... But using points, Draw will "snap" to N.99, N.92, N.87, etc. ...
Draw's general options will not permit setting tab stops below 0.20 inches (or its equivalent in other units). Anybody know why?
acknak wrote:...Draw works internally with metric units, and sometimes imposes precision limits on displayed values...
Edit: I was wrong on this. Calc just rounds to 13 places. See below. |
acknak wrote:If you're working on a small sized project in non-metric units, Draw may not be adequate for work at actual size. You might consider managing the working scale manually (say 1 cm = 1 pt) and then scale the final output down to actual size.
John_Ha wrote:I set Horizontal and Vertical to 5 points; and Subdivision to 1 point. I set Snap range ..., to 1 pixel. It always snaps to the 5 point grid, not to the 1 point subdivision.
John_Ha wrote:If I then set Horizontal and Vertical to 1 points; and Subdivision to 1 point, it snaps to 1 point...
John_Ha wrote:One point = 1/72" = 0.3527777 ... (recurring to infinity) mm so there is no exact correspondence - 1/72 is an irrational number.
It's my understanding that Calc uses IEEE-754 double precision for numbers though I don't know of any official documentation which says it does. If so and your point is that 1/72 (or 25.4/72) cannot be represented exactly by Calc, you are correct. However:John_Ha wrote:One point = 1/72" = 0.3527777 ... (recurring to infinity) mm so there is no exact correspondence - 1/72 is an irrational number.
For most purposes think of Calc as doing calculations to 15 significant digits. Significant digits include those to the left of the decimal place. 28.3464566929134 is 15 significant digits. A larger number like 283464566929.134 can only display three decimal places but it still has 15 significant digits.peterpqa wrote:28.34645669291340000000 using AOO Calc
It looks like Calc will let you add up to 20 decimal places in a cell's number format, but it rounds at the 13th place and shows 7 zeros.
It's not irrational since 72/2.54 is, of course, the ratio of integers 7200 and 254. All rational numbers either repeat or terminate, as was explained in the second sentence of the terminating decimal link I provided. In this case, the repeated digits are of length 42:peterpqa wrote:And I wonder if 72/2.54 eventually terminates, becomes repeating, or is irrational.
28.346456692913385826771653543307086614173228
346456692913385826771653543307086614173228
346456692913385826771653543307086614173228
346456692913385826771653543307086614173228…
NASA doesn't need 13-digit accuracy. The quantities they work with are not known that precisely. For example, the mass of the ascent stage of Apollo's command module was about 4.7×10³ kg. One part in 10¹³ is therefore 4.7×10⁻¹⁰ kg, the mass of a very fine grain of sand. If an astronaut loses an eyelash getting into the capsule it changes the mass in the 11th significant digit. Bird poop while on the launch pad would change it even more. NASA might want 7 digit accuracy but not 13. Keep in mind that much of the basic work for Apollo was done by people using slide rules.peterpqa wrote:I hope NASA doesn't use either one
Edit: Actually, the Newtonian Gravitational Constant (G in the formula F=G×m₁×m₂÷r²) is only known to six significant digits. |
If you're really interested a web search would quickly locate that answer.peterpqa wrote:I wonder what Excel's decimal limit is.
MrProgrammer wrote:Keep in mind that much of the basic work for Apollo was done by people using slide rules.
MrProgrammer wrote:If you're really interested a web search would quickly locate that answer.
Nope.peterpqa wrote:Glad you satisfied my curiosity. I take it you used something other than AOO Calc or macOS Calculator to figure out the 42-digit repetition of 72/2.54. It looks like the ratio of two integers can be an irrational number, just not in this case.
...
Edit: A rational number can be fully expressed in a positional system (such as binary or decimal) if all prime factors in the denominator of the reduced fraction are also prime factors in the base of the positional system. Otherwise, you get a repeating sequence of digits ("decimals"). Binary has base 2, so 1/2 is written as 0.1 and 3/8 as 0.011 ; 1/5 has no exact binary representation, but goes 0.00110011001100.... Decimal has base 2x5=10, so you can write all proper fractions given above in a compact fashion. 0.5, 0.375 and 0.2, respectively. 72ths make some non-representable fractions for both decimal and binary. This may be relevant to the snap issue, or not, depending on what degree of precision you require. Still doesn't help much... |
MrProgrammer wrote:• 1/72 not irrational. It's the ratio of the integers 1 and 72. I suspect you mean that 1/72 is not a terminating decimal.
peterpqa wrote:When I type the macOS Calculator result (16 places) into AOO Calc, Calc rounds it to 13 places ... I hope NASA doesn't use either one...
keme wrote:Definition of rational number: number which can be precisely expressed as a ratio of integers. (Aka. a "simple fraction").
Nope. For all integers X and Y with nonzero Y, tha ratio X/Y is rational (by definition). The rational numbers are exactly those which are the ratio of two integers. It will be a terminating or repeating decimal; I mentioned that earlier. A "non-terminating, non-repeating, infinite decimal sequence" for X/Y is impossible. This is explained in the link I provided which you apparently have not read or not understood. That's OK but I will not reply further to your posts. Goodbye.peterpqa wrote:So if integer X divided by integer Y is a non-terminating, non-repeating, infinite decimal sequence, the ratio X/Y is rational but the result is irrational.
Wikipedia wrote:Among irrational numbers are the ratio π of a circle's circumference to its diameter, Euler's number e, the golden ratio φ, and the square root of two;[1][2][3] in fact all square roots of natural numbers, other than of perfect squares, are irrational.
It can be shown that irrational numbers, when expressed in a positional numeral system (e.g. as decimal numbers, or with any other natural basis), do not terminate, nor do they repeat, i.e., do not contain a subsequence of digits, the repetition of which makes up the tail of the representation. For example, the decimal representation of the number π starts with 3.14159265358979, but no finite number of digits can represent π exactly, nor does it repeat.
peterpqa wrote:1,539,380,400,259 / 490,000,000,000 sure looks like pi to me. I would appreciate it if somebody smarter than me could tell me if I'm right, or why I'm wrong.
Being an irrational number, π cannot be expressed exactly as a fraction (equivalently, its decimal representation never ends and never settles into a permanent repeating pattern). Still, fractions such as 22/7 and other rational numbers are commonly used to approximate π.
peterpqa wrote:You are telling me that 1,539,380,400,259 / 490,000,000,000 does not equal pi just because everybody says it can't.
3.
1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679
8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196
4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273
7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094
3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 830119491
John_Ha wrote:You will just have to accept that there are people with much more knowledge than you who do understand [proofs that pi is irrational].
Edit: There is also a mathematical "proof" that 0.99999... is equal to 1, which it is not. |
peterpqa wrote:
Edit: There is also a mathematical "proof" that 0.99999... is equal to 1, which it is not.
John_Ha wrote:Line 1. 1/9 = 0.1111111 ..., where the digits go to infinity. Agreed?
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