## Math Fun

For discussing anything related to physics, biology, chemistry, mathematics, and their practical applications.

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### Re: Math Fun

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.

Wait what? You lost me.

Draw a circle. Put a dot in the very center. Draw one line from that dot in any direction until it reaches the perimeter of the circle. Draw another one from that dot in any direction until it reaches the perimeter. Then put an axis directly in the middle between those two lines. Both of the two lines will proceed at exactly the same angle away from the axis between them.

I need a graphic. Somebody who knows what the hell I'm trying to explain here, please go find a graphic and post it.
Zoot Allures
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### Re: Math Fun

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:

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?

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:

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?

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.
Last edited by Arminius on Tue Aug 18, 2015 2:34 am, edited 2 times in total.

Arminius
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### Re: Math Fun

phoneutria wrote:
Arminius wrote:The angular degree is the same.

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.

Arminius
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### Re: Math Fun

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.

Now when you reveal the trick and I go 'ohhhhhhh!', I'm going to smack you. Now spit it out.
Zoot Allures
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### Re: Math Fun

Arminius wrote:
phoneutria wrote:
Arminius wrote:The angular degree is the same.

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.

Graph the two angles.

phoneutria
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### Re: Math Fun

If a rooster laid an egg on the top of a 10/12 pitch roof facing north, and an easterly wind of twenty mph was blowing, which side of the roof would the egg roll down?
Zoot Allures
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### Re: Math Fun

Wow ... leave it to Zoot to livin things up ..

Arminius obviously meant "the angles from 12 to the hour hand and 12 to the minute hand are identical when it stopped".

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.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
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Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

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:

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?

Arminius
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### Re: Math Fun

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!

And I thought this was going to be something good.
Zoot Allures
Philosopher

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Joined: Fri Mar 27, 2015 6:50 pm

### Re: Math Fun

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!

And I thought this was going to be something good.

Zeno or no, it is simple algebra/geometry.
Last edited by James S Saint on Tue Aug 18, 2015 3:50 am, edited 1 time in total.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

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:

Phoneutria_Watch.jpg (40.59 KiB) Viewed 1102 times

Arminius
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### Re: Math Fun

Nuh-uh, because at a smaller level, the noise that composes the sub-atomic 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.
Zoot Allures
Philosopher

Posts: 2607
Joined: Fri Mar 27, 2015 6:50 pm

### Re: Math Fun

Arminius wrote:
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:

Phoneutria_Watch.jpg

Your premise did not specify an angle between a clock arm and 12. That's what I mean by "you need another line".

phoneutria
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### Re: Math Fun

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"?
Last edited by Arminius on Tue Aug 18, 2015 6:18 am, edited 3 times in total.

Arminius
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### Re: Math Fun

Zoot Allures wrote:

Nuh-uh, because at a smaller level, the noise that composes the sub-atomic 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.

Arminius
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### Re: Math Fun

phoneutria wrote:
Arminius wrote:
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:

Phoneutria_Watch.jpg

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.

Arminius
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### Re: Math Fun

You have excuses. I know. Show me the solution process and explain it.
Last edited by Arminius on Tue Aug 18, 2015 4:41 am, edited 1 time in total.

Arminius
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### Re: Math Fun

James S Saint wrote:Wow ... leave it to Zoot to livin things up ..

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.

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.
Last edited by Arminius on Tue Aug 18, 2015 6:28 am, edited 5 times in total.

Arminius
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### Re: Math Fun

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.

phoneutria
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### Re: Math Fun

And you have not understood it.

Bologna. 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.
Zoot Allures
Philosopher

Posts: 2607
Joined: Fri Mar 27, 2015 6:50 pm

### Re: Math Fun

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:
And you have not understood it.

Bologna. 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"?
___________________________
Last edited by Arminius on Tue Aug 18, 2015 7:19 pm, edited 2 times in total.

Arminius
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### Re: Math Fun

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.

phoneutria
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### Re: Math Fun

Yes, arminius, after you put your imaginary like there, your premise was complete. Also very cute with my lil spider there.

phoneutria
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Posts: 4265
Joined: Fri May 23, 2014 5:37 am

### Re: Math Fun

Zoot Allures wrote:James and/or Phoneutria. I demand that you solve the problem and answer the question immediately to prevent Arminius from pwning me.

Huh???
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

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.

Arminius
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