Zoot Allures wrote:
„I don't know what you mean by identical ....“ **
The mathematical meaning of the adjective „identical“ is identical
with the mathematical meaning of the adjectives „same“ and „equal“.
Please look at the watch again:
There is no doubt. The same angular degree. The two hands of the watch
have the same angle. Which one it is is easily to find out.
Zoot Allures wrote:
„But I'm not big on geometry ....“ **
And geometry is not enough.
The main part of the task is not a geometrical one, by the way.
Zoot Allures wrote:
„If you mean each angle leaves its point of origin with the same
degree relative to a line or axis drawn between them, then yeah, you
have two congruent lines. But you can do this with any two angles leaving
the same point of origin if you place a line directly between them.“
**
What I mean is easily to find out by the text and the picture of my
post:
Zoot Allures wrote:
„Draw a line from the nut in the middle of the clock that bolts
the hands down to the 12.“ **
No.
Zoot Allures wrote:
„There is your axis line. So each hand would have the same angle
relative to the line.“ **
The 12 is the axis line, but that is already clear because of the text
and because of the picture. Here comes the picture again:
Zoot Allures wrote:
„It would be a little more than a 45 degree angle for each hand,
since the 3 and 9 would be a 90 degree angle while the 12 would be no
angle.“ **
Zoot Allures wrote:
„But I'm not big on geometry ....“ **
Geometrically „no angle“ is not possible.
The equivalents betweenn the numbers of the watch and the degree values:
0 <=> 0°.
1 <=> 30°.
2 <=> 60°.
3 <=> 90°.
4 <=> 120°.
5 <=> 150°.
6 <=> 180°.
7 <=> 210°.
8 <=> 240°.
9 <=> 270°.
10 <=> 300°
11 <=> 330°.
12 <=> 360°.
Look at the watch again:
Zoot Allures wrote:
„No matter where you put the hands, you could draw a line directly
between them, creating the same degree of each angle. That's why I don't
understand what you mean when you say identical.“ **
Yes, I know, but that is irrelevant. Again: What I mean is easily to
find out by the text and the picture of my post:
Zoot Allures wrote:
„There is no such thing as an identical angle because all angles
can be identical depending on the axis line between them.“ **
You know from your own language that the 12 is always the pivotal point.
For example: You know what it means when you say „12 o'clock“,
„3 o' clock“, or „5 past 12“, „5 past 3“,
... and so on. „12 o'clock“ <=> where are both hands of
your watch? „5 past ...“ Why „5“? .... You know? It
is always with reference to the 12.
Zoot Allures wrote:
„Now if you insist that the 12 be the axis line, then putting
the little hand on the 6 and the big hand on the 3, you would not have
identical angles. The little hand would have a 180 degree angle while
the big hand would have a 90 degree angle.“ **
If the pivotal point was (it is not!) „half past 4“, then
both would have identical angles (45 degrees, by the way  but according
to the logic/mathematics and technique of all watches your example it
is not possible, by the way). It is a tiny part of the task that one
has to know what the pivotal point of a watch is.
Zoot Allures wrote:
„Really, mentioning that the angles are identical seems to be
superfluous here.“ **
No. It is exactly the opposite that is true.
Phoneutria wrote:
„If there are only two lines in a circle, the only two angles
that can be the same is 180, that's be either 0915 or 1445. You need
another line.“ **
No.
Zoot Allures wrote:
„I understand everything you've said clearly. We are on the same
page on that part. What I don't understand is why any mention of the
angle is relevant to the problem.
If the big hand is on 10 and the little hand is on 2, and the watch
functions like every other watch in the known universe, and the watch
has stopped working, then it stopped working at 10:10.“ **
You have to read precisely. Your example here is not my example.You
example does not work because of the logic/mathematics and technique of
all watches, as I already said.
Again:
Phoneutria wrote:
„Graph the two angles.“ **
That is obviously your job. You need to do it. Perhaps you will have
the effect of learning by doing.
Nevertheless:
Zoot Allures wrote:
„Oh, it's one of those problems. An exercise in Zeno's paradox.
