Re: pi value - Long division no longer well-known anywhere?!

Gerry Myerson wrote:
In article <c017998a-6622-4c53-9255-a0a182679b52@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
aarklon@xxxxxxxxx wrote:

which is the more correct value of PI...????

a) 22/7

b) 355/113

c) 104348/33215

d) between 223/71 and 22/7

What kind of question is this?

Do you mean, which of these gives the most accurate approximation to pi?

If so, are you unable to find pi to, say, 10 decimals anywhere? Are you unable to compute 22 / 7, etc., to 10 decimals? Are you unable to look at a bunch of decimal expansions and work out which is closer to which?


See http://en.wikipedia.org/wiki/Long_division .

In the netherlands some fierce debates about "long division in elementary school class yes/no" have been going on now for several decades.

These debates go among math and arithmetic teachers, education theoreticians, professors in pure and applied mathematics. In short, all people who are more or less experts in education. The schoolchildren themselves are notoriously absent from these debates!

It seems to me that not only in the netherlands long division is no longer taught and learned, but also in many other countries. Too bad! The schoolchildren are left with an incomplete set of arithmetics operations. Why add =and= subtract, why multiply =and not= divide?

Why teach only guesswork and so-called strategies and not an algorithm that always yields arbitrarily precise and sometimes even exact results?!

Hint:
22/7 = 3.142857142857...... = 3 + 142857/999999; likewise for the other rationals, albeit with much longer decimal periods.

Hint for advanced students: consult theory and practice of continued fractions.

For Mrs/Mr Aarklon: Happy studies - Johan E. Mebius

.

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