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posted by Fnord666 on Wednesday August 14 2019, @11:59PM   Printer-friendly
from the that's-the-combination-to-my-luggage! dept.

https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/

Earlier this week, we received this question from a fan on Facebook who wondered how many decimals of the mathematical constant pi (π) NASA-JPL scientists and engineers use when making calculations:

Does JPL only use 3.14 for its pi calculations? Or do you use more decimals like say: 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360

We posed this question to the director and chief engineer for NASA's Dawn mission, Marc Rayman. Here's what he said:


Original Submission

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  • (Score: 2) by looorg on Thursday August 15 2019, @01:33PM (26 children)

    by looorg (578) on Thursday August 15 2019, @01:33PM (#880562)

    I'm more surprised why they even bother with that. Why would they even use an approximation? Sure it's probably "good enough" (as examplained in the examples) but they could just put it down as the ratio of the circumference over the diameter of the circle as is the standard definition or just put down pi -- after all they are not bothering doing these calculations by hand anyway and whatever maths software they use will insert something useful there instead. So who cares if it's the radius of the known universe or whatever.

    After all a lot of mathematics are not about calculating sad little decimal values, this is from my experience what a lot of students coming to university math fail at, but instead you just use fractions and in the case of PI it wouldn't even have to be typed out more then being PI something something as the answer.

    • (Score: 0) by Anonymous Coward on Thursday August 15 2019, @01:39PM (3 children)

      by Anonymous Coward on Thursday August 15 2019, @01:39PM (#880565)

      What I seem to remember hearing from a different source (not one I can reproduce) is that they simply use math.pi in whatever computing library they are using (typically c). You know, the same thing any of us would use because it is the easiest and most obvious thing.

      • (Score: 2) by zocalo on Thursday August 15 2019, @01:51PM (1 child)

        by zocalo (302) on Thursday August 15 2019, @01:51PM (#880568)
        Yeah, I've read something similar. IIRC they use a standard library, which in turn follows a standard for floating point numbers - IEEE754, perhaps? - which works out to fifteen or sixteen digits in decimal representation. Not sure if that is specific to JPL, or applies across the board at all NASA facilities though.
        --
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        • (Score: 0) by Anonymous Coward on Thursday August 15 2019, @02:16PM

          by Anonymous Coward on Thursday August 15 2019, @02:16PM (#880585)

          The IEEE754 binary64 representation has 53 bits (binary digits) of precision.

          Under the simple approximation that there are 3.3 bits per decimal digit then that is pretty much bang on at 16 decimal digits, which is exactly the number of digits quoted in TFA. However in the general case you actually need a few more digits than this if you want to be able to convert from binary to decimal and back again without losing any information.

          In reality they are probably not using decimal representations of pi at all, and indeed are using binary floating point to perform calculations.

      • (Score: 2) by KritonK on Thursday August 15 2019, @08:02PM

        by KritonK (465) on Thursday August 15 2019, @08:02PM (#880719)

        M_PI in Linux's has a few more digits than the number used by NASA. However, when I printed it, I got a different number, where only the digits used by NASA were the same as in M_PI.

        Java's Math.PI is exactly the same as NASA's pi.

        I guess 3.141592653589793 is the most accurate value of pi that can be represented by a double. Anything more will be ignored/truncated.

    • (Score: 5, Informative) by Immerman on Thursday August 15 2019, @02:12PM (20 children)

      by Immerman (3985) on Thursday August 15 2019, @02:12PM (#880582)

      A bunch of posts in the time it took me to calculate and type this, so here it is at the top:

      What I learned in college science and engineering classes is, just keep the number of significant digits the same.

      Your margin of error is determined by the number of significant digits in the least-precise piece of starting data, and it's pointless to include significantly more precise numbers elsewhere, whether it's pi, the speed of light, or any other constant.