Infinite decimals and shit. Is it almost 10:10, almost almost 10:10,
or almost almost almost 10:10? Holy moly, you can keep dividing the
spaces between the minutes like ..., infinitely!“ **
You have not understood it.
Zoot Allures wrote:
„And I thought this was going to be something good.“ **
Show me the way of the solution, loudmouth. You have not understood
it. This shows me your reaction. Again: Show me the solution process of
the task. As I said: it is geometry, algebra, thus mathematics, and it
is reading precisely, understanding the text, the logic and common sense
in it, thus it is also linguistics. But the core of the task is mathematics.
And you have not understood it.
_________________________________________________________________________________
This thread is about mathematics! What do you expect? Wonders? Miracles?
„Something good“?
Zoot Allures wrote:
„Nuhuh, because at a smaller level, the noise that composes
the subatomic particles that compose the atoms that compose the molecules
that compose the elements that compose the material that the hands are
made of are still moving.
I told you it was a trick.“ **
It was no trick.
Phoneutria wrote:
„Your premise did not specify an angle between a clock arm and
12. That's what I mean by »you need another line«.“
**
No. If you meant it, then you would have said it. In addition: another
line is not needed.
One has to figure out that the 12 is this „line“ you are talking
about. That is common sense but has nothing to do with the mathematical
task. The text of my post was clear. It is your problem, if you are not
capable of imagine a line.
You have excuses. I know. Show me the solution process and explain it.
James S. Saint wrote:
„Arminius obviously meant »the angles from 12 to the hour
hand and 12 to the minute hand are identical when it stopped«.“
**
The first sentence: „Your watch has stopped.“. The second
sentence: „So it does not work anymore.“. So the follwoing sentences
refer to theses first two sentences. Of course!
I wrote:
„Your watch has stopped. So it does not work anymore. The little
hand of the watch indicates approximately ten o'clock, and the big hand
of the watch indicates approximately two o'clock. Both hands of the
watch form an identical angle. When did your watch stop precisely?“
** **
There is no text that begins with the last sentence and ends with the
first sentence.
James S. Saint wrote:
„The answer:
Dubiously assuming that I did the tiny bit of math right:
Time on Clock = 10:9:13.8461538461538.
But you have to figure out how to find it.“ **
No problem
Phoneutria wrote:
„I can imagine to make up for your poor problem constraint definition,
but I can also get two exact angles by drawing a line to 6, getting
a different answer whilw still being correct.“ **
That is irrelevant (see below). The said text with the task clearly
says which angles are meant. Additionally I gave you this:
Mathematically it is absolutely irrelevant
what Phoneutria said, namely that there is also
a line to 6. You just need the information that the angles have the same
degree in order to solve the problem mathematically. But which line you
prefer is absolutely irrelvant for the mathematical solution.
Zoot Allures wrote:
„Either it's a trick, or it comes down to the impossibility of
stopping the division of infinite decimals/fractions between minutes.
This is not an interesting problem. It is an age old paradox that
baffled philosophers who had nothing better to do than be baffled.
James and/or Phoneutria. I demand that you solve the problem and answer
the question immediately to prevent Arminius from pwning me.“ **
Why are you not capable of solving the problem? You have not understood
it.
H = Hours. M = Minutes.
H/12 x 360 + M/60 x 360/12 = 30 H + 0.5 M.
Position of the big hand: M/60 x 360 = 6 M.
Position of the little hand: H/12 x 360 + M/60 x 360/12 = 30 H + 0.5 M.
The sum of both angles is 360°.
So: 30 H + 0.5 M + 6 M = 360.
For H = 10:
300 + 6.5 M = 360 => M = 60/6.5 = 9.231 minutes.
Thus: 9 minutes, 13.8 seconds.
Time on watch: 9 minutes and 13.8 seconds past 10.
___________________________
Zoot Allures, what is „pwning“?
___________________________
Phoneutria wrote:
„I can answer but I am not going to bother with calculating it
because solving problems is fun, doing math isn't. I'll just hint at
how to start solving it, as usual.
