Measures, calendrics and mathematics Inca Empire

inca tunic



tokapu. textiles worn inca elite consisting of geometric figures enclosed rectangles or squares. there evidence designs ideographic language



quipu, 15th century. brooklyn museum

physical measures used inca based on human body parts. units included fingers, distance thumb forefinger, palms, cubits , wingspans. basic distance unit thatkiy or thatki, or 1 pace. next largest unit reported cobo topo or tupu, measuring 6,000 thatkiys, or 7.7 km (4.8 mi); careful study has shown range of 4.0 6.3 km (2.5 3.9 mi) likely. next wamani, composed of 30 topos (roughly 232 km or 144 mi). measure area, 25 50 wingspans used, reckoned in topos (roughly 3,280 km or 1,270 sq mi). seems distance interpreted 1 day s walk; distance between tambo way-stations varies in terms of distance, far less in terms of time walk distance.

inca calendars tied astronomy. inca astronomers understood equinoxes, solstices , zenith passages, along venus cycle. not, however, predict eclipses. inca calendar lunisolar, 2 calendars maintained in parallel, 1 solar , 1 lunar. 12 lunar months fall 11 days short of full 365-day solar year, in charge of calendar had adjust every winter solstice. each lunar month marked festivals , rituals. apparently, days of week not named , days not grouped weeks. similarly, months not grouped seasons. time during day not measured in hours or minutes, in terms of how far sun had travelled or in how long had taken perform task.

the sophistication of inca administration, calendrics , engineering required facility numbers. numerical information stored in knots of quipu strings, allowing compact storage of large numbers. these numbers stored in base-10 digits, same base used quechua language , in administrative , military units. these numbers, stored in quipu, calculated on yupanas, grids squares of positionally varying mathematical values, perhaps functioning abacus. calculation facilitated moving piles of tokens, seeds or pebbles between compartments of yupana. inca mathematics @ least allowed division of integers integers or fractions , multiplication of integers , fractions.

according mid-17th-century jesuit chronicler bernabé cobo, inca designated officials perform accounting-related tasks. these officials called quipo camayos. study of khipu sample va 42527 (museum für völkerkunde, berlin) revealed numbers arranged in calendrically significant patterns used agricultural purposes in farm account books kept khipukamayuq (accountant or warehouse keeper) facilitate closing of accounting books.