numbers and counting: The Americas 785 metical sense extended into artistic works as well as cultural and commercial practices The needs of commerce reflected an underlying culture of mathematics that remained a potent force The utilitarian demand of counting adopted by financial and commercial interests expanded the scope of mathematics It is significant that when the Portuguese arrived in western Africa in 1440, they were impressed by the dexterity shown by the Mandinga merchants, who traded in gold, on the upper reaches of Gambia The use of finely balanced scales inlaid with silver and suspended from cords of twisted silk managed to convey a sense of costs, weights, and proportions The gold dust and nuggets were weighed with brass weights The Africans’ expertise in measuring gold and in other forms of commerce was largely due to the fact that there were professionals within the group with a sense of numbers and counting Nevertheless, that potential was not restricted to trading alone Mathematical ideas were manifested in extraordinary and complex designs through decorative patterns In several African cultures weaving patterns in cloths, carpets, and other products have some kind of symmetrical arrangement This phenomenon suggests that different cultures in Africa arrived at different ways of projecting mathematical ideas African achievements of the medieval period in mathematical ideas and practices stand as positive contributions to man’s heritage of utilitarian creations The Americas by Penelope Ojeda de Huala A great diversity exists in the numbering systems developed in the New World A base-10 system of counting existed among the native groups in both North and South America, including the Algonquin, the Siouan, the Athapascan, the Iroquian, and the Salishan linguistic groups of North America and the Quechua-speaking groups of South America A base-20 system of counting existed amongst the Inuit, the Mesoamericans, and several tribal groups of California The base-10 system, the system used today, developed by using digits of both hands to count The base-20 system, or vigesimal system, employs both hands and feet to count Several number and counting systems were recorded in the period after European contact with North America The sophistication of these systems indicates that they were in use prior to contact Among the Zuñi of New Mexico a digitally based system, using the 10 digits of the hands, was used during the early colonial period For example, the Zuñi word for 10 is astemthla, which means “all of the fingers of the hand.” Similarly, among the Takelma of southwestern Oregon the number 10 is called ixdil, meaning “both hands.” Other native groups in North America also indicate that their words for numbers originate from digit counting For example, among the Omaha the number 7, penompa, means “finger two,” and the number 8, pethatbathi, means “finger three.” For the Inuit people, two hands represent the number 10, a single foot represents the number 15, and two feet represent the number 20 The number 20 also represents a person For example, among the Inuit of southwestern Alaska, the word for the number 20, yuenok, means “man completed.” In this way, two people would represent the number 40, three people the number 60, and so on Five people indicate the number 100, and the term for 100 means “bundle.” This designation probably originates from the fact that animal skins were often bundled in groups of 100 Numbers in between show that the digits of the hands were used for counting For example, among the Inuit of Hudson Bay, the word for the number is kittukleemot, or “middle finger,” and the word for the number 10 is eerkitkoka, or “little finger.” The act of counting is demonstrated even further among the Inuit in Greenland, whose word for the number 9, mikkelerak, means the “fourth finger.” The presence of larger units, such as words for the number 1,000, have been recorded among various tribes, including the Delaware, the Choctaw, the Kwakiutl, the Biloxi, the Wiyot, the Fox, the Dakota, the Cherokee, the Ojibwa, the Osage, the Winnebago, the Wyandot, the Micmac, and the Apache Many tribes seem to include numbers over 1,000 in their counting systems In Mesoamerica a vigesimal system was employed, based on the 20 digits found on a human being, using both hands and feet This system was employed by the Maya (ca 1000 b.c.e.–1521 c.e.), a civilization that dominated parts of Guatemala, southern Mexico, Belize, and Honduras During the Classical Period the erection of stelae, or upright stone slabs, was fundamentally linked to the Mayan concept of time, as stelae were often built to celebrate the passage of a ritually significant period For example, stelae were erected to commemorate k’atuns, or 20-year cycles, the fundamental unit of measuring time These events were set into stone and indicate the importance of time keeping in Mesoamerica For example, a 20-day period was called a uinal Several words exist for the number 20, including kal, may, and uinic Uinic also means “man” or “human being” and refers to the total number of digits on a human being The Maya developed a counting system based on bars and dots A dot indicates a unit of one, and a bar a unit of five The Maya invented the concept of zero, which was represented by a Maltese cross or a shell The Maya developed a capacity to count exponentially, and their monuments record large numbers They were particularly obsessed with recording time, both historic and cosmic events, and were the only