      Example: I measure a circle as being 23.1cm across then the last digit is an estimate - if it's accurate that means the actual diameter is somewhere between 23.05cm and 23.15cm. In practice you'll typically estimate one more digit than your measuring tool offers gradations for, and the margin of error will be even larger (e.g. you made that measurement with a meter stick that doesn't have mm marks, and you just eyeballed it as being 10% of the way to the next cm mark).

      Then I calculate the circumference using many digits of pi as 72.5708cm
      But, given my margin of error, I know the actual circumference is somewhere between 72.414cm and 72.728cm

      My results should definitely not include more significant digits than my data - if I list a result of 72.571cm, and that's all you see, then you're going to assume that the .57 is accurate, and the .001 is estimated. But looking at the results calculated at the margins of error, we can see that even the .5 is an estimate.

      So what happens if we just used the same number of significant digits in pi as in the data? 23.1*3.14 = 72.5 - we arrive at the same result, and it's clear that the .5 is the estimated digit.

      Also, typically you don't want constants in your real world results. If I tell you to cut a beam 7pi cm long I'm just requiring you to do a calculation that invites mistakes. If you're working in math, where everything is theoretical and your numbers exact, that's different. But in science and engineering all your numbers are estimates, and you're going to do something definite with the results, so you want precise numerical results, but only slightly more precise than your actual margin of error.

      • (Score: 3, Insightful) by Runaway1956 on Thursday August 15 2019, @02:29PM (14 children)

        by Runaway1956 (2926) Subscriber Badge on Thursday August 15 2019, @02:29PM (#880592) Journal

        Yes, that exactly. In real life, you're building, or whatever, two or three digits after the decimal is all you're ever going to need. Real life, mind you. If you're measuring in inches, you're not going to use more than two decimals anyway. If you're measuring in feet, ditto, even if you're using an engineer's scale. Using more digits for Pi than you are using in your measuring scale is merely an attempt to prove how smart you is - and it's always a fail. The tooling shop only measures to thousandths of an inch, and when they calculate something, they use three decimals of Pi. Only in academia and rocket surgery are ten or more digits going to matter.

        • (Score: 2) by JNCF on Thursday August 15 2019, @02:43PM (11 children)

          by JNCF (4317) on Thursday August 15 2019, @02:43PM (#880596) Journal

          If you're measuring in inches, you're not going to use more than two decimals anyway.

          Standard rulers and measuring tapes have 1/8th inch marks, which are 0.125 inches in decimal. I have totally used more than two decimals when using inches for carpentry, plumbing, typesetting, and all sorts of other things.

          • (Score: 2) by Immerman on Thursday August 15 2019, @03:26PM (8 children)

            by Immerman (3985) on Thursday August 15 2019, @03:26PM (#880621)

            Yeah, that's one of the big problems with combining a fractional scale and decimal calculations - they really don't mesh well. You absolutely didn't measure anything to thousands of an inch accuracy, but you have to put that much accuracy in your calculation just to avoid losing data in the "unit conversion"

            Similar problem in computers actually - floating point numbers are fractional (binary) rather than decimal, and the conversion can't be done gracefully. One of the big reasons financial calculations are typically done in cents rather than dollars - $0.01 is an infinite repeating decimal in binary, and thus can't possibly be represented correctly. (Alternatively they may use binary coded decimals, but I don't think any modern CPU supports native BCD calculations, and a software implementation is terribly inefficient.)

            • (Score: 2) by Zinho on Thursday August 15 2019, @04:22PM (5 children)

              by Zinho (759) on Thursday August 15 2019, @04:22PM (#880636)

              (Alternatively they may use binary coded decimals, but I don't think any modern CPU supports native BCD calculations, and a software implementation is terribly inefficient.)

              The typical solution for this is to store the value as pennies [1] and represent it with an integer. Modern computers do integer calculations just fine. It's trivial to display the result in dollars with a decimal point in the right place. I think this trick has been used since the COBOL days, and what isn't broke doesn't get fixed.

