Tuesday, 13 March 2012

Simon Stevin's Non-fraction method of Decimals


I mentioned the name of Simon Stevin in relation to decimal fractions the other day and the response I got led me to believe he had never heard of him. I didn't ask, so maybe I was wrong, but it made me think I wanted to post this older blog just to bring his name to some new teachers out there who may not yet have heard of this amazing guy:
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A while back, John Cook at the Endeavour Blog  posted about a comment by Keith Kendig in his book, Conics.

It happened when I started learning about decimals in school. I knew then that ten has one zero, a hundred has two, a thousand three, and so on. And then this teacher starts saying that tenth doesn’t have any zero, a hundredth has only one, a thousandth has only two, and so on. … Only much later did I have enough perspective to put my finger on the problem: The decimal point is always misplaced!


John demonstrates the proposed solution as well. 

The proposed solution is to put the decimal point above the units position rather than after it. Then the notation would be symmetric. For example, 1000 and 1/1000 would look like this:
Of course decimal notation isn’t likely to change, but the author makes an interesting point.


I then commented on John's blog that, in fact, Simon Stevin, who probably is more responsible than anyone else for introducing decimal numbers into the west had used a very similar approach as the one suggested by Keith Kendig. The image below is from De Thiende, which translated into English appeared as Decimal arithmetic. In fact, Stevin didn't think of his method as using fractions at all. In fact the English Translation in the full, self-advertising manner of books of the period, was Decimal arithmetic: Teaching how to perform all computations whatsoever by whole numbers without fractions, by the four principles of common arithmetic: namely, addition, subtraction, multiplication, and division. (My emphasis)

So, as I mentioned at John's blog, "He seems to have viewed the values as integers, much as we now think of minutes and seconds as integers. Few people consciously think of 3 minutes as 3/60 of an hour in regular computations. This was the view that Stevin took. He did not even use fraction names for the place values, but referred to them as prime, second, third, etc. (It has been often suggested that the use of ', ", etc for the minute and second in time, 12 23' 13", date back to the Greeks measure for angles of arc, but Cajori finds no evidence of their use prior to the 16th Century. The names minute and second came from the Latin for "minor part" which gave us minute, and the "second minor part" which gives us seconds.)
The notation, inspite of the objections of folks like Mr. Kendig, didn't seem very useful, and so in 1612 Bartholomaeus Pitiscus opted for the decimal point we use today, and when it was used by John Napier, well here we are.

Now if all he had done was introduce a really nice book on decimal fractions, you could give him a pat on the back and a big
"ataboy" and send him on his way, but:
He was big on hydrostatics, handy if you are Dutch, and in fact he made many improvements in the Dutch windmill pumping system. He also figured out that water pressure depended on height, and not on the shape of the container, and he was the first to explain the tides as the effect of the moon.
And for a walk on the wild side, he invented those land yachts you see racing up and down beaches. The one he made for the Prince of Orange was said to outrun the horses (with 26 passengers!).
he was one of the first to write about the equal temperament musical scale related to the twelfth root of two, which he seems to have gotten from Galileo's father.
And in math, he was the first in the west to write about a general solution to the quadratic equation; which alone should make him a name known to high school students and teachers.

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