Multi-cache Math

[+fauxSteve]

I have had the opportunity to find caches in many states and several countries, and I have seen many different ways in which things are done. Here, however, I want to ask about a common variation I’ve seen that has caught me off guard.

 

Suppose you were seeking a multi-cache with several waypoints, at each of which you get a number that helps solve the final question. For example, at waypoint #1 you count the number of wings on the bird sculpture (A=?), at wp#2 you count the number of windows on the front side of the house (B=?), and so on…

 

After you collect several of these, and in order to find the final cache, you need to do a small amount of math.

 

Here’s my question: what final coordinates would you, as a geocacher, come up with using the following formula? (This is hypothetical, but based on my own experiences.)

 

Let’s say, A=3, B=5, C=6, and D=1.

 

“The final cache is at:

N 40° 07.(A+D)(D+1)D

W 020° 20.(B+A)A(C+D)”

 

Where are you going to look?

[+TeamAO]

I know this is a trick, but I'm going to go the obvious route. (Which I'm sure is wrong.)

 

 

N 40.07421 W 020.20837

[WH]

Heres what I would use:

 

N 40 07.421

W020 20.837

[+Markwell]

I actually made that a problem in one of my first difficult math puzzles. Threw people for a loop. Did I mean for it to be decimal degrees or degrees with decimal minutes. In my case I actually wanted people to use decimal degrees, but since people are so accustomed to degrees with decimal minutes, I knew it would throw them off.

 

I also was courteous to check that the degrees with decimal minutes didn't send them anywhere either likely or dangerous.

[+The Leprechauns]

Where are you going to look?

My "Ignore List."

[+Jennifer&Dean]

Oh Boy! I love getting complaints about order of operations!

 

A=3, B=5, C=6, and D=1.

N 40° 07.(A+D)(D+1)D in real math would = 40*07.8

and

W 020° 20.(B+A)A(C+D) in real math would = 020*20.264

 

Did I get it right?

 

I've had to explain geo-math a few times to folks. Its lots of fun!

-Jennifer

[+TeamAO]

Oh Boy! I love getting complaints about order of operations!

 

A=3, B=5, C=6, and D=1.

N 40° 07.(A+D)(D+1)D in real math would = 40*07.8

and

W 020° 20.(B+A)A(C+D) in real math would = 020*20.264

 

Did I get it right?

 

I've had to explain geo-math a few times to folks. Its lots of fun!

-Jennifer

Where did you learn to do math like that?

[+Stunod]

Oh Boy! I love getting complaints about order of operations!

 

A=3, B=5, C=6, and D=1.

N 40° 07.(A+D)(D+1)D in real math would = 40*07.8

and

W 020° 20.(B+A)A(C+D) in real math would = 020*20.264

 

Did I get it right?

 

I've had to explain geo-math a few times to folks. Its lots of fun!

-Jennifer

While I would never solve cache coords this way, using proper order of operations I agree with you on the latitude, but the longitude I get .168 for the decimal.

[+TeamAO]

Let’s say, A=3, B=5, C=6, and D=1.

 

“The final cache is at:

N 40° 07.(A+D)(D+1)D

W 020° 20.(B+A)A(C+D)”

 

You couldn't argue that in "real-world math" you would simplify the parenthesis (didn't spell that right ) then multiply everything together, which on the west coordinates would turn up a 3 digit number but the north coordinate would be 1 digit. But if they're playing a REAL tricky game the top may be regular coordinate adding, and the west coordinate may be "real math", just to throw you off. In that case it would be.

 

N 40.07421

W 020.20168

Edited July 19, 2005 by Team AlphaOmega

[WH]

This cache of mine uses various equations to solve for the coordinates.

 

I have included checksum values in the hint so people can see if their answers are correct.

[+TeamAO]

This cache of mine uses various equations to solve for the coordinates.

 

I have included checksum values in the hint so people can see if their answers are correct.

I like the idea of instilling some math into caches. So that we can brush up on our arithmatic, which we all need sometimes.

 

A challenge makes the cache all the more worthwhile.

[+Jennifer&Dean]

Oh Boy!  I love getting complaints about order of operations!

 

A=3, B=5, C=6, and D=1.

N 40° 07.(A+D)(D+1)D in real math would = 40*07.8

and

W 020° 20.(B+A)A(C+D) in real math would = 020*20.264

 

Did I get it right?

