May 442 Blog

In this reading we see that the Babylonians are using concrete words to substitute variables we have today. For a mathematical principle, one would have to use those words (such as ush for x, square for x^2)  to represent the varaibles.  “=” sign would be “Result” and any square root sign would be replaced by the word “square root”. An simple modern equation would be substituted by multiple steps described with words. I believe that math is all about generalization and abstraction. without these, math would not be able to represent / solve real life problems. We take these problems and transform them into the “math” form and solve them(using mathematical rules) , then we take it back to the real world. Without generalization and  abstraction, we could not do this.  For more abstract areas, such as number theory, geometries, calculus, graph theory, etc., it would be hard not to use algebra. If we don’t have algebra, number theory could hardly be represented, let a...

3     15 6     7, 30 8     5 ,37,30 12   3 ,45 16   2,48,45

  Speculative phase:   (1) Think for yourself why 60 might be a convenient, significant or especially useful number to use as the base for a number notational system. What is special about the number 60? How is it different from 10?   60 is much bigger than 10, but maybe it is easier for the Babylonians when dividing/using fractions. 60 is divisible by 2,3,5,6,10,12... It contains many factors. Hence, base 60 might be easier to use than base 10 in ancient times when calculations are not as convenient as nowadays.   (2) Then think for yourself how we still use 60s in our own daily lives, in Canada, and across cultures if you have knowledge of other systems (like the Chinese zodiac and time-telling system, for example.) Why is 60 significant in so many situations involving time and/or space?   In China, one day is separated into 12 sections. One year is separated into 12 months. 60 is a multiple of 12. In western cultures, one day is separated into...

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