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Mathematical Mysteries
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merkman
Past MnGCA Board


Joined: 03 Jun 2006

Posts: 2032

PostPosted: Tue May 06, 2008 7:20 am    Post subject: Re: It isn't CO-ORDINATES Reply with quote

firstbass wrote:
I'm required by law, as an occasional teacher of mathematics to elementary teachers, to post this:

12 divided by 3 = 4:
12 objects distributed into 3 boxes = 4 objects per box.

12 divided by 1/3 = 36:
12 objects distributed into 1/3 of a box = 36 objects per box.


AND another math mystery

.9 repeating forever (has to be forever) is equal to 1

1/3 = 0.3333...
1 = 3/3
= 3 * 1/3
= 3 * 0.3333...
= 0.9999...
Proof that 1/3 = 0.3333... is left to the reader.
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firstbass
Past MnGCA Board


Joined: 01 Oct 2007

Posts: 538

PostPosted: Tue May 06, 2008 8:00 am    Post subject: Re: It isn't CO-ORDINATES Reply with quote

merkman wrote:
.9 repeating forever (has to be forever) is equal to 1


I can hear forum readers begging you not to bait me like this. Smile

I'll hijack the thread to lecture on geometric series if you really want me to... Shocked Smile
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MN_Cavepeople
Geocacher


Joined: 02 Feb 2005

Posts: 369

PostPosted: Tue May 06, 2008 8:14 am    Post subject: Re: It isn't CO-ORDINATES Reply with quote

firstbass wrote:
merkman wrote:
.9 repeating forever (has to be forever) is equal to 1


I can hear forum readers begging you not to bait me like this. Smile

I'll hijack the thread to lecture on geometric series if you really want me to... Shocked Smile


Don't you mean "geo-metric series"?
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pfalstad
Geocacher


Joined: 02 Feb 2006

Posts: 1011

PostPosted: Tue May 06, 2008 9:02 am    Post subject: Reply with quote

Proof 0 = 1

0 = 0 + 0 + 0 + 0 ...
0 = (1 + -1) + (1 + -1) + (1 + -1) + ...
rearrange parentheses:
0 = 1 + (-1 + 1) + (-1 + 1) + ...
0 = 1
QED

I predict that firstbass will say that this proof isn't valid because of the "associative law" or some other mathematical mumbo-jumbo. Wink
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MN_Cavepeople
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Joined: 02 Feb 2005

Posts: 369

PostPosted: Tue May 06, 2008 10:09 am    Post subject: Re: It isn't CO-ORDINATES Reply with quote

MN_Cavepeople wrote:
firstbass wrote:
merkman wrote:
.9 repeating forever (has to be forever) is equal to 1


I can hear forum readers begging you not to bait me like this. Smile

I'll hijack the thread to lecture on geometric series if you really want me to... Shocked Smile


Don't you mean "geo-metric series"?


Well, now that they split this off of the "Co-ordinates" thread my "geo-metric" joke doesn't make any sense.

A math mystery tell my little nieces and nephews is to point out that if we live long enough they will catch up to me in age.

Say, if I was 10 when my nephew was born he would be 1/10 my age.
10 years later I'm 20 and he is 10...thats 1/2 my age.
Now, 10 years later I'm 30 and he is 20...now he is 2/3 my age.
10 more years and I'm 40 and he is 30...now he is 3/4 my age.
When I am 100 and he is 90 its only a difference of 1/10 my age...he started out 1/10th my age and now he is 9/10ths my age...so, he is catching up to me.

Well, I think it is interesting anyhow, they usually just look at me like I'm nuts.
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LucidOndine
Past MnGCA President


Joined: 17 Jan 2006

Posts: 1931

PostPosted: Tue May 06, 2008 10:20 am    Post subject: Reply with quote

I wasn't aware of the fact that when children are born they are already 1 year old Laughing

Those hacks with an agenda seem to disagree with what you're saying: http://en.wikipedia.org/wiki/Invalid_proof
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MN_Cavepeople
Geocacher


Joined: 02 Feb 2005

Posts: 369

PostPosted: Tue May 06, 2008 10:39 am    Post subject: Reply with quote

LucidOndine wrote:
I wasn't aware of the fact that when children are born they are already 1 year old Laughing


Well, close enough for my logic.

LucidOndine wrote:
Those hacks with an agenda seem to disagree with what you're saying: http://en.wikipedia.org/wiki/Invalid_proof


If they agree then it must be true!


http://www.toothpastefordinner.com
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firstbass
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Joined: 01 Oct 2007

Posts: 538

PostPosted: Tue May 06, 2008 10:44 am    Post subject: Reply with quote

Watch out, people, I'm gonna go f****** nuts in here. Picking up British waitresses in chain restaurants, math-trolling internet forums -- that's mathmagic, right there. Very Happy

I'm a little bummed, though, that merkman gets credit for the hijack. Smile

OK. 1.
merkman wrote:
.9 repeating forever (has to be forever) is equal to 1


Proof. Let x = 0.999...
10x = 9.999...
10x - x = 9x = 9.
x = 1.

By the way, when we write 0.999..., we mean the infinite geometric series
9/10 + 9/10^2 + 9/10^3 + ...

2.
MN_Cavepeople wrote:
if we live long enough they will catch up to me in age.


Proof. The limit as N goes to infinity of N/(N+10) equals 1.

3.
pfalstad wrote:
I predict that firstbass will say that this proof isn't valid because of the "associative law" or some other mathematical mumbo-jumbo.


No, this proof is totally valid. Good thing -- it makes creating puzzle caches much easier. For example: since 0 = 1, we also have

54.700 = 54.762
and
10.000 = 09.353

Wink
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MN_Cavepeople
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Joined: 02 Feb 2005

Posts: 369

PostPosted: Tue May 06, 2008 10:51 am    Post subject: Reply with quote

firstbass wrote:


OK. 1.
merkman wrote:
.9 repeating forever (has to be forever) is equal to 1


Proof. Let x = 0.999...
10x = 9.999...
10x - x = 9x = 9.
x = 1.

By the way, when we write 0.999..., we mean the infinite geometric series
9/10 + 9/10^2 + 9/10^3 + ...

2.
MN_Cavepeople wrote:
if we live long enough they will catch up to me in age.


Proof. The limit as N goes to infinity of N/(N+10) equals 1.

3.
pfalstad wrote:
I predict that firstbass will say that this proof isn't valid because of the "associative law" or some other mathematical mumbo-jumbo.


No, this proof is totally valid. Good thing -- it makes creating puzzle caches much easier. For example: since 0 = 1, we also have

54.700 = 54.762
and
10.000 = 09.353

Wink


Yeah, I was just about to say all that same stuff.
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LucidOndine
Past MnGCA President


Joined: 17 Jan 2006

Posts: 1931

PostPosted: Tue May 06, 2008 11:38 am    Post subject: Reply with quote

Proof by intimidation, ehh Cavepeople? Wink
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bflentje
Geocacher


Joined: 29 May 2006

Posts: 4033

PostPosted: Tue May 06, 2008 11:44 am    Post subject: Reply with quote

One of my favorite satirical math/pchem stories... don't know if it was really used in a classroom..

A thermodynamics professor had written a take home exam for his
graduate students. It had one question:

Is heck exothermic or endothermic? Support your answer with a proof.

Most of the students wrote proofs of their beliefs using Boyle's Law or
some variant. One student, however wrote the following:

First, we postulate that if souls exist, then they must have some mass.
If they do, then a mole of souls can also have a mass. So, at what rate
are souls moving into heck and at what rate are souls leaving? I think
that we can safely assume that once a soul gets to heck, it will not
leave. Therefore, no souls are leaving. As for souls entering heck,
lets look at the different religions that exist in the world today.
Some of these religions state that if you are not a member of their
religion, you will go to heck. Since there are more than one of these
religions and people do not belong to more than one religion, we can
project that all people and all souls go to heck. With birth and death
rates as they are, we can expect the number of souls in heck to increase
exponentially. Now, we look at the rate of change in volume in heck.
Boyle's Law states that in order for the temperature and pressure in heck
to stay the same, the ratio of the mass of souls and volume needs to stay
constant.

#1 So, if heck is expanding at a slower rate than the rate at which
souls enter heck, then the temperature and pressure in heck will
increase until all heck breaks loose.

#2 Of course, if heck is expanding at a rate faster than the increase of
souls in heck, then the temperature and pressure will drop until heck
freezes over.

So which is it? If we accept the postulate given me by Therese Banyan
during Freshman year, and take into account the fact that I still have
not succeeded in dating her, then #2 cannot be true, and heck is exothermic.

The student got the only A.

inappropriate content removed by SB on 5/6/08
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firstbass
Past MnGCA Board


Joined: 01 Oct 2007

Posts: 538

PostPosted: Tue May 06, 2008 8:09 pm    Post subject: Reply with quote

LucidOndine wrote:
Proof by intimidation, ehh Cavepeople? Wink


Wikipedia wrote:
Proof by intimidation is a jocular term used mainly in mathematics to refer to mathematical proofs which are so complex, so long-winded and so poorly presented by the authors...


Ouch! Would this be an example of Forum Moderation by Intimidation? Smile
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LucidOndine
Past MnGCA President


Joined: 17 Jan 2006

Posts: 1931

PostPosted: Tue May 06, 2008 8:45 pm    Post subject: Reply with quote

Hah! Laughing

It'd be great if Forum Moderation by Intimidation really existed because then I wouldn't have to lock, move, edit, and redirect things. For the time being I'll just continue to stare down wayward posts made by lollygagers, miscreants, and worst of all... mathematicians Wink
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Red_Devil35
Past MnGCA Board


Joined: 26 Apr 2006

Posts: 3095

PostPosted: Thu May 08, 2008 1:06 pm    Post subject: Re: It isn't CO-ORDINATES Reply with quote

MN_Cavepeople wrote:
they usually just look at me like I'm nuts.


Get used to it, I am sure the Cavebaby will be doing it too before long!
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minnesotabrad
Past MnGCA President


Joined: 03 Mar 2007

Posts: 1264

PostPosted: Thu May 08, 2008 1:44 pm    Post subject: Re: It isn't CO-ORDINATES Reply with quote

Red_Devil35 wrote:
MN_Cavepeople wrote:
they usually just look at me like I'm nuts.


Get used to it, I am sure the Cavebaby will be doing it too before long!


We were all looking at him like that last night. Laughing
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