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Arithmetic
Arithmetic
Arithmetic
(from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division. Arithmetic is an elementary part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry, and analysis
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Severus Sebokht
Severus Sebokht (Classical Syriac: ܣܘܪܘܣ ܣܝܒܘܟܬ‎), also Seboukt of Nisibis, was a Syrian scholar and bishop who was born in Nisibis, Syria in 575 and died in 667.Contents1 Biography 2 Work 3 Astrolabe 4 See also 5 References 6 External linksBiography[edit] Although little is known about his early life, he was one of the leading figures in Syria in the 7th century. He taught at the Theological School of Nisibis. In 612, he left the post because of a doctrinal dispute with the Syriac Church of the East. He was a member of the Syriac Orthodox Church. He was a resident of the Monastery of Kennesrin, which was situated near the banks of the Euphrates.[1] His student Jacob of Edessa (d. 708), the major representative of “Christian Hellenism".[2] Work[edit] He was a teacher of the philosophy of Aristotle. In 638, he wrote a major treatise on syllogisms
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Democratic Republic Of The Congo
Coordinates: 2°52′48″S 23°39′22″E / 2.88°S 23.656°E / -2.88; 23.656Democratic Republic of the Congo République démocratique du Congo  (French) Repubilika ya Kôngo ya Dimokalasi  (Kongo) Republíki ya Kongó Demokratíki  (Lingala) Jamhuri ya Kidemokrasia ya Kongo  (Swahili) Ditunga dia Kongu wa Mungalaata  (Luba-Katanga)FlagCoat of armsMotto: "Justice – Paix – Travail" (French) "Justice – Peace – Work"Anthem: Debout Congolais  (French) "Arise, Congolese"Location of  Democratic Republic of the Congo  (dark green)Capital and largest city Kinshasa 4°19′S 15°19′E / 4.317°S 15.317°E / -4.317; 15.317Official languages FrenchRecognised national languagesLingala Kikongo Swahili TshilubaEthnic groups See
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Syriac Christianity
Syriac Christianity
Syriac Christianity
(Syriac: ܡܫܝܚܝܘܬܐ ܣܘܪܝܝܬܐ‎ / mšiḥāiūṯā suryāiṯā) refers to Eastern Christian
Eastern Christian
traditions that employs Syriac in their liturgical rites
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Liu Hui
Liu
Liu
Hui (fl. 3rd century CE) was a Chinese mathematician who lived in the state of Cao Wei
Cao Wei
during the Three Kingdoms
Three Kingdoms
period (220–280) of China. In 263, he edited and published a book with solutions to mathematical problems presented in the famous Chinese book of mathematics known as The Nine Chapters on the Mathematical Art, in which he was possibly the first mathematician to discover, understand and use negative numbers. He was a descendant of the Marquis of Zi District (菑鄉侯) of the Eastern Han dynasty, whose marquisate is in present-day Zichuan District, Zibo, Shandong. He completed his commentary to the Nine Chapters in the year 263
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Counting Rods
Counting rods
Counting rods
(traditional Chinese: 籌; simplified Chinese: 筹; pinyin: chóu; Japanese: 算木; rōmaji: sangi; Korean: sangaji) are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number. The written forms based on them are called rod numerals. They are a true positional numeral system with digits for 1–9 and a blank for 0, from the Warring states period (circa 475 BCE) to the 16th century.Contents1 History 2 Using counting rods2.1 Place value3 Rod numerals 4 Fractions 5 Rod calculus 6 Unicode 7 See also 8 References 9 External linksHistory[edit] Chinese arithmeticians used counting rods well over two thousand years ago
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Greek Numerals
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals
Roman numerals
are still used elsewhere in the West. For ordinary cardinal numbers, however, Greece
Greece
uses Arabic numerals.Contents1 History 2 Description 3 Table 4 Higher numbers 5 Zero 6 See also 7 References 8 External linksHistory[edit] The Minoan and Mycenaean civilizations' Linear A
Linear A
and Linear B alphabets used a different system, called Aegean numerals, which included specialized symbols for numbers: 𐄇 = 1, 𐄐 = 10, 𐄙 = 100, 𐄢 = 1000, and 𐄫 = 10000.[1] Attic numerals, which were later adopted as the basis for Roman numerals, were the first alphabetic set
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Pythagoreanism
Pythagoreanism
Pythagoreanism
originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras
Pythagoras
and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism. Later revivals of Pythagorean doctrines led to what is now called Neopythagoreanism
Neopythagoreanism
or Neoplatonism
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Hellenistic Civilization
The Hellenistic
Hellenistic
period covers the period of Mediterranean
Mediterranean
history between the death of Alexander the Great
Alexander the Great
in 323 BC and the emergence of the Roman Empire
Roman Empire
as signified by the Battle of Actium
Battle of Actium
in 31 BC[1] and the subsequent conquest of Ptolemaic Egypt
Egypt
the following year.[2] The Ancient Greek
Ancient Greek
word Hellas (Ἑλλάς, Ellás) is the original word for Greece, from which the word "Hellenistic" was derived.[3] At this time, Greek cultural influence and power was at its peak in Europe, North Africa
North Africa
and Western Asia, experiencing prosperity and progress in the arts, exploration, literature, theatre, architecture, music, mathematics, philosophy, and science
