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The Egyptians were interested in practical applications of mathemat- ics, not theories. They were very good at manipulating numbers, and  used their skill to solve real world problems faced on the job by engi- neers, tax collectors, construction supervisors, and military officers.  The major surviving Egyptian mathematical document, the Rhind  Papyrus, is a collection of mathematical problems with solutions. The Egyptians multiplied by repeated addition, and divided by  repeated subtraction.

Egyptian Mathematics

Ancient Egyptian Math

In other words, they calculated 2 times 3 by adding 2 plus 2 plus 2. The calculated 9 divided by 3 by seeing how many  times they could subtract 9 minus 3. They used fractions, but only with  a one in the numerator, such as ½, ⅓, and ¼. They did not know about  the concept of zero. They used a hieroglyphic decimal system. Units were represented  by vertical strokes arranged in rows. A spiral represented 100, 200  was two spirals, 10,000 was a finger, 100,000 was a tadpole. A god  with upraised arms meant 1 million—or “I can count no further.” Accounting, bookkeeping, land measurement, and setting the  boundaries of land (called surveying) were very advanced.

Accountant-scribes knew how to determine accurate property boundaries and  calculate crop yields based on land area. They could estimate labor and  materials needed for construction projects. They could also figure out  how much food and other goods a particular district would use, based  on its population. They were skilled at drawing plans. For designing complexes of  buildings, they used a primitive theodolite, a surveying instrument that  measures angles. They used practical mathematics to figure out the  best ways to transport and put up huge blocks of stone, massive obe- lisks, and giant statues.

Ancient Egyptian Math

The Egyptians invented the 365-day calendar.  they actually used three calendars: a lunar  (based on the cycles of the moon) agricultural  calendar tied to the seasons, a civil calendar  based on the 365-day year, and a lunar reli- gious calendar based on the moon but tied to  the civil calendar. the agricultural year had three seasons of  four months each. the seasons were akhet  (inundation), peret (sprouting, growth), and  shemu (warm season, harvest, and possi- bly the source of the word “summer”). new  year’s day, the first day of akhet, occurred  each summer when the star Sopdet (Sirius)  rose precisely at sunrise. the civil year had 360 days, divided into  12 months of 30 days each.

Each month had  three 10-day weeks called decades. to make 365, five days were added, celebrated as the  birthdays of five gods. misalignments between the calendars  made keeping track of religious festivals  (often tied to phases of the moon) difficult, so  the Egyptians also invented a lunar religious  calendar. the inconsistencies among their calen- dars did not trouble the Egyptians. their  great insight into calendar making was that  any calendar is artificial, so it might as well be  simple, practical, and useful. multiple calen- dars worked fine for them for 3,000 years. the calendar we use today traces its roots  to the Egyptian civil calendar. When Julius  caesar needed a simple, accurate calendar  for the roman Empire, that is the one he  chose.