              [1] if you're doing accounting for a gas station where the values stored look like $5.4321 the same trick still works, you just keep track of how many places to shift the decimal from your smallest value when displaying.

              --
              "Space Exploration is not endless circles in low earth orbit." -Buzz Aldrin
              • (Score: 0) by Anonymous Coward on Thursday August 15 2019, @09:53PM (2 children)

                by Anonymous Coward on Thursday August 15 2019, @09:53PM (#880742)

                You guys are both a bit off.
                For financial calculations, you use a language that supports decimal arithmetic.
                COBOL is one such language, and Java is another. (Java can do integer, floating point, and decimal arithmetic.)
                It wouldn't surprise me if LISP could do it too.
                Doing arithmetic in "pennies" is only accurate for sums and differences. In short, here's a nickel, kid: buy a real language!

                • (Score: 2) by Immerman on Friday August 16 2019, @01:56AM (1 child)

                  by Immerman (3985) on Friday August 16 2019, @01:56AM (#880821)

                  The language doesn't matter - the problem is that the CPU itself can't do decimal arithmetic. Full stop. (aside from BCD on some uncommon processors). If the language looks like it's doing decimal arithmetic, then it's playing inefficient software-based tricks behind the scenes. In the case of Java's BigDecimal, *dangerous* software tricks that can easily cause numerous problems that can truncate your results from either end (loss of most- or least- significant digit information) if used carelessly without fully understanding its weaknesses. I assume COBOL is more robust given its business pedigree, but don't know it well enough to comment.

                  • (Score: 0) by Anonymous Coward on Friday August 16 2019, @05:39PM

                    by Anonymous Coward on Friday August 16 2019, @05:39PM (#881194)

                    What are you going on about?
                    Java BigDecimal is a very well though out system.
                    The fact that the arithmetic is done "in software" versus "in the CPU" is of no consequence.
                    There is nothing about "in the CPU" that makes a system of arithmetic foolproof.
                    There are things you have to be aware of with IEEE floating point arithmetic as well so that you don't accidentally end up with bad accuracy in your results.

              • (Score: 2) by Immerman on Friday August 16 2019, @02:35AM (1 child)

                by Immerman (3985) on Friday August 16 2019, @02:35AM (#880843)

                As I said. It does have some serious weaknesses if you might care about fractions of a penny in some situations though.

                There is also the possibility of something resembling decimal floating-point numbers - aka integer + decimal exponent (e.g. ddddddd*10^x rather than the normal IEEE-754 binary floating-point format of 1.bbbbbbb*2^x) I don't know of any languages do that, but I'll freely admit that it's not a topic I'm well versed in. I assume there are at least as many caveats and gotchas to such a format as there are for binary floating points, and massively fewer people who care enough to sort them out.

                • (Score: 0) by Anonymous Coward on Friday August 16 2019, @05:42PM

                  by Anonymous Coward on Friday August 16 2019, @05:42PM (#881196)

                  If you read AC comments, you would have seen a discussion of decimal arithmetic supported in COBOL and Java.
                  Stay uninformed -- your choice.

            • (Score: 2) by sjames on Thursday August 15 2019, @08:56PM (1 child)

              by sjames (2882) on Thursday August 15 2019, @08:56PM (#880729) Journal

              Interestingly, computer based floating point meshes much better with the way common measures do fractional units. 1/8 is quite easy to represent in binary. If a calculator (or program) had a good way to input 8ths, it could be precisely represented in a way that wouldn't screw with significant digits.

              As several others have pointed out, in cases where the needed precision is known in advance, integer values are simply scaled, but that doesn't overcome the fact that 1/8 (or worse, 1/3) wouldn't be handled very neatly.

              Of course, non power of 2 fractions would still be an issue. Another option is to store and perform computations based on ratios.