 

I've had to explain geo-math a few times to folks.  Its lots of fun!

-Jennifer

Where did you learn to do math like that?

Oops, misread the equation for the second one, it shoud be 168. Sorry.

But to elaborate:

 

When evaluating arithmetic expressions, the order of operations is:

 

* Simplify all operations inside parentheses.

* Perform all multiplications and divisions, working from left to right.

* Perform all additions and subtractions, working from left to right.

 

Now, I'll admit I screw up my math stuff all the time.

Thats why Dean does the math and I don't.

But when I see an equation like that, what it tells me to do is completely different from what most folks seem to see. Math is kinda like that for me.

 

I know that I can ignore everything before the 07. so I see the parahtheses and go:

(3+1)(1+1)1

(4)(2)1

(now the magic happens and you multiply the () stuff together)

(8)1

8

Which gives me 40 degrees 07.8

 

For the second part I see:

(5+3)3(6+1)

(8)3(7)

24(7)

168

[robertlipe]

Oh Boy!  I love getting complaints about order of operations!

 

A=3, B=5, C=6, and D=1.

N 40° 07.(A+D)(D+1)D in real math would = 40*07.8

and

W 020° 20.(B+A)A(C+D) in real math would = 020*20.264

 

Did I get it right?

 

I've had to explain geo-math a few times to folks.  Its lots of fun!

-Jennifer

Where did you learn to do math like that?

Probably in high school math class where he learned that '2(x+y)' means "two times X + Y". so it's not a stretch to read it as:

 

(3+1)(2)(1) = 8

(5+3)(3)(6+1) =168. (I can only get 264 if I implement that last term as "C+B" and not "C+D"

 

I'm not saying I would have done it this way, but it is reasonable interpretation (well at least if I assume the substitution error...)

 

I have to say that a depressing percentage of puzzle caches ambiguity problems.

Edited July 19, 2005 by robertlipe

[+Stunod]

edit: forget it...error corrected in original post.

Edited July 19, 2005 by Stunod

[+Jennifer&Dean]

Oh Boy!  I love getting complaints about order of operations!

 

A=3, B=5, C=6, and D=1.

N 40° 07.(A+D)(D+1)D in real math would = 40*07.8

and

W 020° 20.(B+A)A(C+D) in real math would = 020*20.264

 

Did I get it right?

 

I've had to explain geo-math a few times to folks.  Its lots of fun!

-Jennifer

Where did you learn to do math like that?

Probably in high school math class where he learned that '2(x+y)' means "two times X + Y". so it's not a stretch to read it as:

 

(3+1)(2)(1) = 8

(5+3)(3)(6+1) = 315. (I can only get 264 if I implement that last term as "C+B" and not "C+D"

 

I'm not saying I would have done it this way, but it is reasonable interpretation (well at least if I assume the substitution error...)

 

I have to say that a depressing percentage of puzzle caches ambiguity problems.

substitution error! and I'm sticking with it.

 

-J

[+TeamAO]

Oh Boy!  I love getting complaints about order of operations!

 

A=3, B=5, C=6, and D=1.

N 40° 07.(A+D)(D+1)D in real math would = 40*07.8

and

W 020° 20.(B+A)A(C+D) in real math would = 020*20.264

 

Did I get it right?

 

I've had to explain geo-math a few times to folks.  Its lots of fun!

-Jennifer

Where did you learn to do math like that?

Oops, misread the equation for the second one, it shoud be 168. Sorry.

But to elaborate:

 

When evaluating arithmetic expressions, the order of operations is:

 

* Simplify all operations inside parentheses.

* Perform all multiplications and divisions, working from left to right.

* Perform all additions and subtractions, working from left to right.

 

Now, I'll admit I screw up my math stuff all the time.

Thats why Dean does the math and I don't.

But when I see an equation like that, what it tells me to do is completely different from what most folks seem to see. Math is kinda like that for me.

 

I know that I can ignore everything before the 07. so I see the parahtheses and go:

(3+1)(1+1)1

(4)(2)1

(now the magic happens and you multiply the () stuff together)

(8)1

8

Which gives me 40 degrees 07.8

 

For the second part I see:

(5+3)3(6+1)

(8)3(7)

24(7)

168

And the 40.078? Just fill in zeros? If the cache hider went into that much detail that might have been kind enuff to allow you to multiply by 100 so you don't just have to "assume" because doing the order of operations and just adding things together it's 3 slots for numbers may be 100 miles apart. So, with gas prices the way they are, and the range of the two answers apart, this cache will quickly find my ignore list if the hider doesn't give me a more specific answer.

