Precise snap - yes for inches & centimeters, not for points

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Precise snap - yes for inches & centimeters, not for points

Postby peterpqa » Thu Aug 03, 2017 2:42 am

I'm using AOO 4.1.3 on macOS Sierra 10.12.5. In Draw, using points as the unit of measure, with "snap to grid" turned on, Draw will not snap to precise "N.00 points" for drawing object positions or dimensions. Using inches or centimeters, Draw will snap to precisely N.00. But using points, Draw will "snap" to N.99, N.92, N.87, etc. Am I missing a secret decoder ring setting, or is this an AOO bug?

Another grid question: Draw's general options will not permit setting tab stops below 0.20 inches (or its equivalent in other units). Anybody know why?

Thanks.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby acknak » Thu Aug 03, 2017 9:25 am

... But using points, Draw will "snap" to N.99, N.92, N.87, etc. ...

I suspect it's a limitation of Draw's unit conversion/management. Because Draw works internally with metric units, and sometimes imposes precision limits on displayed values, there are lots of places where working in non-metric units leads to such results, and smaller measurement units lead to more problems.

Draw's general options will not permit setting tab stops below 0.20 inches (or its equivalent in other units). Anybody know why?

Sorry, no idea. Doesn't seem like a critical limitation; is it?

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.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby John_Ha » Thu Aug 03, 2017 1:48 pm

Tools > Options > OODRaw > Grid ...

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.

If I then set Horizontal and Vertical to 1 points; and Subdivision to 1 point, it snaps to 1 point - ie there are 36 snap positions I can choose between 1 and 36.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby peterpqa » Thu Aug 03, 2017 7:59 pm

acknak wrote:...Draw works internally with metric units, and sometimes imposes precision limits on displayed values...

Points per centimeter does completely resolve, albeit at 13 decimal places.
 Edit: I was wrong on this. Calc just rounds to 13 places. See below. 
So it's not like pi. I guess AOO doesn't care about being truly precise. I like using points as a unit of measure in Draw because font sizes are always in points.

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.

My projects aren't that small. And I hate mickey-mouse workarounds like that. But thanks for the suggestion. I can live with points snap being off by 0.15 or more. But I have to take extra time looking at positions and dimensions to confirm that they're close enough to what I want. It's irritating.
Last edited by peterpqa on Fri Aug 04, 2017 12:14 am, edited 1 time in total.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby John_Ha » Thu Aug 03, 2017 8:18 pm

One point = 1/72" = 0.3527777 ... (recurring to infinity) mm so there is no exact correspondence - 1/72 is an irrational number.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby peterpqa » Thu Aug 03, 2017 10:13 pm

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.

Subdivision is snap intervals ("spaces") between snap resolution units. If resolution is 1 inch and subdivision is 16 spaces, Draw snaps to every 1/16 inch, 8 spaces snaps to every 1/8 inch, and 1 space snaps to every whole inch. I don't think snap range is relevant here.

John_Ha wrote:If I then set Horizontal and Vertical to 1 points; and Subdivision to 1 point, it snaps to 1 point...

I'll bet it snaps to about 1 point. When I draw an 18 x 24 rectangle at X = 6 and Y = 12, my status bar says it's position is X = 5.95 and Y = 11.91, and its dimensions are 17.86 x 23.81. Draw's snap is precise to "N.00" with metric units and inches, but not with points.

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.

1/72 = 0.013(8), which is inches per point. 0.352(7) is mm per point. Both irrational, but if AOO used more decimal places for its internal conversions, Draw would snap so close to precise points that it would display "N.00" for object positions and sizes.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby MrProgrammer » Thu Aug 03, 2017 10:31 pm

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:
• 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.
• "Terminating decimal" is a necessary requirement for a number to be exactly representable in Calc.
• "Terminating decimal" is not a sufficient requirement for a number to be exactly representable in Calc since 0.1 is a counterexample.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby peterpqa » Fri Aug 04, 2017 12:00 am

Thanks, MrProgrammer. I guess precision is a relative thing, even in software. For instance, when computing points per centimeter (72/2.54), it "equals"

    28.34645669291340000000 using AOO Calc (out to its maximum 20 decimal place cell number format), but it is
    28.3464566929133858 using macOS Calculator.
When I type the macOS Calculator result (16 places) into AOO Calc, Calc rounds it to 13 places. 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. I tried entering a 30-decimal number into macOS Calculator, but its limit appears to be 16 places. I hope NASA doesn't use either one... I wonder what Excel's decimal limit is.