              • (Score: 2) by Immerman on Friday August 16 2019, @02:06AM

                by Immerman (3985) on Friday August 16 2019, @02:06AM (#880827)

                Common measures? You mean the uncommon non-SI units used only by the 3rd, 26th, and 124th largest nations in the world? (okay, and several others in common parlance, but rarely for real work)

                But yes, ironically enough binary is better suited to power-of-two fractional measures than decimal ones. Ironically, because typically there's no way to input or read those values except as gratuitously long decimal values. I've used a few pieces of software that will actually accept a value like 3+7/8 in a numerical field, but they're so few and far between as to be really noteworthy.

          • (Score: 2) by Zinho on Thursday August 15 2019, @04:07PM

            by Zinho (759) on Thursday August 15 2019, @04:07PM (#880627)

            Unless you are using a decimal-marked inch scale (like the 1:10 side of an engineer's scale [wikipedia.org]) then you'll have a mismatch between the implied precision of the measurement you took and the exact decimal representation of that measurement.

            When you're using your tape measure and read to the 7/32 mark, your measurement's precision is +/- 1/64. The decimal representation of 7/32 (0.21875) appears to have a precision of +/- 0.00005 inch; in reality it's more like +/- 0.01 inch or +/- 0.02 inch (truncating or rounding 0.015625). This is the exact problem we have with decimal-to-binary number conversion, and there's not a practical solution.

            If you're keeping track of all 6 decimal places worth of those 1/64 inch measurements to avoid losing accuracy due to rounding after number conversion, feel free. Especially if you're getting high-quality results, don't think I'm trying to stop you. If, at the end of your calculations, you're shifting the result into a CNC machine for the final cut it's important for your mental health to realize that truncating or rounding at the 1/1000 inch place is all the precision you've gained for your effort, and the machine won't benefit from any extra digits.

            --
            "Space Exploration is not endless circles in low earth orbit." -Buzz Aldrin
          • (Score: 2) by janrinok on Thursday August 15 2019, @06:36PM

            by janrinok (52) Subscriber Badge on Thursday August 15 2019, @06:36PM (#880692) Journal

            The rulers we had in schools in the 1960s-1990s had 1/10th inch marks too. A 12" ruler had 6" of 1/8th graduations and 6" of 1/10th graduations. The other side was centimeters and millimeters.

        • (Score: 0) by Anonymous Coward on Thursday August 15 2019, @04:20PM

          by Anonymous Coward on Thursday August 15 2019, @04:20PM (#880634)

          Exactly - that's why I always trim off the USELESS extra digits to get a nice speed bump.

          double pi = round(M_PI*100)/100;

        • (Score: 0) by Anonymous Coward on Thursday August 15 2019, @05:20PM

          by Anonymous Coward on Thursday August 15 2019, @05:20PM (#880652)

          Yet another dramatic reproduction of the Dunning-Koeger Effect! Our confirmation rate must be close to 99.999, but that could be us just trying to show off how smart we is.

      • (Score: 2) by looorg on Thursday August 15 2019, @03:09PM (4 children)

        by looorg (578) on Thursday August 15 2019, @03:09PM (#880609)

        Sure it's fairly standard to just use the number of decimals in the answer as in the data given if one has to.

        That said if it's for building small things just change the scale down to mm and you don't, or shouldn't, have to bother with decimals. But sure for some hands-on buildings some sort of calculation to an actual number is helpful. That said a lot of machines used in construction and cutting can/could probably take a 7pi cm cut as a valid input these days; it's been a long time since I had to program anything for a CNC.

        • (Score: 2) by Immerman on Thursday August 15 2019, @03:17PM (3 children)

          by Immerman (3985) on Thursday August 15 2019, @03:17PM (#880616)

          Not the number of decimals - the number of significant digits.

