Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

I am embarrassed to show this. Since that vine is spiralling up the tree I thought of a helix.

Where a is the radius. And rises by 2πb units of height per revolution.

So we have the 3 parametric equations.

Now I just need the arc length of the 3.

Now the only excuse I have for this is recently I worked on one of these parametric arc length problems and I guess it was fresh in my mind. Or maybe all that parametric jazz my brother tried to teach me when I was trying to learn the tensor calculus finally surfaced. I knew that stuff would ruin me.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

That's a nice solution.
My method may get complicated for conical helix!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

Thanks but I think these words apply here:

Do not use a cannon to kill a mosquito.

Yours is the right way.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

Problem is knowing which weapon is good enough!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

You are so right!

New problem!

We have the sequence {1,2,3,4,...,n}. When we remove one we get an average of 17 000 000 + 1 / 3. Find n and find the removed number.

A says) Beautiful problem, I'll bet B won't get it. There are 3 answers.

B says) Sorry A there is only one answer.

C says) I burned out my CPU trying to find it.

D says) I don't think this sort of question should be allowed. But I say no solutions!

How many answers are there?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

Is it the average?

Last edited by gAr (2011-03-15 23:52:30)

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

Yes, I am sorry. It is the mean or average. I have fixed the problem.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

Ok, I was trying with that assumption anyway.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

New problem!

with

What is:

A says) 5 / 2

B says) I did not get that. I got...

C says) Me too.

D says) I got 2.25.

Can you find the limit. Can you offer a convincing argument for your assertion. Can you prove it?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: What do you think?

Hi Bobby,

Last edited by phrontister (2011-03-16 14:52:29)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi phrontister;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: What do you think?

Hi Bobby,

Oops! I'd copied my #620 post and didn't change everything that I needed to for this one. I've corrected my previous post.

Funny cartoon! Expresses it well!

Here's a link to a funny YouTube video along those lines.

Last edited by phrontister (2011-03-16 15:38:43)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

Finally solved for the product after a good sleep!

And good solution phrontister, I used 2 unknowns and did it unnecessarily long!

Last edited by gAr (2011-03-16 15:50:34)

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi phrontister;

Thanks for providing that. Thanks for the vid, there were other ones there also that were good. What was the time for your spreadsheet do you remember?

Hi gAr;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

Thanks!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

Thanks for that. I did it a little bit different. I heard that it was considered an easy problem so I was wondering if there was an easy method.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

By "easy", did you mean without computer aid?

And how did you solve for the infinite product?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Yes, I have a method that does not require a computer. But it does require a couple of tries. Luckily in this case it worked on the first try!

For the infinite product, are you familiar with the works of Jonathan and Peter Borwein and others on what they call experimental math?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Oh, okay, I'll see if I can get something else.

I haven't heard of that, how is it solved by experimental math?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: What do you think?

Hi Bobby,

What was the time for your spreadsheet do you remember?

It took 10 to 15 minutes, I think. All I did was change the figures on the spreadsheet that I'd made for the other average problem in your post #616 (my answer was in post #620), as the two problems are very similar. I'd already done all the thinking back then, so there wasn't much to do this time around.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi phrontister;

Okay, thanks. Yes it is very similar to another problem. I was just wondering about the speed.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

I have split the post to avoid any confusion as I am posting to both you and phrontister at the same time.

Experimental math, well I cannot explain it as well as this.

http://en.wikipedia.org/wiki/Experimental_mathematics

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: What do you think?

Hi Bobby,

The first problem (#616) probably took an hour or so, but most of that would have been thinking about it.

I was initially going to try to write one in LB but quickly ditched that idea because nothing leapt out at me.

Then I thought I'd try Excel but had to do some research because I didn't know the formula for obtaining the average of the sum of the elements of a sequence. Once the idea gelled it didn't take long to complete the spreadsheet...by setting up a row and then copy-dragging it down the page. And "hey presto": there was the answer, just a few rows down.

Luckily the two puzzles were close enough together time-wise for the solution concept not to have been obliterated entirely from my brain!

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson