Egypt Vs Babylon - Egypt Vs Babylon Long lived, stable...

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Egypt Vs Babylon Long lived, stable civilizations Several waves of conquerors- lots of various empires Not attacked until centuries after Lots of math was ‘monolithic’= did not change Technology very consistent Engineers stayed the same because nomads needed the river to survive (needed to engineer the river for crops) Used egyptian knowledge, but used their own style for calculations Came up with the 24 hour day Fractions of the day in base 60 Not positional system -symbols are specific -but have to use lots of symbols Used a positional system!! -base 60 hieratics for papyrus (easier to draw) /hieroglyphics for clay hundreds of clay tablets  could show their work??? used a counting table (physical rods are in columns) no intermediate steps are seen multiplication is binary system/ repeated addition base 60 multiplication table 3x3 grid same! No zero -resistance against it, some laws made against it No place holder for a zero paper valuable- didn’t show work
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hundreds of clay tablets- same notation!! -written language stayed the same because nomads didn’t have written language multiplication: any # can be written as a sum of powers of 2 - no ‘proofs’ of the method -don’t know if they even cared if it was true -never did a general algorithm, just showed algorithms with specific examples Division- same as multiplication Only if answer was an integer Fractions- unit fractions (numerator = 1) No adding of ‘common denominator’ ‘look up’ from tables made it easy for ‘splitting up’ (eg bread) tables of reciprocals wrote them with real numerators   easily handle fractions with denominators of fractions of 60 Geometry Nile floods every year, so need to resurvey Essential to nile society Knew circumference, area of circle, but thought pi was 3 Pythagoras?? Right Angle- Don’t know if they knew what it was, but knew that 3^2 + 4^2= 5^2 Had tablets with Pythagorean triples Pi- approximate! 3.16049 Assumed Pi= 3 Knew linear problems (two variables!) Comfortable with Quadratic equations (+) roots only Used an algorithm Truncated Pyramids Don’t have the v= h/3 (a2 +ab + b2) equation, but their equations eventually equaled this Don’t know if they knew the ‘full pyramid’
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Because of their need for only a ‘year’s worth of stones’
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Egyptian Unit fractions Disadvantages -adding fractions is a big endeavor -no ‘common denominator’ adding -used a table to look it up, and just ‘place’ the answer down can’t see the process Advantages The table lookup- worked decent for them since they couldn’t show their work anyways- expensive papyrus Splitting up portions- if do our way, it ends up contributing to people thinking of inequity…. In their way, could just cut up 5 loaves in half, and then 1/10 each as well… so could SEE that they are all the same, instead of two ‘end’ loaves vs one whole loaf. The tables allowed for selecting different combinations of fractions to
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Egypt Vs Babylon - Egypt Vs Babylon Long lived, stable...

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