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| rr100:
In fact I was too quick with the example above, this is the one that does something closer to the "fingerprinting" test (before I put only the first and last conversion): --- Code: ---> 180/Pi*arcsin(180/Pi*arccos(180/Pi*arctan(tan(Pi/180*(cos(Pi/180*(sin(9*Pi/180)))))))); 9 > %-9; 0 --- End code --- Of course the functions can be redefined to work in degrees directly but it's not worth it. Also some intermediary result (as in didn't type all conversions) from Maple: --- Code: ---> 180/Pi*arcsin(arccos(180/Pi*arctan(tan(Pi/180*(cos(Pi/180*(sin(9*Pi/180)))))))); Pi 180 arcsin(1/180 Pi sin(----)) 20 ------------------------------ Pi --- End code --- |
| ciccio:
--- Quote from: quarks on November 18, 2012, 09:01:10 pm ---That's interesting. Because I just worked with Excel2010 before I saw this. I tried it and was very surprised when ARCSIN(ARCCOS(ARCTAN(TAN(COS(SIN(9))))))=0,42477796076938 showed up. This seems to be the result with radians instead of degree angle. Does anyone know how to change this in excel. --- End quote --- I use EXCEL 2003, and for what I understand it works in radians, not in degrees. There is a function that converts radians in degrees (GRADI in my Italian Excel) and another one to convert degrees in radians (RADIANTI). I get lost with long formulas in Excel, so I prefer to put every single part of the formula in a separate cell. The following image is a screeenshot of the formula, showing the great accuracy of the result. Best regards |
| rr100:
Technically to do the same as the pocket calculators you'll need to convert each function in between to radian operation, not only first and last one (easy trap, I went for it as well, see above). Also it would be interesting to see what is I1-9 or even better (I1-9)*100000000 for example to see if anything hides behind 9.0000... Open question: anyone knows some "pocket calculator" where you can set higher precision for this kind of operations? And I mean larger than the usual 8-20 digits, maybe 50-100, or even much more. This isn't a really challenging task in itself assuming you have reasonable RAM (and by that I mean even 1-2MB would be plenty), probably the hard part is the user interface itself. And this can have (somehow) practical applications... for example: http://what-if.xkcd.com/20/ At some point the damn cat steps on the keyboard ... and we start with a speed of 0.9999999999999999999999951c (that is almost c, speed of light, max speed permitted in this universe). You just can't do 1-0.9999999999999999999999951^2 (for example) on any calculator I know of (or I don't know how). And you might need precisely this speed squared, it is something that comes up immediately in this context. Of course you can do it on paper "old style" like you transform your number in something like (1-49/10^25) and then you do by hand (1-49/10^25)^2. But sometimes you have stuff that doesn't play that nice or you just want to do the calculation and get the result without any tricks. So, is there any pocket calculator that can do 1-0.9999999999999999999999951^2 with some reasonable precision ? |
| IanB:
--- Quote from: rr100 on November 21, 2012, 10:21:05 pm ---So, is there any pocket calculator that can do 1-0.9999999999999999999999951^2 with some reasonable precision? --- End quote --- Fortunately you don't need a calculator for this. You can do this one in your head (well OK, you might need a pencil and the back of an envelope). First of all we need 0.9999999999999999999999951^2. A quick application of the binomial theorem tells us that the answer is 0.9999999999999999999999902 (we subtract 51 from 100 to give 49, double it to give 98, subtract that from 100 to give 02, and replace 51 with 02). Next we need to know 1 - 0.9999999999999999999999902. This is easily seen to be 0.0000000000000000000000098, or 9.8 x 10-24. And there's our answer. |
| rr100:
As I mentioned above the question isn't how to do (1-49/10^25)^2 by hand, that is clear. By the way from (a-b)=a^2-2ab+b^2 you ignored b^2 because b is very small (49/10^25 in our case) and b^2 is even smaller; this is fine (in fact this is THE way you do it on paper usually). However sometimes you just don't want to think how to expand a given expression, sometimes it isn't possible, etc. I don't want arbitrary/infinite precision, I don't want clever optimizations or a symbolical calculation engine that knows more tricks than most math students, I just want some calculator that uses more than the usual 8-12-16-20 digits for the "significant digits" in the float/scientific numbers. It's not that much a question of resources, the "standard" quad precision will give you roughly 34 digits while using 16 bytes (including for sign and signed exponent). It isn't that much and it wouldn't be even if have it 10x or 20x times larger. But problem is everything (I mean scientific calculators, including TI-89) don't do even half of that. |
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