          23.1 cm, 231mm, 0.231m 0.000231km or 231,000um all have 3 significant digits even though the number of decimals varies wildly

          Admittedly there's a little bit of assumption made with the 231,000um - we're assuming three significant digits as there's no accepted way to indicate whether any of the zeros are measured values rather than placeholders, but that doesn't actually come up in real-world situations very often.

          • (Score: 2) by Osamabobama on Thursday August 15 2019, @04:39PM (1 child)

            by Osamabobama (5842) on Thursday August 15 2019, @04:39PM (#880645)

            There's a good story [scienceabc.com] about precision of the initial measurement of Mount Everest. It was measured at exactly 29,000 feet (five significant digits), but Sir George Everest published the measurement at 29,002 to imply the actual precision, even though it was less accurate than reality.

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            Appended to the end of comments you post. Max: 120 chars.
            • (Score: 2) by Immerman on Friday August 16 2019, @02:45AM

              by Immerman (3985) on Friday August 16 2019, @02:45AM (#880845)

              Now you've got me wondering why he didn't use 29,001 feet instead, and half the error or the same result.

              I suppose measuring to a fraction of a foot in those days would be rough, leaving 29,000.0 as unacceptable.

              It does bear mentioning that I've seen a convention in many science and engineering books of representing such an "exact" integer with a trailing decimal point - e.g. as 29,000. - but it's far from ubiquitous. It also isn't generally flexible - it doesn't help you if your measuring method is accurate to 10 feet.

              Plus, as your link indicates, he was actually off by 29 feet, so clearly he was overestimating the precision of his measurement technology by 1.5 orders of magnitude.

          • (Score: 2) by FatPhil on Friday August 16 2019, @08:17AM

            by FatPhil (863) <pc-soylentNO@SPAMasdf.fi> on Friday August 16 2019, @08:17AM (#880949) Homepage
            Hard science will often use uncertainty indicators, the equivalent of an error bar. E.g. the Fine Structure Constant is 7.2973525693(11) * 10^-3 where the (11) means a possible uncertainty of 11 in the final digits, and therefore that the last three digits 963 might in reality range from 682 to 704. Astronomy in particular will sometimes give asymmetric uncertainty indicators, but that requires fancier typesetting.
            --
            Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
    • (Score: 2) by DeVilla on Saturday August 17 2019, @04:18PM

      by DeVilla (5354) on Saturday August 17 2019, @04:18PM (#881547)
      Now you have me wondering if the space bending effects of gravity or inflation have any affect on calculating the ratio of the circumference over the diameter at the 109 lightyear scale.
  • (Score: 4, Informative) by EvilSS on Thursday August 15 2019, @01:43PM (3 children)

    by EvilSS (1456) Subscriber Badge on Thursday August 15 2019, @01:43PM (#880566)

    For JPL's highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793.

    • (Score: 2) by tangomargarine on Thursday August 15 2019, @02:41PM (2 children)

      by tangomargarine (667) on Thursday August 15 2019, @02:41PM (#880593)

      I liked the part where I clicked through to the comments expecting there was a break in the summary, and instead the summary just ends on a colon /s

      What a twist!

      --
      "Is that really true?" "I just spent the last hour telling you to think for yourself! Didn't you hear anything I said?"
      • (Score: 2, Funny) by nitehawk214 on Thursday August 15 2019, @03:02PM

        by nitehawk214 (1304) on Thursday August 15 2019, @03:02PM (#880607)

        Apparently he said "Original Submission". I don't even see how that is an answer.

        --
        "Don't you ever miss the days when you used to be nostalgic?" -Loiosh
      • (Score: 2) by maxwell demon on Thursday August 15 2019, @03:12PM

        by maxwell demon (1608) on Thursday August 15 2019, @03:12PM (#880612) Journal

        The twist is that this is not a summary. If it were, it would have included that line. Or simply would say "16 significant digits".

