HISTORY OF MATHEMATICS

How did math join the curriculum of scholars in medieval times?

Boethius provided a place for mathematics in the curriculum in the 6th century when he coined the term quadrivium to describe the study of arithmetic, geometry, astronomy, and music.

Who were the most prosperous mathematicians in the Song Dynasty and the Yuan Dynasty?

Four outstanding mathematicians arose during the Song Dynasty and Yuan Dynasty, particularly in the twelfth and thirteenth centuries: Yang Hui, Qin Jiushao, Li Zhi (Li Ye), and Zhu Shijie.

Where did Greek mathematicians live?

Greek mathematicians lived in cities spread over the entire Eastern Mediterranean, from Italy to North Africa, but were united by culture and language.

What drove people to become mathematicians in Medieval Europe?

Medieval European interest in mathematics was driven by concerns quite different from those of modern mathematicians. One driving element was the belief that mathematics provided the key to understanding the created order of nature, frequently justified by Plato's Timaeus and the biblical passage (in the Book of Wisdom) that God had ordered all things in measure, and number, and weight.

What was the center of mathematical education and research in the third century BC?

The Musaeum of Alexandria.

Describe the appearance of the suanpan.

Usually, a suanpan is about 20 cm (8 in) tall and it comes in various widths depending on the application. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads on each rod in the bottom deck. This configuration is used for both decimal and hexadecimal computation. The beads are usually rounded and made of a hardwood.

What was the first written evidence of mathematics in Egypt?

Written evidence of the use of mathematics dates back to at least 3000 BC with the ivory labels found in Tomb U-j at Abydos.

How many volumes does Euclid's Elements contain?

13

What is the Plimpton 322?

A Babylonian clay tablet, notable as containing an example of Babylonian mathematics. This tablet, believed to have been written about 1800 BC, has a table of four columns and 15 rows of numbers in the cuneiform script of the period.

What was Euclid's Elements?

A mathematical and geometric treatise consisting of 13 books written by the ancient Greek mathematician Euclid in Alexandria.

What was the oldest counting board ever found?

A tablet found on the Greek island Salamis in 1846 AD (the Salamis Tablet), dates back to 300 BC, making it the oldest counting board discovered so far.

What was the most important center of learning during the Hellenistic Period?

Alexandria.

How were the Indian mathematical works transmitted?

All mathematical works were orally transmitted until approximately 500 BCE; thereafter, they were transmitted both orally and in manuscript form.

What was the work of Luca Pacioli regarding mathematics?

An important figure in the late 15th and early 16th Centuries is an Italian Franciscan friar called Luca Pacioli, who published a book on arithmetic, geometry and book-keeping at the end of the 15th Century which became quite popular for the mathematical puzzles it contained.

What was Ancient Egyptian mathematics?

Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt c. 3000 to c. 300 BC.

How were Egyptian mathematics written?

Ancient Egyptian texts could be written in either hieroglyphs or in hieratic. In either representation the number system was always given in base 10. The number 1 was depicted by a simple stroke, the number 2 was represented by two strokes, etc.

What language was the mathematics of ancient and medieval India in?

Ancient and medieval Indian mathematical works were all composed in Sanskrit.

Did the Babylonians have algebra?

As well as arithmetical calculations, Babylonian mathematicians also developed algebraic methods of solving equations. Once again, these were based on pre-calculated tables.

What was Babylonian mathematics?

Babylonian mathematics was any mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited.

How did trade influence the development of mathematics in Medieval Europe?

By the 12th Century, though, Europe, and particularly Italy, was beginning to trade with the East, and Eastern knowledge gradually began to spread to the West. Robert of Chester translated Al-Khwarizmi's important book on algebra into Latin in the 12th Century, and the complete text of Euclid's "Elements" was translated in various versions by Adelard of Bath, Herman of Carinthia and Gerard of Cremona. The great expansion of trade and commerce in general created a growing practical need for mathematics, and arithmetic entered much more into the lives of common people and was no longer limited to the academic realm.

Explain the creation of the Hindu-Arabic numeral system.

Despite the numeral system being described as the "Hindu-Arabic numeral system", the system had been developed by Hindu mathematicians and in use extensively throughout India before spreading.

How did mathematics develop in medieval Islam?

