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11 Cards in this Set
- Front
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describe the Egyptian hieroglyphic writing system and its usage
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read left to right, base 10, symbols only for powers of 10 (ie, if 10 = b, 1 = a, 23 is written aaabb), used for monuments, contained a character for 0 (as in the 0th floor). Dates to 3000 BCE.
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describe the Egyptian hieratic writing system and its usage
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read left to right, base 10, a ciphered system with symbols for 1,...9, used in everyday situations, 0 is not a number in this system. Dates to 3000 BCE
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where did historians learn about the Egyptians' knowledge of math?
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From the Rhind papyrus and Moscow Papyrus, both inscribed around 1850 BCE
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In the Egyptian number system, how were fractions represented?
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Unit fractions such as 1/3 were represented as <span style="text-decoration: overline">3</span>, and fractions such as 2/3 were represented by a 3 with two bars on top (html skillz fail here).
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In the Egyptian system, how would they multiply 18*12?
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They do all their multiplication by picking one number and applying repeated doubling.
1...12 2...24 4...48 8...96 16...192 As 18 = 2 + 16 we get 16*18 = 16(2+16), so looking at our table, 18 = 24+192 = 216, which is correct |
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How did the Egyptians do division? For instance, 18/12
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They would represent 18/12 as 18*1/12, and then begin doubling as required.
1...1/12 2...1/6 4...1/3 8...2/3 (or 1/2+1/6) 16...4/3 (or 1 and 1/3, a doubling of the above simplification of 2/3) Thus, 18 = (2+16) so 1/12*18 = 1/12(2+16) =1/6+4/3 = 9/6 = 1.5 as rqd. |
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name the two ways Egyptians solved algebraic equations
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they solved them using 1. modern day algebraic procedures and 2. false position
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how would you use false position to solve x + 1/4x = 15.
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As done in class, false position uses an intentionally bad guess to get rid of fractions. Then, they scale up the incorrect answer to get the solution. Example:
x + 1/4x = 15, guess 4. 4 + 1 = 5 ≠ 15 However, 5*3 = 15, thus for x=4*3 = 12, x + 1/4x = 5*3 = 15, giving us the solution x = 12. This method shows that the Egyptians understood order of operations. |
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what is the Egyptian formula for area of a circle based on the diameter? what does this tell us about their approximation for pi?
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The Egyptian area formula is (8/9*d)^2.
Area of a circle is pi*r^2 = 1/4*pi*d^2. The Egyptian formula (8/9d)^2 = 64/81d^2 = 1/4*256/81*d^2. Thus, the Egyptian approximation for pi works out to 256/81 ≈ 3.16. Historians believe this formula arises from computing the area of an octagon inscribed in a square. |
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describe the Babylonian numbering system
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base 60 system, uses place value, left to right, used multiplication tables extensively.
Example: 29,703 written as 3+15*60+8*60^2. Babylonians would write 29703 as 3,15,08. The fraction 3/4 = 45/60 is written (0;45). |
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What did Babylonians know about triangles?
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Babylonians knew the Pythagorean theorem, and have tables of Pythagorean triples.
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