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Maya Numerals
The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal (base-20) positional numeral system. The numerals are made up of three symbols; zero (shell shape, with the plastron uppermost), one (a dot) and five (a bar). For example, thirteen is written as three dots in a horizontal row above two horizontal bars; sometimes it is also written as three vertical dots to the left of two vertical bars. With these three symbols each of the twenty vigesimal digits could be written.400s20s1s33 429 5125Numbers after 19 were written vertically in powers of twenty. The Mayan used powers of twenty, just as our Hindu-Arabic numeral system uses powers of tens.[1] For example, thirty-three would be written as one dot, above three dots atop two bars. The first dot represents "one twenty" or "1×20", which is added to three dots and two bars, or thirteen. Therefore, (1×20) + 13 = 33
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Vigesimal
The vigesimal or base 20 numeral system is based on twenty (in the same way in which the decimal numeral system is based on ten).Contents1 Places1.1 Converting table2 Fractions 3 Cyclic numbers 4 Real numbers 5 Use5.1 Africa 5.2 Americas 5.3 Asia 5.4 In Europe5.4.1 Etymology 5.4.2 Examples5.5 Related observations6 Examples in Mesoamerican languages6.1 Powers of twenty in Yucatec
Yucatec
Maya and Nahuatl 6.2 Counting in units of twenty7 Further reading 8 NotesPlaces[edit] In a vigesimal place system, twenty individual numerals (or digit symbols) are used, ten more than in the usual decimal system. One modern method of finding the extra needed symbols is to write ten as the letter A20 (the 20 means base 20), to write nineteen as J20, and the numbers between with the corresponding letters of the alphabet. This is similar to the common computer-science practice of writing hexadecimal numerals over 9 with the letters "A–F"
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Roman Abacus
The Ancient Romans developed the Roman hand abacus, a portable, but less capable, base-10 version of the previous Babylonian abacus. It was the first portable calculating device for engineers, merchants and presumably tax collectors. It greatly reduced the time needed to perform the basic operations of arithmetic using Roman numerals. As Karl Menninger says on page 315 of his book,[1] "For more extensive and complicated calculations, such as those involved in Roman land surveys, there was, in addition to the hand abacus, a true reckoning board with unattached counters or pebbles. The Etruscan cameo and the Greek predecessors, such as the Salamis Tablet and the Darius Vase, give us a good idea of what it must have been like, although no actual specimens of the true Roman counting board are known to be extant. But language, the most reliable and conservative guardian of a past culture, has come to our rescue once more
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Ancient Greek
The Ancient Greek language
Greek language
includes the forms of Greek used in ancient Greece
Greece
and the ancient world from around the 9th century BC to the 6th century AD. It is often roughly divided into the Archaic period (9th to 6th centuries BC), Classical period (5th and 4th centuries BC), and Hellenistic period
Hellenistic period
(Koine Greek, 3rd century BC to the 4th century AD). It is antedated in the second millennium BC by Mycenaean Greek and succeeded by medieval Greek. Koine is regarded as a separate historical stage of its own, although in its earliest form it closely resembled Attic Greek
Attic Greek
and in its latest form it approaches Medieval Greek
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Tally Marks
Tally marks, also called hash marks, are a unary numeral system. They are a form of numeral used for counting. They are most useful in counting or tallying ongoing results, such as the score in a game or sport, as no intermediate results need to be erased or discarded. However, because of the length of large numbers, tallies are not commonly used for static text
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Egyptian Numerals
The system of ancient Egyptian numerals
Egyptian numerals
was used in Ancient Egypt
Ancient Egypt
from around 3000 BC[1] until the early first millennium AD. It was a system of numeration based on multiples of ten, often rounded off to the higher power, written in hieroglyphs
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Counting Board
The counting board is the precursor of the abacus, and the earliest known form of a counting device (excluding fingers and other very simple methods). Counting boards were made of stone or wood, and the counting was done on the board with beads, or pebbles etc. Not many boards survive because of the perishable materials used in their construction. The oldest known counting board, the Salamis Tablet (c. 300 BC) was discovered on the Greek island of Salamis in 1899.[1] It is thought to have been used by the Babylonians in about 300 BC and is more of a gaming board than a calculating device. It is marble, about 150 x 75 x 4.5 cm, and is in the Greek National museum in Athens. It has carved Greek letters and parallel grooves. The German mathematicican Adam Ries described the use of counting boards in Rechenbuch auf Linien und Ziphren in allerlei Handthierung / geschäfften und Kaufmanschafft
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