 

 

PS...I don't have an ignore list, it was used for dramatic effect.

[+Jennifer&Dean]

Yep, just put in zeros. That always confuses folks. So the final North location would be 40 degrees 07.800 (or more easily written as 40*07.800 but don't get me started by the confusion that using a * instead of a degree symbol can cause)

-J

Edited July 19, 2005 by Jennifer&Dean

[+Jennifer&Dean]

From one of our caches:

 

The final location of the cache is:

N 46*45. 0 ((9*Y)+2)

W 114*05. ((128*X)-X)

 

Do you know what screws folks up the most? The fact that Y is used in the North coordinate equation, and X is used in the West coordinate location.

 

From another cache of ours:

47*ZA.KEC

111*YZ.NP(Z-Y)

 

No complaints yet about the math, but give it time.

 

And if you really want to see folks whineing about coordinate math, check out the logs on this now archived cache that Jennifer "helped" fix the equation on:

Rainbow Kisser

 

-Jennifer

[+Allanon]

Let’s say, A=3, B=5, C=6, and D=1.

 

“The final cache is at:

N 40° 07.(A+D)(D+1)D

W 020° 20.(B+A)A(C+D)”

 

Where are you going to look?

 

My first thought would be NON math related (at least in the use of 'brackets' and multiplication), but only because I don't think most non-math people think about the algebra...

 

So:

40° 07.421

020° 20.837

[Dinoprophet]

Yep, just put in zeros.  That always confuses folks.  So the final North location would be 40 degrees 07.800  (or more easily written as 40*07.800 but don't get me started by the confusion that using a * instead of a degree symbol can cause)

-J

At first, that's how I would have solved it. But after a moment's thought, I think the north coordinate is 40*07.008. The solution to the math is 8, so the decimal portion of the number should be 8.

 

Where are all the decimal degree answers coming from? The OP clearly poses it as degrees decimal minutes. Unless that's some mathmatical interpretation of the degree symbol I don't know about (and that's possible), I don't see why you would replace the degree symbol with a decimal point.

My first thought would be NON math related (at least in the use of 'brackets' and multiplication), but only because I don't think most non-math people think about the algebra...

 

So:

40° 07.421

020°  20.837

I'm going the other way, that the puzzle was designed assuming most geocachers would solve it that way, when in fact they're supposed to use real algebra.

Edited July 20, 2005 by Dinoprophet

[+Pablo Mac]

To me, the "unspoken expectations" include triple-checking whatever kind of math you use in a multi-cache, and then having someone else proof it for you before you submit the new cache for approval.

 

I say that because I have wasted many hours and much gas on a certain local cacher's math-based multis, only to come home and find she made a mistake and posted the correction hours or even days after the cache was approved. On my latest exercise in futility hunting one of her caches, she waited until 2 or 3 cachers wasted their time and contacted her about it before she fixed the issue, and I happened to load the cache into my CacheMate PDA moments beforehand, leaving me in the field with obsolete data days after the cache was placed and approved! I deleted my original DNF and note logs because the her replies on the cache page were, uh...nothing I wanted to be associated with.

 

She owns well over 100 caches (most placed within the last 2 or 3 months), so she must be overworked on the maintenance side.

 

Love that "Ignore Listing" button. I'm going to wear mine out!

 

Enough ranting...where were we?

[+TeamAO]

There are too many possibilites of how a person may interpret the problem data. The hider should most definately clarify with an example.

 

I.E.

 

(A*2)B(C+4)

 

Solve Like

 

(4*2)3(5)

(8)3(5)

24*5

120

 

If the hider doesn't demonstrate you will have cachers running all over the place and DNF's will pile up so quickly that no one will attempt the cache because it's either too diffucult or they don't read the logs just assume it's taken by the multiple DNF's.

 

Always remember, even if you tell some exactly what to do, you can still make the problem diffucult, but don't leave the problem out in the open.

[+tabulator32]

There are too many possibilites of how a person may interpret the problem data.

There is only one result for the equation presented by the OP.

 

If you have "multiple interpretations," you may need to brush up on your math skills.