During the Golden Age of Islam, mathematics saw important developments, such as the full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra, and advances in geometry and trigonometry. Arabic works also played an important role in the transmission of mathematics to Europe during the 10th to 12th centuries.

Why was mathematics not as advanced in Medieval Europe?

During the centuries in which the Chinese, Indian and Islamic mathematicians had been in the ascendancy, Europe had fallen into the Dark Ages, in which science, mathematics and almost all intellectual endeavor stagnated.

Why do we believe Chinese mathematics developed independently from that of other civilizations?

Early Chinese mathematics is so different from that of other parts of the world that it is reasonable to assume independent development.

What was the format of entries in the Nine Chapters on the Mathematical Art?

Entries in the book usually take the form of a statement of a problem, followed by the statement of the solution, and an explanation of the procedure that led to the solution.

What is some evidence of Egyptian mathematics using a base 10 number system?

Evidence of the use of the base 10 number system can be found on the Narmer Macehead which depicts offerings of 400,000 oxen, 1,422,000 goats and 120,000 prisoners.

What do we know about Al-Khwarizmi?

Few details of al-Khwārizmī's life are known with certainty. He was born in a Persian family and Ibn al-Nadim gives his birthplace as Khwarezm in Greater Khorasan (modern Xorazm Region, Uzbekistan).

Explain mathematics in Europe from the 4th to the 12th Century.

From the 4th to 12th Centuries, European knowledge and study of arithmetic, geometry, astronomy and music was limited mainly to Boethius' translations of some of the works of ancient Greek masters such as Nicomachus and Euclid. All trade and calculation was made using the clumsy and inefficient Roman numeral system, and with an abacus based on Greek and Roman models.

What was Greek mathematics?

Greek mathematics refers to the mathematics written in the Greek language from the time of Thales of Miletus (~600 BC) to the closure of the Academy of Athens in 529 AD. Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics.

What was the difference between Greek mathematics and that of previous civilizations?

Greek mathematics was much more sophisticated than the mathematics that had been developed by earlier cultures. Greek mathematicians, unlike previous mathematicians, used deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms, and used mathematical rigor to prove them.

What is Thales known as the first mathematician?

He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. As a result, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed.

How didi Al-Khwarizmi develop the concept of algebra?

His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his 830 book on the subject, "The Compendious Book on Calculation by Completion and Balancing".

What was the beginning of what we know as Greek mathematics?

Historians traditionally place the beginning of Greek mathematics proper to the age of Thales of Miletus (ca. 624-548 BC).

Explain the work of Italian mathematicians regarding cubic equations.

In Italy, during the first half of the 16th century, Scipione del Ferro and Niccolò Fontana Tartaglia discovered solutions for cubic equations. Gerolamo Cardano published them in his 1545 book Ars Magna, together with a solution for the quartic equations, discovered by his student Lodovico Ferrari. In 1572 Rafael Bombelli published his L'Algebra in which he showed how to deal with the imaginary quantities that could appear in Cardano's formula for solving cubic equations.

Were there any differences between the two groups of Babylonian mathematics?

In respect of content there is scarcely any difference between the two groups of texts. Thus Babylonian mathematics remained constant, in character and content, for nearly two millennia.

How accurate was the Chinese approximation of π?

In the 5th century AD Zu Chongzhi computed the value of π to seven decimal places, which remained the most accurate value of π for almost the next 1000 years.

Where did Indian mathematics emerge?

Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1600 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Mahāvīra, Bhaskara II, Madhava of Sangamagrama and Nilakantha Somayaji.

How did Islamic mathematicians deal with irrational numbers?

Islamic mathematicians including Abū Kāmil Shujāʿ ibn Aslam slowly removed the distinction between magnitude and number, allowing irrational quantities to appear as coefficients in equations and to be solutions of algebraic equations. They worked freely with irrationals as objects, but they did not examine closely their nature.

What did Euclid's Elements consist of?

It consists of a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions.

Explain the spread of the Hindu-Arabic numeral system.

It was adopted by Persian mathematicians in India and passed on to the Arabs further west. The numeral system was then transmitted to Europe in the Middle Ages by Fibonacci. The use of Arabic numerals spread around the world through European trade, books.

What was Khayyám's work on the theory of parallels?

Khayyám wrote a book entitled Explanations of the difficulties in the postulates in Euclid's Elements. The book consists of several sections on the parallel postulate (Book I), on the Euclidean definition of ratios and the Anthyphairetic ratio (modern continued fractions) (Book II), and on the multiplication of ratios (Book III).

How was Fibonacci?

Leonardo Bonacci also known as Fibonacci was an Italian mathematician, considered to be "the most talented Western mathematician of the Middle Ages". Fibonacci popularized the Hindu-Arabic numeral system to the Western World primarily through his composition in 1202 of Liber Abaci (Book of Calculation). He also introduced to Europe the sequence of Fibonacci numbers which he used as an example in Liber Abaci.

What was the Liber Abaci?

Liber Abaci (1202, also spelled as Liber Abbaci) is a historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci. Liber Abaci was among the first Western books to describe Hindu-Arabic numbers traditionally described as "Arabic Numerals". By addressing the applications of both commercial tradesmen and mathematicians, it contributed to convincing the public of the superiority of the new numerals.

What was Pacioli's book called and what was it mostly used for?

Luca Pacioli's book was called the Summa de Arithmetica, Geometria, Proportioni et Proportionalità. It was written primarily for, and sold mainly to, merchants who used the book as a reference text, as a source of pleasure from the mathematical puzzles it contained, and to aid the education of their sons.[

Who introduced the symbols for plus and minus for the first time in printed books?

Lucas Pacioli.

What is the relationship between mathematics and the Six Arts?

Math was one of the Liù Yì (六艺) or Six Arts, students were required to master during the Zhou Dynasty (1122-256 BC). Learning them all perfectly was required to be a perfect gentleman, or in the Chinese sense, a "Renaissance Man". Six Arts have their roots in the Confucian philosophy.

When did mathematics emerge in China?

Mathematics in China emerged independently by the 11th century BC.

Where have most of the Greek mathematical texts been found?

Most of the mathematical texts written in Greek have been found in Greece, Egypt, Asia Minor, Mesopotamia, and Sicily.

Who was Al-Khwarizmi?

Muḥammad ibn Mūsā al-Khwārizmī was a Persian mathematician, astronomer and geographer during the Abbasid Caliphate, a scholar in the House of Wisdom in Baghdad.

Why is so little known about Qin mathematics?

Not much is known about Qin dynasty mathematics, or before, due to the burning of books and burying of scholars, circa 213-210 BCE.

Explain the Chinese place value decimal system.

Of particular note is the use in Chinese mathematics of a decimal positional notation system, the so-called "rod numerals" in which distinct ciphers were used for numbers between 1 and 10, and additional ciphers for powers of ten.

Who was Omar Khayyám?

Omar Khayyám was a Persian mathematician, astronomer, philosopher, and poet, who is widely considered to be one of the most influential scientists of the middle ages. He wrote numerous treatises on mechanics, geography, mineralogy and astronomy.

How did Al-Khwarizmi's book spread the Hindu-Arabic numeral system?

On the Calculation with Hindu Numerals written about 825, was principally responsible for spreading the Hindu-Arabic numeral system throughout the Middle East and Europe. It was translated into Latin as Algoritmi de numero Indorum. Al-Khwārizmī, rendered as (Latin) Algoritmi, led to the term "algorithm".

Where does our knowledge of Babylonian mathematics come from?

Our knowledge of Babylonian mathematics is derived from some 400 clay tablets unearthed since the 1850s. Written in Cuneiform script, tablets were inscribed while the clay was moist, and baked hard in an oven or by the heat of the sun. The majority of recovered clay tablets date from 1800 to 1600 B.C.

Describe Pacioli's study of the Golden Ratio?

Pacioli also investigated the Golden Ratio of 1 : 1.618... (see the flashcards on Fibonacci) in his 1509 book "The Divine Proportion", concluding that the number was a message from God and a source of secret knowledge about the inner beauty of things.

Who was Pythagoras?

Pythagoras was an Ionian Greek philosopher, mathematician, and has been credited as the founder of the movement called Pythagoreanism. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem

Who introduced zero to Chinese mathematics?

Qin Jiushao (c. 1202-1261) was the first to introduce the zero symbol into Chinese mathematics. Before this innovation, blank spaces were used instead of zeros in the system of counting rods.

How are Babylonian mathematical texts classified?

Regarding time, they fall in two distinct groups: one from the Old Babylonian period and the other mainly Seleucid from the last three or four centuries BC.