And I wonder if 72/2.54 eventually terminates, becomes repeating, or is irrational.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby MrProgrammer » Fri Aug 04, 2017 1:49 am

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.
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:And I wonder if 72/2.54 eventually terminates, becomes repeating, or is irrational.
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:
28.346456692913385826771653543307086614173228
346456692913385826771653543307086614173228
346456692913385826771653543307086614173228
346456692913385826771653543307086614173228…

peterpqa wrote:I hope NASA doesn't use either one
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.
 Edit: Actually, the Newtonian Gravitational Constant (G in the formula F=G×m₁×m₂÷r²) is only known to six significant digits. 

peterpqa wrote:I wonder what Excel's decimal limit is.
If you're really interested a web search would quickly locate that answer.
Last edited by MrProgrammer on Fri Aug 04, 2017 4:50 am, edited 1 time in total.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby peterpqa » Fri Aug 04, 2017 4:30 am

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.

MrProgrammer wrote:Keep in mind that much of the basic work for Apollo was done by people using slide rules.

I've got a circular sliderule, shirt-pocket size, from when I was a kid. And one of my uncles was a NASA scientist from the 1950s to the 2000s. This thread has strayed rather far from AOO Draw snaps using point units, but I appreciate the mathematical enlightenment.

MrProgrammer wrote:If you're really interested a web search would quickly locate that answer.

I'm not really interested. Microsoft is the anti-Christ. That's why I use Macs and AOO.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby keme » Fri Aug 04, 2017 8:58 am

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.
...
Nope.

Definition of rational number: number which can be precisely expressed as a ratio of integers. (Aka. a "simple fraction").

 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... 
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby John_Ha » Fri Aug 04, 2017 2:04 pm

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.

Oops :oops: You are, of course, absolutely correct. I was mixing up the meanings but you have interpreted what I was trying to say correctly.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby John_Ha » Fri Aug 04, 2017 2:16 pm

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...

The moon is about 384,000km from earth. An error in the 13th place corresponds to about 0.04mm.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby peterpqa » Fri Aug 04, 2017 6:28 pm

keme wrote:Definition of rational number: number which can be precisely expressed as a ratio of integers. (Aka. a "simple fraction").

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.

As for the snap issue, AOO just needs to add more decimal places to its cm-points conversion factor, or use a ratio instead of a fixed number. I presume that would be a feature request.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby MrProgrammer » Fri Aug 04, 2017 10:30 pm

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.
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.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby peterpqa » Fri Aug 04, 2017 10:54 pm

I did read it. I'm not a mathematician, but I have been trying to improve my understanding.

Doesn't 1,539,380,400,259 (no decimal places) / 490,000,000,000 (no decimal places) = pi? And isn't pi an irrational number (per the link you sent)?

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.

If this is a revelation in mathematics, that the ratio of two integers can be an irrational number, I want credit for it. :D
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby RoryOF » Fri Aug 04, 2017 11:08 pm

The ratio you quote gives Pi for most reasonable purposes (in fact Pi=3.1416 is adequate for most day to day purposes); but Pi being irrational it goes on for ever and doesn't stop. Whether the figures further down the tail are of use is another matter and depends on the case under discussion.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby peterpqa » Fri Aug 04, 2017 11:42 pm

Thanks, RoryOF. But my point was not about computing pi, or the usefulness of "figures further down the tail." It was to show that the ratio of two integers can indeed be an irrational number - in this case, pi. MrProgrammer said this is not possible.

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.

By the way, I entered my original "snap to points" problem in Bugzilla. The input from earlier in this topic helped me refine it quite a lot. Thanks to all.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby John_Ha » Sat Aug 05, 2017 12:11 pm

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.

You are wrong.

pi is an irrational number which means it cannot be expressed as a ratio between two integers, so it cannot be expressed as pi = a/b. It does not matter how many digits you put in a or in b to get your answer closer and closer to pi, because the division will never equal pi. The division can get closer and closer to pi, but it will never equal it.

See wiki entry on pi which says
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.

Similarly, the square root of 2 (1.414...) is an irrational number - it cannot be expressed as a/b. The proof is staggeringly simple:

Clipboard01.png
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby peterpqa » Sat Aug 05, 2017 5:36 pm

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. Everybody used to say the earth was flat and the sun revolved around it. I would like someone to compute 1,539,380,400,259 / 490,000,000,000 and show where it fails to equal pi. AOO Calc only computes to 15 significant digits, as MrProgrammer pointed out. I wasn't asking about the square root of 2.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby John_Ha » Sat Aug 05, 2017 6:08 pm

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.

No.

I am telling you that you are wrong because you are wrong - the fraction does not equal pi.

I cited the proof sqrt(2) is irrational as a simple example, which people with no mathematical skill can follow, so you can get used to the idea that you can easily prove that something is irrational.

There are many proofs that pi is irrational but, as the proofs are generally somewhat more complex than for sqrt(2), I doubt you will understand them. You will just have to accept that there are people with much more knowledge than you who do understand them. There are six different proofs (Lambert's proof, Hermite's proof, Cartwright's proof, Niven's proof, Bourbaki's proof and Laczkovich's proof) given in Proof that π is irrational ... and there are other proofs as well.