This is more akin to the hare and the turtle paradox, zoot, because
both arms are constantly moving. By the time you reach 10 minutes, the
hour clock has moved forward whatever much an hour arm moves in 10 minutes,
making that not an exact angle, so one would have to calculate how many
degrees of an angle per minute each of the arms move, (the hour arm
moves 360 degrees in 12 hours and the minutes arm moves 360 in 1 hour),
or something... I'd do the rest later. I'm tired.“ **
You do not have to do anything of that, because the
solution and the solution process are already given.
H = Hours. M = Minutes.
H/12 x 360 + M/60 x 360/12 = 30 H + 0.5 M.
Position of the big hand: M/60 x 360 = 6 M.
Position of the little hand: H/12 x 360 + M/60 x 360/12 = 30 H + 0.5 M.
The sum of both angles is 360°.
So: 30 H + 0.5 M + 6 M = 360.
For H = 10:
300 + 6.5 M = 360 => M = 60/6.5 = 9.231 minutes.
Thus: 9 minutes, 13.8 seconds.
Time on watch: 9 minutes and 13.8 seconds past 10.
Phoneutria wrote:
„Yes, Arminius, after you put your imaginary like there, your
premise was complete. Also very cute with my lil spider there.“
**
Zoot Allures wrote:
„Thanks guys. I understand now. But I'm still stuck on the infinite
divisibility of the units of time thing. Also, what if the watch, which
isn't digital, stopped before the gear system which turns the hands
stopped before the gear teeth were completely seated? You know each
each 'ticktock' is the turn of the gear wheel.. so what if the tension
created by the winding, which powers the gears, was at zero percent
before the watch completed its final tick?
What time would it then be? You see the infinite divisibility of time
units I'm talking about now in a different way. The watch's gear teeth
need to be seated in order for a unit of its time to be recognized.
It could have stopped somewhere between 10:10 and 10:10.1 for all we
know. We have Zeno's wrist watch.“ **
James S. Saint wrote:
„They used spiral gears  smooth, no slack.
And even if you wanted to quantize the whole thing, you would still
solve it in the same way but then truncate the answer to the nearest
quantum step.“ **
If the said watch was digital, then there would be
no geometrical aspect in the said task. It would become senseless, because
there would be no geometrical circle but merely numbers. The task is about
realising the facts given in the text, the recognition of the geometric
facts, and the finding of the algebraic solution.
Carleas wrote:
„Not a solution, but: EDIT: oops, missed a page of discussion
on this one, :oops: Anyway, this is my untainted first stab.
I'm assuming the equal angle is between the hands of the clock and
the vertical. I'm also assuming that the hands are meant to be moving
fluidly, such that at exactly 10 O'clock, the hour hand points straight
at 10 and the minute hand points straight at 12. At 10:15, the minute
hand points straight at three, and the hour hand points at the spot
1/4 of the way between 10 and 11.
So, we can narrow the answer down to between 10 and 10:15.
To find the answer, we need to convert time to radians, take the speed
of each hand in radians/second, such that the speed of the minute hand
12x faster than the speed of the hour hand, and then find where the
values cross (using the absolute value and counting up to pi and back
down).
Does that at least get the question right?“ **
I have already given the solution process.
H = Hours. M = Minutes.
H/12 x 360 + M/60 x 360/12 = 30 H + 0.5 M.
Position of the big hand: M/60 x 360 = 6 M.
Position of the little hand: H/12 x 360 + M/60 x 360/12 = 30 H + 0.5 M.
The sum of both angles is 360°.
So: 30 H + 0.5 M + 6 M = 360.
For H = 10:
300 + 6.5 M = 360 => M = 60/6.5 = 9.231 minutes.
Thus: 9 minutes, 13.8 seconds.
Time on watch: 9 minutes and 13.8 seconds past 10.