Why was the place value system used by ancient Chinese mathematicians more advanced than other ones?

Rod numerals allowed the representation of numbers as large as desired and allowed calculations to be carried out on the suan pan, or Chinese abacus.

What was the relationship between science, math, and art in the Renaissance?

Science, math, and art were still very much interconnected and intermingled at this time, as exemplified by the work of artist/scientists such as Leonardo da Vinci.

Who was Sharaf al-Dīn al-Ṭūsī?

Sharaf al-Dīn al-Muẓaffar ibn Muḥammad ibn al-Muẓaffar al-Ṭūsī (died 1213/4)[1] was a Persian mathematician and astronomer of the Islamic Golden Age (during the Middle Ages)

What was Sharaf al-Dīn al-Ṭūsī's work regarding cubic equations?

Sharaf al-Dīn al-Ṭūsī (? in Tus, Iran - 1213/4) developed a novel approach to the investigation of cubic equations—an approach which entailed finding the point at which a cubic polynomial obtains its maximum value.

Who was Thales of MIletus?

Thales of Miletus was a pre-Socratic Greek philosopher and mathematician from Miletus in Asia Minor. Many, regard him as the first philosopher in the Greek tradition.

What numerals did the Babylonians use?

The Babylonian system of mathematics was sexagesimal (base 60) numeral system. From this we derive the modern day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 degrees in a circle.

Did the Babylonians have a place-value system?

The Babylonians had a true place-value system, where digits written in the left column represented larger values much like our base ten system.

What did the Babylonians use as a tool for doing correct arithmetic?

The Babylonians used pre-calculated tables to assist with arithmetic. For example, two tablets found at in 1854, dating from 2000 BC, give lists of the squares of numbers up to 59 and the cubes of numbers up to 32. The Babylonians used the lists of squares together with the certain formulas to assist in multiplication.

What are some of the accomplishments achieved by Chinese mathematicians?

The Chinese independently developed very large and negative numbers, decimals, a place value decimal system, a binary system, algebra, geometry, and trigonometry.

What was the Greek abacus?

The Greek abacus was a table of wood or marble, pre-set with small counters in wood or metal for mathematical calculations. It was used in Achaemenid Persia, the Etruscan civilization, Ancient Rome and, until the French Revolution, the Western Christian world.

How did Greek mathematicians deal with irrational numbers?

The Greeks had discovered irrational numbers, but were not happy with them and only able to cope by drawing a distinction between magnitude and number. In the Greek view, magnitudes varied continuously and could be used for entities such as line segments, whereas numbers were discrete. Hence, irrationals could only be handled geometrically; and indeed Greek mathematics was mainly geometrical.

What is the positional notation of Hindu-Arabic numeral system?

The Hindu numeral system is designed for positional notation in a decimal system. In a more developed form, positional notation also uses a decimal marker and also a symbol for "these digits recur ad infinitum." In modern usage, this latter symbol is usually a vinculum. In this more developed form, the numeral system can symbolize any rational number using only 13 symbols

What is the Hindu-Arabic numeral system?

The Hindu numeral system, or Hindu-Arabic numeral system a positional decimal numeral system, is the most common system for the symbolic representation of numbers in the world. It was invented between the 1st and 4th centuries by Indian mathematicians.

What was the Nine Chapters on the Mathematical Art?

The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th-2nd century BCE. It is one of the earliest surviving mathematical texts from China. It lays out an approach to mathematics that centres on finding the most general methods of solving problems.

What was the mathematical center of the world in the 4th century BC?

The Platonic Academy.

What was the Renaissance?

The Renaissance is a period in Europe, from the 14th to the 17th century, considered the bridge between the Middle Ages and modern history.

What was the Suan Pan?

The Suan Pan is an abacus of Chinese origin first described in a 190 CE book of the Eastern Han Dynasty, namely Supplementary Notes on the Art of Figures written by Xu Yue.

What was the Suàn shù shū?

The Suàn shù shū (筭數書), or the Writings on Reckoning (also as Book on Numbers and Computation), is one of the earliest known Chinese mathematical treatises. It was written during the early Western Han Dynasty, sometime between 202 BC and 186 BC.

What does the Suàn shù shū consist of?

The Suàn shù shū consists of 69 mathematical problems from a variety of sources, two names Mr Wáng and Mr Yáng were found, probably two of the writers. Each problem has a question, an answer, followed by a method.

