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Re: Yet another 4-place Nat-Haversine Table project?
Date: 2018 Dec 8, 17:07 -0500
Tony

Roger's suggestion was the best (at least in my opinion, and yes, I do hold a degree in mathematics).

Place a superscript exponent before the number, indicating how many leading zeros.  Its crisp.  Its clear.  It preserves all of the significant digits!

Others, of course, are free to disagree

On Sat, Dec 8, 2018, 11:24 AM Tony Oz <NoReply_TonyOz@fer3.com wrote:

Hello!

I was thinking about the proposed - let's call it "scaling" - way to regain the resolution near the table's ends.

I'm not the Mathematician to talk authoritatively here. My fear is that even if performed correctly (everywhere - on the table-creator's and on the table-user's sides) it could do more harm in the middle of the table.

My reasoning: in the middle of the table (where there is more than three leading non-zeroes) the values are rounded. I use OpenOffice Calc (v4.1.5m1 build 9789 ref.1817495), which implements some well-recognised rounding method. I expect that the, say, multiplication of two numbers - one originally rounded in the 4th place, the other being re-scaled from  3rd place - the result will not be as good as one could expect. I'm not sure that after the multiplication result rounding all the noise would remain lower than the fifth place.

So, at the cost of clearly making better resolution near the zero-end of the table we risk loosing the resolution in the middle. The near-1-end is also at risk.

Not to say if the user makes a mistake in re-scaling the tabulated value.

As a reason "I do it because I can" - I'll try to create such table, but the overall merit of such an enhancement must be properly discussed by professional Mathematicians.

Regards,

Tony

60°N 30°E

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