Your fraction calculates to the number below which, I think you will agree, goes wrong at the 16th place where it gives 5 instead of 3.

3.14159265358979 59183673469387755 ... your fraction
3.14159265358979 32384626433832795028841971693993751 ... the first 50 digits of pi.

These are the first 500 digits of pi. Or go to Digits of Pi - Up to 1 Million Digits for 10,000 digits and links to sites with 4 million, 50 million, 4 billion and 5 trillion digits of pi.
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
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby peterpqa » Sat Aug 05, 2017 10:14 pm

I'm glad you updated your last reply, and you added the calculations and pi digits. For a circle with radius 7, AOO Calc gave me 153.9380400259 for =PI()*(7^2). That's 13 significant digits. Since Calc's limit is 15 significant digits, I presumed the 13-digit number was precisely exact. Obviously, not so. You can guess the rest. AOO Calc is apparently a rather crude tool for these kinds of numbers. Thanks for proving me wrong - with actual numbers, not theories.

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].

This is exactly the kind of attitude amongst academe that makes people distrust the so-called experts. "Now now, you poor benighted ignoramus. We, the educated elite, know the truth, even if your neanderthal brain can't comprehend it. Just trust us." Then, next week or next month or next year, you say, "Oops, we were wrong before. Here's the new truth. Trust us." That kind of snotty elitism is what makes some people think climate change is a hoax.

 Edit: There is also a mathematical "proof" that 0.99999... is equal to 1, which it is not. 
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby John_Ha » Sun Aug 06, 2017 1:25 pm

peterpqa wrote:
 Edit: There is also a mathematical "proof" that 0.99999... is equal to 1, which it is not. 

I am very sorry but you are displaying your ignorance. 0.999999 ... is equal to 1 wherethe digits go to infinity. Remember it is often better to remain silent, and let people think you are stupid; than speak, and remove all doubt.

Just because you do not understand something does not mean it is wrong.

You either have to educate yourself to the level at which you understand these things; or you have to trust the people who have so educated themselves, and who therefore know more than you know. You trust your doctor, your brain surgeon, you trust the engineer who designed your phone and your car. Every time you use the internet to buy something you trust the mathematicians who designed the cryptography making the transaction secure. You trust your GPS but you undoubtedly have no idea of Einstein's General Theory of Relativity, the Sagnac Effect, or the change in the rate at which time passes (time dilation) due to the satellite's speed and the change in the rate at which time passes due to gravitational potential. Fortunately Neil Ashby and his colleagues did understand all these and incorporated them into the GPS system design, which is why GPS works. Learn to trust those who know more than you.

Nobel Prize winner Feynman famously had "If I cannot prove it, I don't understand it" at the top of his office blackboard. Take a lesson from him.

The best skill you can acquire is the judgement to choose who to trust, and not to say "I don't understand it so it must be wrong".

The proof that 0.999999 ... is equal to 1 where the digits go to infinity is so extremely simple - just 2 lines - that I hope you will be able to understand it.

Line 1. 1/9 = 0.1111111 ..., where the digits go to infinity. Agreed?

Now, you can multiply both sides of the equation by 9. Agreed?

Let's do so.

Line 2: 1 = 0.9999999 ..., where the digits go to infinity.

Therefore you must agree that 0.9999999 ..., where the digits go to infinity, is equal to 1.

QED

Note that I can tell you this proof, but I cannot understand this proof for you - you have to understand it for yourself.

Can I suggest you read Georg Cantor on infinities (infinities come in different sizes). He also explains why irrational numbers cannot be expressed as ratios of integers. The fact that 0.99999... is equal to 1 is an essential part of Cantor's Diagonal, and hence Goedel's Incompleteness Theorems.

The next time you see something you think is wrong (like pi can be expressed as a fraction, or 0.999999... = 1) you really need to prove that it is wrong before you criticise it. If you cannot prove that something you think is wrong actually is wrong, then do not say that it is wrong.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby peterpqa » Sun Aug 06, 2017 6:30 pm

It's so disappointing that you have descended into insults.

John_Ha wrote:Line 1. 1/9 = 0.1111111 ..., where the digits go to infinity. Agreed?

I don't know that for certain. Do you? Have you actually computed 1/9 out to, say, the 753 centillionth digit? Maybe 1/9 resolves to a terminating decimal somewhere before infinity. And where exactly is infinity, anyway? And what is beyond infinity?

You can twist and torture the equations all you like. You can use all the mathematical tricks and assumptions and formulae up your sleeve (but not actual numbers) to make it look like 0.999... equals 1. But it does not.

That which is not a thing cannot be that thing. That which is not 1 cannot be 1. 0.999... is not 1. Therefore, 0.999... cannot be 1.
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Re: Precise snap - yes for inches & centimeters, not for poi

Postby RoryOF » Sun Aug 06, 2017 6:38 pm

I doubt that this thread is going to achieve a meeting of minds and will now lock it.
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