How did the printing press allow math to develop even more during this period of time?

The advent of the printing press in the mid-15th Century also had a huge impact. Numerous books on arithmetic were published for the purpose of teaching business people computational methods for their commercial needs and mathematics gradually began to acquire a more important position in education.

Explain what the history of mathematics is(as a subject).

The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.

How are suanpans used?

The beads are counted by moving them up or down towards the beam. Suanpans can be used for functions other than counting. Unlike the simple counting board used in elementary schools, very efficient suanpan techniques have been developed to do multiplication, division, addition, subtraction, square root and cube root operations at high speed.

How did the Renaissance begin and spread?

The cultural, intellectual and artistic movement of the Renaissance, which saw a resurgence of learning based on classical sources, began in Italy around the 14th Century, and gradually spread across most of Europe over the next two centuries.

What were the contributions of Indian mathematics to our modern day math?

The decimal number system in use today was first recorded in Indian mathematics. Indian mathematicians made early contributions to the study of the concept of zero as a number, negative numbers, arithmetic, and algebra. In addition, trigonometry was further advanced in India, and, in particular, the modern definitions of sine and cosine were developed there.

Did the Greeks have tools similar to the abacus?

The earliest archaeological evidence for the use of the Greek abacus dates to the 5th century BC.[17] Also Demosthenes (384 BC-322 BC) talked of the need to use pebbles for calculations too difficult for your head. A play by Alexis from the 4th century BC mentions an abacus and pebbles for accounting, and both Diogenes and Polybius mention men that sometimes stood for more and sometimes for less, like the pebbles on an abacus.

What were the earliest documents regarding mathematics in Egypt?

The earliest true mathematical documents date to the 12th dynasty (ca 1990-1800 BC). The Moscow Mathematical Papyrus, the Egyptian Mathematical Leather Roll, the Lahun Mathematical Papyri which are a part of the much larger collection of Kahun Papyri and the Berlin Papyrus 6619 all date to this period. The Rhind Mathematical Papyrus which dates to the Second Intermediate Period (ca 1650 BC) is said to be based on an older mathematical text from the 12th dynasty.

Elaborate regarding evidence of math in the Old Kingdom.

The evidence of the use of mathematics in the Old Kingdom (ca 2690-2180 BC) is scarce, but can be deduced from inscriptions on a wall near a mastaba in Meidum which gives guidelines for the slope of the mastaba.

What does the first section of the Liber Abaci describe?

The first section introduces the Hindu-Arabic numeral system, including methods for converting between different representation systems.

What does the fourth section of the Liber Abaci describe?

The fourth section derives approximations, both numerical and geometrical, of irrational numbers such as square roots.

Where do the glyphs we use come from?

The glyphs in actual use are descended from Brahmi numerals and have split into various typographical variants since the Middle Ages.

How did the concept of "number" evolve over time?

The idea of the "number" concept evolving gradually over time is supported by the existence of languages which preserve the distinction between "one", "two", and "many", but not of numbers larger than two.

Describe the modern suanpan.

The modern suanpan has 4+1 beads, colored beads to indicate position and a clear-all button. When the clear-all button is pressed, two mechanical levers push the top row beads to the top position and the bottom row beads to the bottom position, thus clearing all numbers to zero.

Which are the oldest mathematical texts available?

The most ancient mathematical texts available are Plimpton 322 (Babylonian c. 1900 BC), the Rhind Mathematical Papyrus (Egyptian c. 2000-1800 BC) and the Moscow Mathematical Papyrus (Egyptian c. 1890 BC).

Explain how the sexagesimal (base 60) helped the Babylonians.

The number 60 is a superior highly composite number, having factors of 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, facilitating calculations with fractions.

How were the powers of ten represented in Ancient Egyptian math?

The numbers 10, 100, 1000, 10,000 and 1,000,000 had their own hieroglyphs. Number 10 is a hobble for cattle, number 100 is represented by a coiled rope, the number 1000 is represented by a lotus flower, the number 10,000 is represented by a finger, the number 100,000 is represented by a frog, and a million was represented by a god with his hands raised in adoration.

How did Greek mathematics originate?

The origins of Greek mathematics are not easily documented. The earliest advanced civilizations in the country of Greece and in Europe were the Minoan and later Mycenean civilization, both of which flourished during the 2nd millennium BC. However, they left behind no mathematical documents.