 

[+TeamAO]

There are too many possibilites of how a person may interpret the problem data.

There is only one result for the equation presented by the OP.

 

If you have "multiple interpretations," you may need to brush up on your math skills.

 

You can interpret it in all the ways listed above.

 

You don't know what the person who hid it intended to be interpreted. Maybe they didn't assume that people will interpret in mathematically. There are variables in every situation.

[+Isonzo Karst]

In the OP's original example I'd probably do both solutions: 40°07.421 20°20.837 and 40°07.800 20°20.168, then drop them into Expert GPS (or google maps!) and DeLorme Street Atlas & eyeball the locations for the likelyhood of having a cache.

[+TeamAO]

In the OP's original example I'd probably do both solutions: 40°07.421 20°20.837 and 40°07.800 20°20.168, then drop them into Expert GPS (or google maps!) and DeLorme Street Atlas & eyeball the locations for the likelyhood of having a cache.

Agreed. Find which coordinate is closer, and if one is 50 miles away from you, it's probably wrong.

[+Hoppingcrow]

Let’s say, A=3, B=5, C=6, and D=1.

 

“The final cache is at:

N 40° 07.(A+D)(D+1)D

W 020° 20.(B+A)A(C+D)”

 

Where are you going to look?

Because I am a geocacher and accustomed to seeing cache coordinates given in DD.MM.MMM, I would assume that the parenthetical values would each represent a single number, giving decimals .421 and .837. It would, however, be better to write it in the following format to eliminate all possibility of misinterpretation:

N 40° 07.abc W 020° 20.xyz

a = A + D

b = D + 1

c = D

x = B + A

y = A

z = C + D

[+tabulator32]

There are too many possibilites of how a person may interpret the problem data.

There is only one result for the equation presented by the OP.

 

If you have "multiple interpretations," you may need to brush up on your math skills.

 

You can interpret it in all the ways listed above.

 

You don't know what the person who hid it intended to be interpreted. Maybe they didn't assume that people will interpret in mathematically. There are variables in every situation.

"All the ways listed above" were not correct and were summarily examined and corrected as the thread progressed.

 

There is only one finite answer using the correct mathematical rules.

 

All the variables AND THEIR VALUES were given in the very first post.

 

You can "interpret" the data as much as you desire. There is only one answer.

[+caderoux]

Precisely for this confusion about the meanings or whether any operations are intended, in my puzzle and multi-cache, I've only used letters as a single digit substitutions and put any math in terms of those single digits.

 

Anything more complicated, I think I would spell out explicitly.

[+caderoux]

Simple digit substitution can in some cases allow finders to work out some math quicker through the process of elimination, but never leaves room for confusion.

 

e.g. in N AB° CD.EFG: You know that A * 10 + B <= 90. You know that C * 10 + D <= 59. Stuff like that.

 

It can still be made interesting - for instance this cache: http://www.geocaching.com/seek/cache_detai...1c-1388a65afdb8 based on this image http://img.Groundspeak.com/cache/9345d93f-...25fb03927c4.jpg which works the cacher's handle into the digits - way cool.

 

When you look at something like:

 

N 40° 07.(A+D)(D+1)D

W 020° 20.(B+A)A(C+D)

 

it isn't even valid mathematical notation no matter what your interpretation. No one would write 40° 07.xyz - you can't mix constant notation with variables that way; the valid scalar expression would be 40 + (7 + x * 10 ^ -1 + y * 10 ^ -2 + z * 10 ^ -3) / 60 - or as some might have it: 40 + (7 + x * y * z * 10 ^ -3) / 60 or 40 + (7 + x * y * z * 10 ^ -1) / 60.

 

I think if you are giving the user the expectation that it is really a math-based puzzle, you need to meet their expectations and not expect them to try to re-interpret some "new" math, but conform to traditional mathematical notation. There are lots of ways to make the users think and do research. The digits could come from a binomial expansion, coefficients of a power series, digits of pi, digits of e, etc. But using brackets as delimiters instead of operational grouping can be misleading. Or if the longitude is supposed to be .008 or .8 or whatever, you can probably make a way to spell it out with substitution or whatever.

 

Maybe I'll give the coordinates to my next cache in radians - it would be so much cleaner than all these degrees and minutes!