        --
        The Tao of math: The numbers you can count are not the real numbers.
  • (Score: 3, Interesting) by All Your Lawn Are Belong To Us on Thursday August 15 2019, @01:50PM

    by All Your Lawn Are Belong To Us (6553) on Thursday August 15 2019, @01:50PM (#880567) Journal

    How Many Decimals of Pi Do We Really Need?

    None.... it's an irrational number.

    Oh, you meant how many decimals of Pi do we need if we're estimating it's value for calculations! Different question, and not nearly as sexy for a headline....

    </pedantic mode>

    Fox Mulder, "Nobody likes a math geek, Scully."

    --
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  • (Score: 2) by All Your Lawn Are Belong To Us on Thursday August 15 2019, @01:51PM

    by All Your Lawn Are Belong To Us (6553) on Thursday August 15 2019, @01:51PM (#880569) Journal

    .... cool story and nice catch!

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    This sig for rent.
  • (Score: 1, Interesting) by Anonymous Coward on Thursday August 15 2019, @01:52PM (3 children)

    by Anonymous Coward on Thursday August 15 2019, @01:52PM (#880570)

    What happened? Did a server fail, or did Google not like the story about them?

    • (Score: 2) by SomeGuy on Thursday August 15 2019, @02:00PM (1 child)

      by SomeGuy (5632) on Thursday August 15 2019, @02:00PM (#880573)

      Did a server fail, or did Google not like the story about them?

      Probably both. Piss of The Goog and things stat breaking mysteriously.

      Perhaps they accidentally instructed the server to calculate the last digit of Pi?

      • (Score: 0) by Anonymous Coward on Thursday August 15 2019, @10:51PM

        by Anonymous Coward on Thursday August 15 2019, @10:51PM (#880753)

        This is one of those times where the difference between of and off really matters.

    • (Score: 2) by takyon on Thursday August 15 2019, @02:00PM

      by takyon (881) <reversethis-{gro ... s} {ta} {noykat}> on Thursday August 15 2019, @02:00PM (#880574) Journal

      Update post should be live on the hour.

      --
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  • (Score: 5, Funny) by anotherblackhat on Thursday August 15 2019, @01:53PM (5 children)

    by anotherblackhat (4722) on Thursday August 15 2019, @01:53PM (#880571)

    640 digits of pi ought to be enough for anybody.

    • (Score: 0) by Anonymous Coward on Thursday August 15 2019, @02:03PM

      by Anonymous Coward on Thursday August 15 2019, @02:03PM (#880578)

      In what number base?

    • (Score: 3, Informative) by maxwell demon on Thursday August 15 2019, @03:13PM (3 children)

      by maxwell demon (1608) on Thursday August 15 2019, @03:13PM (#880613) Journal

      That's 640k digits.

      --
      The Tao of math: The numbers you can count are not the real numbers.
      • (Score: 2) by AthanasiusKircher on Friday August 16 2019, @12:15AM (2 children)

        by AthanasiusKircher (5291) on Friday August 16 2019, @12:15AM (#880786) Journal

        What the hell is a "k digit"? What is this, base 21?

        • (Score: 2) by Immerman on Friday August 16 2019, @02:09AM (1 child)

          by Immerman (3985) on Friday August 16 2019, @02:09AM (#880830)

          Dude, your mind is going to be blown the fist time you encounter km or kCal...

          SI prefixes - they're not just for SI units anymore.

          • (Score: 2) by FatPhil on Friday August 16 2019, @08:21AM

            by FatPhil (863) <pc-soylentNO@SPAMasdf.fi> on Friday August 16 2019, @08:21AM (#880953) Homepage
            And can cause chaos when applied to currencies! OK, $100M seems clear, but is $100G a thousand times larger or smaller?
            --
            Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
  • (Score: 2) by takyon on Thursday August 15 2019, @02:00PM

    by takyon (881) <reversethis-{gro ... s} {ta} {noykat}> on Thursday August 15 2019, @02:00PM (#880572) Journal

    I only use the exact value of the rational number known as π, which totally does terminate.

