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.

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.

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.

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.

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.