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786 numbers and counting: Asia and the Pacific culture in the Americas to develop a real written language that could be read phonetically This basis of counting contributed to the development of the ritually significant calendar, since the main purpose of counting was related to calendrics Like most Mesoamerican cultures, the Maya used a 260-day ritual calendar called a tzolkin This calendar, which has its origin in the Preclassic Period, probably reflects the gestation period of an infant, from the time of the first missed menstrual cycle to birth It is divided not by months but by 20 day names and 13 day numbers In conjunction with the ritual calendar, a 365-day solar calendar was also used, consisting of 18 months (also with individual names) of 20 days (this period of 360 days is called a tun) plus five unnamed days called the Uayeb These two calendars were used together, simultaneously, a cycle taking 52 years to complete This period, related to our concept of a century, was called a calendar round To distinguish between different 52-year periods, another counting system was created, called the Long Count This count, which began for the Maya at the mythical date that corresponds to the year 3114 b.c.e of our dating system, was a way for the Mayan kings to record historical time The Aztec (ca 1200–1521), who spoke Nahuatl, developed a pictorial language, using a mixture of pictograms, ideograms, and phonetics Bark paper books from after European contact include sections on the 260-day ritual calendar, called the tonalpohualli, and the 365-day solar calendar, called the xihuitl Like the Mayan version, these calendars worked in conjunction with each other and were used for ritual divination; they were also similarly divided, including the 52-year cycle, which was called a xuihpohualli The Aztec picture books also include information on Aztec counting practices Like the Maya, the Aztec used a base-20 system Symbols were used to represent each number; for example, the flag symbol stood for the number 20, and a tree stood for the number 400 Like many indigenous groups, the meaning of certain numbers reveals their digital counting origin For example, the number 5, macuilli, probably derived from the word maitl, or “hand.” In the Andes no written form of language existed prior to European contact However, records were documented by the Inca (1438–1533), a civilization that dominated the entire South American continent, including present-day Ecuador, Bolivia, Peru, Chile, and parts of Argentina and Columbia Records were kept using a knotted textile device called a quipu, which recorded various kinds of information, such as tax or census data The quipu contained a main horizontal cord from which yarns of different colors were vertically Different-colored string as well as the type of knots, cord length, and position on the cord indicated different informa- tion Specialists created and read these instruments, and the development of the quipu reflects the importance of textiles in the Andean region Chronicles from after European contact indicate that a base-10 system of counting was used in the Andes The Quechuan (Incan) term for 10 was chunka Asia and the Pacific by Tom Streissguth The counting and numbering system of medieval China had its earliest origins in the writing of the Shang Dynasty of the second millennium b.c.e Historians have theorized that Shang numerals were phonetic, with the symbols for the numbers correlating to the shape of certain objects The Chinese juxtaposed figures to create larger numbers: For example, the symbol for 4,000 combines the symbol for and the symbol for 1,000 Shang numerals had given way to a more abstract system of horizontal and vertical lines by the time of the Han Dynasty, which lasted until the fourth century c.e The short lines of Han numerals derived from the use of counting boards for calculations and arithmetic The counting board had a series of columns, with places for counting rods made of contrasting materials or colors A blank space without a rod indicated zero There were arrangements of the rods for nine different values and a place-value system that changed the value of the symbols depending on their position in the matrix The far-right column represented single digits, for example, while the next left column represented multiples of 10, the next multiples of 100, and so on The famous Xiahou Yang suanjing (Mathematical Manual) of Xiahou Yang (ca 400–ca 470), written in the fifth century, explains the various methods of addition, subtraction, multiplication, and division on the counting board Mathematics was an essential part of China’s educational system, which prepared young men for service in the imperial government A standard textbook known as the Jiuzhang suanshu (Nine Chapters on the Mathematical Art), dating to the Han Dynasty, includes 246 word problems covering many different topics in arithmetic, trigonometry, and geometry as applied to real-world problems in engineering, finance, farming, and marketing The book provides solutions as well as detailed explanations for how the problems are solved The method inspired many able medieval mathematicians, including Ding Ju (fl 1355), He Pingzo, Wu Jing (fl 1450), and Liu Shilong (fl 1424), to write detailed commentaries on the Jiuzhang suanshu Historians believe that the concept of zero was introduced to China during the Tang Dynasty, which began in the early seventh century At this time Chinese merchants, pilgrims, and explorers were traveling to the Indian Subcon-
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