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  • (Score: 3, Informative) by Immerman on Thursday August 15 2019, @02:06PM (1 child)

    by Immerman (3985) on Thursday August 15 2019, @02:06PM (#880580)

    Your margin of error is determined by the number of significant digits in the least-precise piece of starting data, and it's pointless to include significantly more precise numbers elsewhere.

    Example: I measure a circle as being 23.1cm across then the last digit is an estimate - if it's accurate that means the actual diameter is somewhere between 23.05cm and 23.15cm. In practice you'll typically estimate one more digit than your measuring tool offers gradations for, and the margin of error will be even larger (e.g. you made that measurement with a meter stick that doesn't have mm marks, and you just eyeballed it as being 10% of the way to the next cm mark).

    Then I calculate the circumference using many digits of pi as 72.5708cm
    But, given my margin of error, I know the actual circumference is somewhere between 72.414cm and 72.728cm

    My results should definitely not include more significant digits than my data - if I list a result of 72.571cm, and that's all you see, then you're going to assume that the .57 is accurate, and the .001 is estimated. But looking at the results calculated at the margins of error, we can see that even the .5 is an estimate.

    So what happens if we just used the same number of significant digits in pi as in the data? 23.1*3.14 = 72.5 - we arrive at the same result, and it's clear that the .5 is the estimated digit.

  • (Score: 2) by DutchUncle on Thursday August 15 2019, @03:02PM (5 children)

    by DutchUncle (5370) on Thursday August 15 2019, @03:02PM (#880606)

    That one wrongly insisted on 3.2. I forget which state said that for tax computation purposes (22/7) (as found by Archimedes) was "close enough approximation for hand calculation."

    • (Score: 1) by nitehawk214 on Thursday August 15 2019, @03:11PM (4 children)

      by nitehawk214 (1304) on Thursday August 15 2019, @03:11PM (#880611)

      It probably is, though I am wondering how Pi could be useful in a tax calculation. Maybe a property line defined as a circle?

      --
      "Don't you ever miss the days when you used to be nostalgic?" -Loiosh
      • (Score: 4, Funny) by maxwell demon on Thursday August 15 2019, @03:18PM (2 children)

        by maxwell demon (1608) on Thursday August 15 2019, @03:18PM (#880617) Journal

        In tax calculations, you sometimes have to round. You know what is round? Circles. And what do you need in calculations involving circles? Pi. So that's why pi is useful in tax calculations. :-)

        --
        The Tao of math: The numbers you can count are not the real numbers.
        • (Score: 3, Touché) by nitehawk214 on Thursday August 15 2019, @05:28PM (1 child)

          by nitehawk214 (1304) on Thursday August 15 2019, @05:28PM (#880656)

          You have brought me around to your line of thinking.

          --
          "Don't you ever miss the days when you used to be nostalgic?" -Loiosh
      • (Score: 3, Touché) by All Your Lawn Are Belong To Us on Thursday August 15 2019, @06:58PM

        by All Your Lawn Are Belong To Us (6553) on Thursday August 15 2019, @06:58PM (#880703) Journal

        Don't give the government their piece of it and you will learn to your detriment exactly why it's useful to do so. :O

        --
        This sig for rent.
  • (Score: 0) by Anonymous Coward on Thursday August 15 2019, @03:14PM (1 child)

    by Anonymous Coward on Thursday August 15 2019, @03:14PM (#880614)

    sometimes if you know some geometry, you dont even need to know math ^_^

  • (Score: 2) by ElizabethGreene on Thursday August 15 2019, @04:19PM

    by ElizabethGreene (6748) Subscriber Badge on Thursday August 15 2019, @04:19PM (#880633) Journal

    On my Casio fx-9750GII pi has an internal 15 digit mantissa, but it's rounded to 10 digits for display.