[+fauxSteve]

Heres what I would use:

 

N 40 07.421

W020 20.837

So far, so good! This has been a great discussion. In some of my recent caching, multi-caches are everywhere, and this type of "equation" keeps popping up. The answer that would have gotten you to the cache at many of them is the one quickly given by WH and followed up by a few others (quoted above). I, of course, mutiplied the numbers at first.

 

But I think a few other interpretations have popped up that are really interesting and of good value to cache hiders (i.e., zeros before or after a single digit). It's always good to know how your hiders might interpret your instructions if you want to avoid problems (unless you're one of those evil hiders, of course)!

 

Edited to change one letter!

Edited July 20, 2005 by fauxSteve

[+horsegeeks]

WHEW, give me a bison tube in a holly tree in the middle of a forest anytime.

[cezanne]

it isn't even valid mathematical notation no matter what your interpretation. No one would write 40° 07.xyz - you can't mix constant notation with variables that way;

You are wrong. 07.xyz is of course a correct mathematical notation provided that x,y and z are digits and not objects that could not be placed behind the decimal point without prior definition (like trees, matrices, integrals whatever).

 

In mathematical notation constants and variables are mixed all the time - this is daily routine (also with an infinite number of digits behind the decimal point as this is needed to represent fractions which do not have a finite expansion in the chosen number system).

 

Since multiplication behind the decimal point is not defined, it would be definitely wrong to visit the coordinates

N 40° 07.8

in case N 40° 07.xyz' is to be visited and x=1 y=2 and z=4

 

N 40 ° 07.124' is the only correct solution in that case.

 

The version with parentheses and more complex epressions like (A+D) instead of a single variable is not formally correct - it typically is used as a kind of short-hand notation instead of introducing new variables for the blocks inside the parentheses.

In any case, multiplying the terms behind the decimal comma is a much stronger abuse of notation that just pasting together the components.

 

Cezanne

[NMCoach]

I ran into a similar problem this past week. Here is what it said:

 

Subtract one from the other (larger # on on top) then add what you get to your existing North Coords.

N32.15.???

W101.27.102

 

Once at the new coords. Look at the north side. Use this formula to get the value of N32.15.XXX

Month x 4 - 4 = XXX

Use this formula to get the value of W101.27.ZZZ

Day x 8 -2 = ZZZ.

 

Well the two answers were 2046 and 1996. So the answer was 50. So I put in 500. That took me to a shopping center where I obviously wasn't going to get anything for the second set.

 

So, I put in 050. It took me back close to the area of the first cache only I was almost in the middle of the street.

 

There was a third date on the structure and so I got the number 100. It put me on a fence. I gave up and it got too dark to do some other caches I had logged. I e-mailed the owner for help and my e-mail came back to me yesterday as undeliverable.

 

It was really frustrating! So I say as some others have; be specific about how the math is used.

[+caderoux]

You are wrong. 07.xyz is of course a correct mathematical notation provided that x,y and z are digits and not objects that could not be placed behind the decimal point without prior definition (like trees, matrices, integrals whatever).

 

In mathematical notation constants and variables are mixed all the time - this is daily routine (also with an infinite number of digits behind the decimal point as this is needed to represent fractions which do not have a finite expansion in the chosen number system).

With all due respect, that's simply not true. Arithmetic operations are not regularly combined with string-rewriting in the mish-mash you suggest. Yes constants are added together with expressions, and string rewriting systems exist which are designed to carry out logical operations (which is how you prove many of the advanced theorems of logic like Godel's theorem), but when they are combined, there are combined in an unambiguous notation with definitions.

 

And yes, parentheses are used for a lot of different things in mathematics, from functions to grouping to bracketing. There are plenty of notations for many different branches of mathematics, but there is none which does as you suggest and simply lumps several together higgledy piggledy.

 

That is not to say you can't make up a notation or operators, but the question the OP had was about expectations, implicit meaning and conventions. I think it's polite that if you are implying that a problem is a straight mathematical problem, to use only conventional notations. If you want to make it a mystery or obfuscate it in that way, that's fine too, but don't pass it off as a straightforward puzzle.

[cezanne]

You are wrong. 07.xyz is of course a correct mathematical notation provided that x,y and z are digits and not objects that could not be placed behind the decimal point without prior definition (like trees, matrices, integrals whatever).

 

In mathematical notation constants and variables are mixed all the time - this is daily routine (also with an infinite number of digits behind the decimal point as this is needed to represent fractions which do not have a finite expansion in the chosen number system).

