From the article: "real examples and applications are messy, with ugly roots made of decimals or irrational numbers"
Maybe we should move to an all-calculator future, and just do everything with decimal numbers. We should stop trying to figure out that 1.41 is really sqrt(2) and there's a simplification, and instead we just plough ahead with typing the 1.41 into our calculator apps.
My high-school kid just finished off a math class. So many examples included a "and now simplify the fraction" step. As a person with an actual math degree, how about no? Real-world mathematics doesn't require simplifying fractions.
For example, I have a great book on sundials which includes tons of formulas for calculation where the sun will be on arbitrary days in arbitrary locations. And half of the exposition is all about when you can ignore part of the equations, or when to convert long constants (1.2345) into shorter ones (1.23).
Either you're only doing the calculations occasionally, in which reading about the approximations takes far more time than the calculation. Or you're doing a bunch, in which case you'll write a little program (or Excel function), and the approximations aren't useful.
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[ 3.3 ms ] story [ 17.0 ms ] threadMaybe we should move to an all-calculator future, and just do everything with decimal numbers. We should stop trying to figure out that 1.41 is really sqrt(2) and there's a simplification, and instead we just plough ahead with typing the 1.41 into our calculator apps.
My high-school kid just finished off a math class. So many examples included a "and now simplify the fraction" step. As a person with an actual math degree, how about no? Real-world mathematics doesn't require simplifying fractions.
For example, I have a great book on sundials which includes tons of formulas for calculation where the sun will be on arbitrary days in arbitrary locations. And half of the exposition is all about when you can ignore part of the equations, or when to convert long constants (1.2345) into shorter ones (1.23).
Either you're only doing the calculations occasionally, in which reading about the approximations takes far more time than the calculation. Or you're doing a bunch, in which case you'll write a little program (or Excel function), and the approximations aren't useful.