Mathematics |
Although the Egyptians lacked the symbol for zero, they calculated numbers based on the decimal and the repetitive (numbers based on the power of 10). The following signs were used to represent numbers in the decimal system:
1 | 10 | ||||
100 | 1000 | ||||
10,000 | 100,000 | ||||
1,000,000^{*} |
Numbers were usually written left to right, starting with the highest denominator. For example, in the number 2,525 the first number to appear on the left would be 2000, then 500, 20 and 5, as follows:
The Egyptians did not develop abstract mathematical formulas. They used the simple arithmetic of addition and subtraction. To multiply and divide, they referred to tables of duplication that gave the multiplier and the multiplicand. For example, to multiply 9 by 15, they would double and redouble the multiplier as follows:
multiplier | multiplicand | ||||
1 | x | 15 | = 15 | ||
2 | x | 15 | = 30 | ||
4 | x | 15 | = 60 | ||
8 | x | 15 | = 120 | ||
16 | x | 15 | = 240 |
Once a multiplier was reached that was equal to half or more of the desired multiplier, no further doubling was required. For example, to arrive at the correct answer for 9 x 15, they would refer to the table (8 x 15 = 120 plus 1 x 15 = 15) to arrive at 135 (120 + 15). Division was achieved by reversing this process.
The Egyptians knew about fractions and used special signs for two-thirds, three-quarters, four-fifths and five-sixths. They also had some basic knowledge of geometry, such as the fact that the area of a rectangle was equal to its length multiplied by its width, and they were able to calculate the area of a circle according to the length of its diameter.
When building the pyramids , the hypostyle hall at Karnak with its gigantic pillars and colossal statues, and the many temples and palaces throughout the land, architects and engineers used their knowledge of mathematics to design and develop the specifications. To calculate length, they used a cubit , which was the length of the forearm, from the elbow to the tip of the thumb (approximately 52.5 cm or 20.6 in.). A cubit was subdivided into seven "hands", each equalling 1/7 of a cubit.
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