces, finite metric spaces, finite topological spaces.

The time scale calculus is a unification of the theory of difference equations with that of differential equations, which has applications to fields requiring simultaneous modelling of discrete and continuous data. Another way of modeling such a situation is the notion of hybrid dynamical systems.

Discrete geometry
Discrete geometry and combinatorial geometry are about combinatorial properties of discrete collections of geometrical objects. A long-standing topic in discrete geometry is tiling of the plane.

In algebraic geometry, the concept of a curve can be extended to discrete geometries by taking the spectra of polynomial rings over finite fields to be models of the affine spaces over that field, and letting subvarieties or spectra of other rings provide the curves that lie in that space. Although the space in which the curves appear has a finite number of points, the curves are not so much sets of points as analogues of curves in continuous settings. For example, every point of the form $$V(x-c) \subset \operatorname{Spec} K[x] = \mathbb{A}^1$$ for $$K$$ a field can be studied either as $$\operatorname{Spec} K[x]/(x-c) \cong \operatorname{Spec} K$$, a point, or as the spectrum $$\operatorname{Spec} K[x]_{(x-c)}$$ of the local ring at (x-c), a point together with a neighborhood around it. Algebraic varieties also have a well-defined notion of tangent space called the Zariski tangent space, making many features of calculus applicable even in finite settings.

Discrete modelling
In applied mathematics, discrete modelling is the discrete analogue of continuous modelling. In discrete modelling, discrete formulae are fit to data. A common method in this form of modelling is to use recurrence relation. Discretization concerns the process of transferring continuous models and equations into discrete counterparts, often for the purposes of making calculations easier by using approximations. Numerical analysis provides an important example.

Challenges

The history of discrete mathematics has involved a number of challenging problems which have focused attention within areas of the field. In graph theory, much research was motivated by attempts to prove the four color theorem, first stated in 1852, but not proved until 1976 (by Kenneth Appel and Wolfgang Haken, using substantial computer assistance).

In logic, the second problem on David Hilbert's list of open problems presented in 1900 was to prove that the axioms of arithmetic are consistent. Gödel's second incompleteness theorem, proved in 1931, showed that this was not possible – at least not within arithmetic itself. Hilbert's tenth problem was to determine whether a given polynomial Diophantine equation with integer coefficients has an integer solution. In 1970, Yuri Matiyasevich proved that this could not be done.

The need to break German codes in World War II led to advances in cryptography and theoretical computer science, with the first programmable digital electronic computer being developed at England's Bletchley Park with the guidance of Alan Turing and his seminal work, On Computable Numbers. The Cold War meant that cryptography remained important, with fundamental advances such as public-key cryptography being developed in the following decades. The telecommunication industry has also motivated advances in discrete mathematics, particularly in graph theory and information theory. Formal verification of statements in logic has been necessary for software development of safety-critical systems, and advances in automated theorem proving have been driven by this need.

Computational geometry has been an important part of the computer graphics incorporated into modern video games and computer-aided design tools.

Several fields of discrete mathematics, particularly theoretical computer science, graph theory, and combinatorics, are important in addressing the challenging bioinformatics problems associated with understanding the tree of life.

Currently, one of the most famous open problems in theoretical computer science is the P = NP problem, which involves the relationship between the complexity classes P and NP. The Clay Mathematics Institute has offered a $1 million USD prize for the first correct proof, along with prizes for six other mathematical problems.

title: Discrete mathematics