Explain the origins of mathematical thought.

The origins of mathematical thought lie in the concepts of number, magnitude, and form. Such concepts would have been part of everyday life in hunter-gatherer societies.

What was the Sumerian abacus?

The period 2700-2300 BC saw the first appearance of the Sumerian abacus, a table of successive columns which delimited the successive orders of magnitude of their sexagesimal number system. It is the belief of Old Babylonian scholars that Old Babylonians "may have used the abacus for the operations of addition and subtraction; however, this primitive device proved difficult to use for more complex calculations".

What do religious texts tell us about the size of numbers being used?

The religious texts of the Vedic Period provide evidence for the use of large numbers. By the time of the Yajurvedasaṃhitā- (1200-900 BCE), numbers as high as 10^12 were being included in the texts.

What does the second section of the Liber Abaci describe?

The second section presents examples from commerce, such as conversions of currency and measurements, and calculations of profit and interest.

How did algebra develop?

The study of algebra, which itself is an Arabic word meaning "reunion of broken parts", flourished during the Islamic golden age. Al-Khwarizmi is, along with the Greek mathematician Diophantus, known as the father of algebra.

How did the study of mathematics begin?

The study of mathematics as a demonstrative discipline begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek μάθημα (mathema), meaning "subject of instruction".

What glyphs does the Hindu-Arabic numeral system use?

The system is based upon ten (originally nine) different glyphs. The symbols (glyphs) used to represent the system are in principle independent of the system itself.

What symbols does the Hindu-Arabic numeral system use?

The ten digits, decimal marker, vinculum, and an optional prepended dash to indicate a negative number.

What does the third section of the Liber Abaci describe?

The third section discusses a number of mathematical problems; for instance, it includes (ch. II.12) the Chinese remainder theorem, perfect numbers and Mersenne primes as well as formulas for arithmetic series and for square pyramidal numbers. Another example in this chapter, describing the growth of a population of rabbits, was the origin of the Fibonacci sequence for which the author is most famous today.

What Liber Abaci actually mean?

The title of Liber Abaci means "The Book of Calculation". Although it has also been translated as "The Book of the Abacus", Sigler (2002) writes that this is an error: the intent of the book is to describe methods of doing calculations without aid of an abacus, and as Ore (1948) confirms, for centuries after its publication the algorismists (followers of the style of calculation demonstrated in Liber Abaci) remained in conflict with the abacists (traditionalists who continued to use the abacus in conjunction with Roman numerals).

Did the Egyptians use the abacus?

The use of the abacus in Ancient Egypt is mentioned by the Greek historian Herodotus, who writes that the Egyptians manipulated the pebbles from right to left, opposite in direction to the Greek left-to-right method. Archaeologists have found ancient disks of various sizes that are thought to have been used as counters. However, wall depictions of this instrument have not been discovered.

How did the Indian contributions to mathematics travel and influence other mathematicians?

These mathematical concepts were transmitted to the Middle East, China, and Europe and led to further developments that now form the foundations of many areas of mathematics.

What are the families that divide and classify the glyphs?

These symbol sets can be divided into three main families: Hindu numerals used in the Indian subcontinent, the Eastern Arabic numerals used in Egypt and the Middle East and the Arabic numerals used in the Greater Maghreb and in Europe.

What does Plimpton 322 contain?

This table lists what are now called Pythagorean triples, i.e., integers a, b, c satisfying a^2+b^2=c^2. From a modern perspective, a method for constructing such triples is a significant early achievement, known long before the Greek and Indian mathematicians discovered solutions to this problem.

What civilizations are believed to have influenced Greek mathematics?

Though no direct evidence is available, it is generally thought that the neighboring Babylonian and Egyptian civilizations had an influence on the younger Greek tradition.

Give an example of how the Chinese place value decimal system write numbers?

Thus, the number 123 would be written using the symbol for "1", followed by the symbol for "100", then the symbol for "2" followed by the symbol for "10", followed by the symbol for "3".

Which Chinese mathematician discovered and proofed Pascal's Triangle?

Yang Hui was also the first person in history to discover and prove "Pascal's Triangle", along with its binomial proof (although the earliest mention of the Pascal's triangle in China exists before the eleventh century AD).