  • (Score: 0) by Anonymous Coward on Thursday August 15 2019, @07:16PM (1 child)

    by Anonymous Coward on Thursday August 15 2019, @07:16PM (#880707)

    Thinking the number digits and 12billion miles and being off by your little finger on 2pi*r.

    Easy to visualize...

    wrap a "steel" band all the way the earth equator so it is a tight "belt". Now cut it and weld in another 6.2FT (or meters or miles your choice types). How high will that "belt" be above the ground all the wau around the world?

    1FT (or meters or miles your choice types).

    It does not matter the what the round obecjts is: Tin Can, or the Sun (maybe something better than steel then). the answer is always 1.

    Now how much lint is in you rbelly button?

    • (Score: 1) by sfm on Thursday August 15 2019, @08:39PM

      by sfm (675) on Thursday August 15 2019, @08:39PM (#880724)

      "wrap a 'steel' band all the way the earth equator so it is a tight 'belt. Now cut it and weld in another 6.2FT .
                    How high will that "belt" be above the ground all the way around the world?"

      Shouldn't that be 6.28 FT ??

  • (Score: 2) by DannyB on Thursday August 15 2019, @07:50PM (2 children)

    by DannyB (5839) Subscriber Badge on Thursday August 15 2019, @07:50PM (#880718) Journal

    Back in the 70's I heard it said that 8 digits is enough precision to get from here to Pluto within inches of accuracy. (Not that I worked it out for myself.)

    So I'm stumped for an application of PI that needs so many digits.

    Big Integers with thousands of digits or more, of course, are useful. You like SSL / TLS don't you?

    --
    People today are educated enough to repeat what they are taught but not to question what they are taught.
    • (Score: 0) by Anonymous Coward on Thursday August 15 2019, @11:30PM

      by Anonymous Coward on Thursday August 15 2019, @11:30PM (#880766)

      Claiming you have them is the only reason. Also how much power was used. but Bitcoin is winning on that front.

    • (Score: 2) by FatPhil on Friday August 16 2019, @08:29AM

      by FatPhil (863) <pc-soylentNO@SPAMasdf.fi> on Friday August 16 2019, @08:29AM (#880956) Homepage
      > Not that I worked it out for myself

      But you probably could. Assuming you know the earth is ~93 million miles or 150 million kilometers from the sun, then you know that 8 digits precision gives you mile precision at sun-earth distances. It therefore cannot give you inch (5 more digits) precision at sun-pluto distances (2 more digits).
      --
      Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
  • (Score: 1) by cyberthanasis on Friday August 16 2019, @07:04AM (1 child)

    by cyberthanasis (5212) on Friday August 16 2019, @07:04AM (#880931)

    15 (decimal) significant digits is the best precision you get from IEEE 1754 double precision floating point numbers, used by virtually all contemporary computers.
    To that, I would add one more digit, as the binary digits of the double precision value do not correspond to exactly 15 significant decimal digits. And this is exactly the approximation used by NASA.

    • (Score: 2) by DutchUncle on Friday August 16 2019, @12:52PM

      by DutchUncle (5370) on Friday August 16 2019, @12:52PM (#881025)

      IBM System 360 packed decimal instructions could operate on 32 bytes / 63 digits (plus sign). No decimal point, but back in the slide rule generation the idea of fixed-point / implied-point calculation was normal practice.

      Hmm. Multiplying 15 digit numbers gets you 30 digit numbers, so maybe the effective carry-through precision isn't much better.

  • (Score: 2) by Azuma Hazuki on Saturday August 17 2019, @12:02AM

    by Azuma Hazuki (5086) on Saturday August 17 2019, @12:02AM (#881354) Journal

    IIRC, the Planck length is 10e-61, so something like 60-65 digits ought to do it since, if I understand this right, it simply is not meaningful to speak of smaller distances. Not, of course, that we're capable of artificing at that scale, but this should be a reasonable hard limit for the universe as we know it.

    --
    I am "that girl" your mother warned you about...
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