With all due respect, that's simply not true. Arithmetic operations are not regularly combined with string-rewriting in the mish-mash you suggest. Yes constants are added together with expressions, and string rewriting systems exist which are designed to carry out logical operations (which is how you prove many of the advanced theorems of logic like Godel's theorem), but when they are combined, there are combined in an unambiguous notation with definitions.

I did not say that the notation with parentheses which was part of the OP's question is formally correct. But 07.xyz with x,y and z being digits is a formally correct mathematical notation. I am not writing this from the point of view of geocaching, but from being a professional mathematician. I objected because you wrote that no one would use a notation like 7.xyz which is simply not true. This notation is needed (and used) in mathematics (I am talking about the science mathematics here and not about the sort of arithmetics which occurs in the daily life of most people) on a routine basis (both in teaching and research at university level). [it is straightforward to come up with hundreds of examples which demonstrate that I am right and what you claim is wrong. Sentences like "Let 0.a_1a_2a_3a_4 .... (a_i is shorthand for a with index i) be the decimal representation of the number x" are standard and they even occur in simple calculus exams on the undergraduate level.]

 

 

Whether you have 7.345 or 7.xyz with x=3, y=4 and z=5 or a.xyz with a=7 and x, y, z as in the second case, makes no difference at all since mathematicians do not care about mixing constants and variables in a single term as long as everything fits together. The underlying convention in all cases is the standard notation for decimal numbers. The situation would change, of course, if the numbers are not with respect to the base 10 and this fact is not mentioned somewhere). The type of argument you were giving would mean that you could not write 4.56, but would have to explain each time that this means 4+5*10^{-1}+6*10^{-2} which is simply crazy.

(BTW: In your explanation you used division by 60 which is a second mistake in your previous posting since if the minutes are giving as decimal minutes as it was the case in the given example you need to convert with 10 and 100. I do know that some cachers argued that it might be part of the puzzle to use the decimal notation and mean something else, but I am talking about mathematical correctness and I do not care at all about various forms of puzzles.)

 

Clearly almost all standard notations are based on some sort of convention (even using natural numbers and what addition, subtraction means etc). Similarly, the number pi needs to be defined once, however, it is standard to use it without defining it all the time. The same holds true for the example with 07.xyz I came up with above.

 

Cezanne

 

(PS: If correctness is important for you, you should write Gödel or G"odel (in case you do not know the ASCII-code of the letter ö) when you are refererring to a theorem of Kurt Gödel and not a person called Godel. Changing ö into o makes a significant difference.)

Edited July 21, 2005 by cezanne

[CoyoteRed]

Because I am a geocacher and accustomed to seeing cache coordinates given in DD.MM.MMM, I would assume that the parenthetical values would each represent a single number...

This is the only way I've ever seen it.

 

Additionally, the clue might be in the form of a puzzle where you are supposed to figure the proper way to massage the numbers.

 

Instead of having a check sum you could have the hint say something about the area that is different from the other results. This would prevent unnecessary searching.

[+wimseyguy]

As a mathematician I would expect to multiply data inside (_), but as a geocacher I would expect that each formula for for a single digit of Nxxdeg.xx.xxx etc.

 

I'm actually working on a multi puzzle that will have some simple math to generate the coords for the final stage. I'll be sure to use all the lessons learned in theis thread, and maybe even to use [] instead of (). (err brackets don't have any deeper meaning in math do they? )

Edited July 21, 2005 by wimseyguy

[+caderoux]

In your explanation you used division by 60 which is a second mistake in your previous posting since if the minutes are giving as decimal minutes as it was the case in the given example you need to convert with 10 and 100.

You should re-read the expression given for understanding the purpose of the 60.

[cezanne]

In your explanation you used division by 60 which is a second mistake in your previous posting since if the minutes are giving as decimal minutes as it was the case in the given example you need to convert with 10 and 100.

You should re-read the expression given for understanding the purpose of the 60.

I had read your formulae already at my first reading, but as you did not add units of measurement (degrees, minutes etc), I misinterpreted what you wrote as I focussed only on the second part (not the degree part which has no influence on the issue).

 

For the discussion of whether 7.xyz is a valid mathematical notation (which it is and you could not come up with a convincing counter-argument) it plays no role whatsoever which units are involved. Combining the degree part with the minutes part does not contribute to the issue at the heart of this discussion.

 

Do you still claim that no mathematician would use a notation like

0.a_1a_2a_3.... with a_i being variables? (Do you really want to say that this

would be written all the time as infinite series??)

 

BTW: The notation N 40.07.345 which seems to be used by some cachers here for

N 40° 07.345' is no valid mathematical notation whatsoever as there do not exist numbers with two decimal points. (I am aware of the fact that points are used as separation signs in many places, for example quite often when the input format of some numbers is specified, but this does not mean that this is a valid mathematical notation and the issue here is about mathematical correctness.)

 

Cezanne

Edited July 21, 2005 by cezanne

[+caderoux]

Do you still claim that no mathematician would use a notation like

0.a_1a_2a_3.... with a_i being variables? (Do you really want to say that this

would be written all the time as infinite series??)

I'm claiming no mathematician would use the notation:

 

N 40° 07.(A+D)(D+1)D

W 020° 20.(B+A)A(C+D)

 

As I said, single digit substitution is fine, but it wouldn't be mixed up with the arithmetic like this, because it is ambiguous whether a_1 is (A+D) or a_1 is (A+D)(D+1)D or even (A+D)(D+1)

 

Conceivably,

 

N 40° 07.a_1a_2a_3

W 020° 20.b_1b_2b_3

 

where:

a_1 = A + D

a_2 = D + 1

a_3 = D

 

b_1 = B + A

b_2 = A

b_3 = C + D

 

would be a suitable notation.

[+AtoZ]

solving it mathmatically using the associative property you get

N 40° 07.6

W 020° 20.144

 

but if they imply and it is very POOR form to do this then you may get whatever.

 

cheers

[+StarBrand]

How about this one I ran across recently:

 

Instructions said to take a 6 digit number (something like: 423958)

And then subtract the first 3 numbers from the last 3 numers. Then add the resulting numbers to 999. So does that mean

 

958 - 423 + 999= or

 

(9 + 5 + 8) - (4 + 2 + 3) + 999 or

 

9-4=5 5-2=3 8-3=5 5 + 3 + 5 + 999

 

Oddly the answer was the 3rd example.

[cezanne]

 

As I said, single digit substitution is fine, but it wouldn't be mixed up with the arithmetic like this, because it is ambiguous whether a_1 is (A+D) or a_1 is (A+D)(D+1)D or even (A+D)(D+1)

Do you still claim that no mathematician would use a notation like

0.a_1a_2a_3.... with a_i being variables? (Do you really want to say that this

would be written all the time as infinite series??)

I'm claiming no mathematician would use the notation:

 

N 40° 07.(A+D)(D+1)D

W 020° 20.(B+A)A(C+D)

 

.....

 

What you write now is certainly true, but what you wrote previously was something different.

 

No one would write 40° 07.xyz - you can't mix constant notation with variables that way; .....

 

My objection was against that claim - such a notation provided that x, y and z are digits is common practice in mathematics.

 

I already wrote in my first statement that

the version with parentheses and more complex terms like the one arising in the OP is formally incorrect (unless it is defined prior to being used). Replacing the terms inside the parentheses by variables and removing the parentheses results, however, again in a valid expression, and that was the point of my first posting in this thread.

 

As the 07.(A+D)(D+1)D example is regarded,

what I said was only that multiplication behind the decimal point is not defined. This implies that those who believe that multplying the terms inside the parentheses is something which is mathematically correct are wrong anyway.

 

Cezanne

[+caderoux]

No one would write 40° 07.xyz - you can't mix constant notation with variables that way; .....

 

My objection was against that claim - such a notation provided that x, y and z are digits is common practice in mathematics.

You are right - the example I gave in my earlier post was trying to combine two concepts and it didn't do a very good job:

 

it isn't even valid mathematical notation no matter what your interpretation. No one would write 40° 07.xyz - you can't mix constant notation with variables that way; the valid scalar expression would be 40 + (7 + x * 10 ^ -1 + y * 10 ^ -2 + z * 10 ^ -3) / 60 - or as some might have it: 40 + (7 + x * y * z * 10 ^ -3) / 60 or 40 + (7 + x * y * z * 10 ^ -1) / 60.

 

I was trying to show use xyz as a substitution for the parenthesized expression, and show how you might want to write it as a single expression which didn't have any of the degree, parentheses and decimal point issues.