Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#526 2011-02-04 00:59:23

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Yes!


"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."

Offline

#527 2011-02-07 02:09:09

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

A real dilly?!

2,4,4,6,6,6,6,8,8,8,8,8,8,8,8,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10...

1) Find the 2012th term.

2) Sum the first 2012 terms.

3) What term has the last 2012?


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.

Offline

#528 2011-02-07 06:44:22

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."

Offline

#529 2011-02-07 13:50:23

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.

Offline

#530 2011-02-07 17:50:08

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

cool!


"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."

Offline

#531 2011-02-11 15:15:08

Howardroark
Member
Registered: 2010-10-10
Posts: 382

Re: What do you think?

Hi bobbym,

bobbym wrote:

A real dilly?!

2,4,4,6,6,6,6,8,8,8,8,8,8,8,8,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10...

1) Find the 2012th term.

2) Sum the first 2012 terms.

3) What term has the last 2012?


I come from a civilization which has given the world the number 0..

Offline

#532 2011-02-11 15:24:12

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

Hi Howardroark;

That is correct, good work.


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.

Offline

#533 2011-02-11 20:11:04

Howardroark
Member
Registered: 2010-10-10
Posts: 382

Re: What do you think?

Hi bobbym,

Nice question


I come from a civilization which has given the world the number 0..

Offline

#534 2011-02-12 23:08:16

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

Thanks for looking at the problem.

New problem!

A guy draws a rectangle. Near each vertex he draws a circle with radius 1 that is tangent to the adjacent sides. He fits a circle with radius 4 inside the rectangle and finds that the circle is tangent to all four of the other circles. See the diagram. What is the area of the rectangle?

A says) 81
B says) 81.57999
C says) 81.67677
D says) 81.67984

Who do you agree with?


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.

Offline

#535 2011-02-13 00:32:24

Howardroark
Member
Registered: 2010-10-10
Posts: 382

Re: What do you think?

Hi bobbym,


I come from a civilization which has given the world the number 0..

Offline

#536 2011-02-13 00:38:38

Howardroark
Member
Registered: 2010-10-10
Posts: 382

Re: What do you think?

Hi bobbym,


I come from a civilization which has given the world the number 0..

Offline

#537 2011-02-13 01:07:21

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Hi bobbym,

I don't think it has a unique solution. Under the same constraints, angle between the diagonals may be varied, isn't it?


"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."

Offline

#538 2011-02-13 01:40:07

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

Hi gAr;

I do think it has a unique solution. The rectangle is bigger than the largest circle which has all four little circles touching it and the rectangle. Can you draw two different looking rectangles that work?


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.

Offline

#539 2011-02-13 01:57:09

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Hi bobbym,

Sorry for not reading the question properly. I thought we are drawing the circle first.
I'll try again.


"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."

Offline

#540 2011-02-13 01:59:30

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

Hi;

That is okay, I welcome the input. I do not have a really good method on this problem so I am not sure either.


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.

Offline

#541 2011-02-13 02:21:11

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Hi,

But still, I'm wondering that the order of drawing either circle or rectangle doesn't matter. Since you haven't mentioned about the distance between the smaller circles, there is room to move those circles by a small distance. Hence the area is not fixed.
Hope I read the question properly this time!

I'm struggling to draw it, I'm no expert in geogebra!


"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."

Offline

#542 2011-02-13 02:37:11

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

Hi gAr;

Howard has a solution very close to mine. But it is not an exact answer. I think because the unit circles are tangent to the rectangle and to the big circle that there is an exact answer.I will keep working on 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.

Offline

#543 2011-02-13 02:53:13

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Oh, ok, I thought of it again. They must have a unique solution indeed.
Sorry, I posted everything in haste!


"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."

Offline

#544 2011-02-13 05:22:07

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,880

Re: What do you think?

Hi Bobby,

From your drawing and the 1:4 radii it appeared to me at first glance that there might be a 5x4 grid of smaller circles within the rectangle...and so I produced a scaled drawing in Word.

After drawing the 5x4 grid with a centred large circle in it I drew a rectangle with sides that touch the outer edges of the outer circles.

The rectangle measures exactly 10x8 (area = 80). That's only graphically accurate, of course, and it doesn't work well with a couple of other circle dimensions I tried it on.

I couldn't find a formula from the drawing's info. I also tried some other ideas, including relating the areas of the small and large circles, but got nowhere.

Also, I don't know how to work out the length of the rectangle's diagonal, given that it doesn't pass through the centre of the corner circles.


"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

Offline

#545 2011-02-13 06:14:40

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Hi bobbym,

I thought the solution would be a square. Got the solution as: (2+5√2)² = 82.2843 sq. units.

But phrontister's solution appears to be good as well. Perhaps, there really are multiple solutions.


"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."

Offline

#546 2011-02-13 06:19:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

Hi phrontister and gAr.

Yes, I asked for another example and phrontister has produced it. His is a proof without words so please post yours.


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.

Offline

#547 2011-02-13 14:06:04

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,880

Re: What do you think?

Hi Bobby,

I don't see any solutions other than the two so far.

Also, my formula can't be the same as gAr's because the rectangle's shape relates to circle placement that differs in each case, resulting in different areas.

Off to work now...


"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

Offline

#548 2011-02-13 14:21:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

Hi Howardroark, gAr and phrontister;

Very nice solutions. More than I expected.


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.

Offline

#549 2011-02-13 23:47:17

Howardroark
Member
Registered: 2010-10-10
Posts: 382

Re: What do you think?

Hi bobbym,

Thank you..


I come from a civilization which has given the world the number 0..

Offline

#550 2011-02-14 01:10:55

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,880

Re: What do you think?

Thanks, Bobby.

Do you have a non-graphical solution for the area of the unequal-sided rectangle?


"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

Offline

Board footer

Powered by FluxBB