Phoneitria wrote:
„Arminius wrote:
»Realising the facts given in the text.« **
**
....“ **
I said this:
„The task is about realising the facts given in the text, the
recognition of the geometric facts, and the finding of the algebraic
solution.“ **
**
Mathematically it is absolutely irrelevant
what Phoneutria said, namely that there is also
a line to 6. You just need the information that the angles have the same
degree in order to solve the problem mathematically. But which line you
prefer is absolutely irrelvant for the mathematical solution.
Phoneitria wrote:
„He means this fact ....“ **
No. You have not understood it.
To find out that the 12 is the line is already part of the task, namely
the part that refers to the common sense. Everything you say about the
time on the watch refers to 12, e.g.: „... o'clock“, „10
past ...“, „20 past ...“, „10 to ...“, ... and
so on, thus it depends on the position of the big hand (minute hand).
Mathematically it is absolutely irrelevant
what Phoneutria said, namely that there is also
a line to 6. You just need the information that the angles have the same
degree in order to solve the problem mathematically. But which line you
prefer is absolutely irrelvant for the mathematical solution.
Again:
Your watch has stopped. So it does not work anymore. (Thus:
The hands of the watch do not move anymore!) The little hand of
the watch indicates approximately ten o'clock, and the big hand of the
watch indicates approximately two o'clock. Both hands of the watch form
an identical angle. (Thus: Both hands form the same
angle [to 12 or to 6  indifferent for the mathematical solution!], so
they have the same number of degree! The imvisible line is irrelevant
for the mathematical solution!) When did your watch stop precisely?
Duh!
Yes. But the line is irrelevant when it comes
to find the mathematical solution!
Phoneutria wrote:
„Arminius wrote:
»Zoot Allures, what is ›pwning‹?« **
**
....“ **
That was meant ironically, Phoneutria. I had just given him the solution
process.
I wrote:
„Zoot Allures, what is »pwning«?
H = Hours. M = Minutes.
H/12 x 360 + M/60 x 360/12 = 30 H + 0.5 M.
Position of the big hand: M/60 x 360 = 6 M.
Position of the little hand: H/12 x 360 + M/60 x 360/12 = 30 H + 0.5
M.
The sum of both angles is 360°.
So: 30 H + 0.5 M + 6 M = 360.
For H = 10:
300 + 6.5 M = 360 => M = 60/6.5 = 9.231 minutes.
Thus: 9 minutes, 13.8 seconds.
Time on watch: 9 minutes and 13.8 seconds past 10.“ **
**
Phoneutria wrote:
„Help a linguist out.“ **
That is not necessary (see above).
Phoneutria wrote:
„Arminius wrote:
»You do not have to do anything of that, because the solution
and the solution process are already given.“ **
**
So you put solutions in tabs, but you don't know why?
Should tabs  in this thread (!)  not be used because of discretion?
Phoneutria wrote:
„Ah, ok. You're just really bad at irony.“ **
Very bad!
Phoneutria wrote:
„Tabs are used so when you give the solution, you don't spoil
it for people who want to try to solve by themselves.“ **
I called it „descretion“.
Phoneutria wrote:
„Carleas knows that he can click the tabs and see the answer,
but he wants to try to solve it on his own. Threads like this aren't
really about being the first to solve (since anyone can probably just
google for the answers).“ **
Ah, I see.
Carleas! Good luck!
Phoneutria wrote:
„Threads like this aren't really about being the first to solve
(since anyone can probably just google for the answers).“ **
Yes, I know.
Since the beginning of the socalled „Neolithic Revolution“
the human beings have been (unconsciously or even consciously) creating
something in order to be replaced someday. This „something“
and this „someday“ come nearer and nearer.
In my job as a private teacher I have to explain very much, and I am
pretty sure that I am good at explaining.
On ILP the situation is a bit different:
Unfortunately ILP has not much to do with explaining, because most ILP
members just want recognition and nothing beside it. And unfortunately
I have to translate all my thoughts into a foreign language. I am not
looking for excuses, because I have to admit that I do not want to address
many but merely some ILP members, namely those who are really interested
in the topic of the thread.
So actually I am not much interested in making a topic attractive to
posters.
They are either interested or not interested.
It is the economic reality that mainly dictates, for example the (part
of) reality that money causes.
