What do you think?

bobbym · 2011-02-14 01:14:25

Hi Howard;

You are welcome and thanks for looking at the problem.

Hi phrontister;

No, I do not and I do not need one. That is a really pretty solution that you came up with there. It is like a proof without words.

Everyone did a much better job on this problem than I did.

bobbym · 2011-02-14 22:19:23

New problem!

The probability of 1 kid is 1/6. Two kids is 1/3. Three kids is 1/3 and four kids is 1 / 6. Everyone gets married and has kids.
What is the chance that a couple has exactly 5 grandkids?

A says 1 / 8
B says 4 / 129
C says (1 / 9)^4
D says ( 1 / 3 )^5

gAr · 2011-02-15 05:09:01

Hi bobbym,

For the rectangle, I guess its minimum area is 80 sq. units and maximum area is a square with 82.2843 sq. units, and can have any number of solutions in between.

phrontister · 2011-02-15 11:13:50

gAr wrote:

For the rectangle, I guess its minimum area is 80 sq. units and maximum area is a square with 82.2843 sq. units, and can have any number of solutions in between.

That's right, I think, gAr.

The rectangle with the minimum area has two sides (only) that touch the large circle, and they are opposite each other. As those two sides move away from the large circle they do so at an equal rate and the other two sides move towards it (also at an equal rate), until eventually all sides are equally-far away from the circle. At that point the rectangle is a square.

At each change of the rectangle's dimension its area also changes, ranging from a minimum 80 sq.units to a maximum 82.2843 sq. units, as you said.

Opposite sides are always the same distance from the large circle as each other.

As the rectangle changes shape the corner circles reposition symmetrically around the large circle's perimeter.

Just out of curiosity I worked out these dimensions where all four sides of the rectangle touch the large circle (the rectangle being a square):
a) Large circle radius 4, small circle radius approx 0.69;
b) Small circle radius 1, large circle radius approx 5.8

Last edited by phrontister (2011-02-15 12:32:01)

bobbym · 2011-02-15 12:11:56

Well guys I do not believe any of that math stuff. To me a rectangle is a square that has poor posture.

gAr · 2011-02-15 14:47:44

Hi phrontister,

Thanks for explaining, that's what I thought too.

Hi bobbym,

Did you not believe in the names or the area?
Did you check my answer to probability, which I'm not very sure?

bobbym · 2011-02-15 15:05:18

Hi gAr;

I was just razzing phrontisters excellent explanation and discovery of another solution.

I have not checked your answer yet. I have been busy all afternoon with trifles.

gAr · 2011-02-15 15:25:08

Hi bobbym,

Oh, I see. I thought you had another solution!

I thought you missed to see my solution, so I asked. No hurry!

bobbym · 2011-02-15 15:55:11

Hi gAr;

gAr · 2011-02-15 22:35:03

Hi bobbym,

Cool! Thanks.

phrontister · 2011-02-16 01:16:14

bobbym wrote:

Well guys I do not believe any of that math stuff. To me a rectangle is a square that has poor posture.

To a rectangle a square lacks style!

Here's a 4-position animation demonstrating the multiple-solution concept from min to max areas.

Last edited by phrontister (2011-02-16 01:17:52)

gAr · 2011-02-16 01:19:54

Hi phrontister,

That's good!

phrontister · 2011-02-16 01:39:07

Thanks, gAr.

I drew the four positions in Word, captured them with SnagIt, saved them as jpegs and created an animated gif at picasion.com (free). The order is 1,2,3,4,3,2...which then repeats from 1.

Someone will probably want to use it for their avatar!

Last edited by phrontister (2011-02-16 01:40:59)

gAr · 2011-02-16 01:51:35

Thanks for telling, phrontister, I was wondering how you did it!

bobbym · 2011-02-16 05:03:41

Hi phrontister;

Very nice! Have you seen the program geogebra? It is freeware and can do animations and geometry in an amazing way!

phrontister · 2011-02-16 12:00:59

Hi Bobby,

No, I've only seen GeoGebra referred to several times lately by yourself and gAr. I didn't really know what is was and I'd assumed it might be a bit advanced for me. I've just installed it and I'm looking forward to trying it out.

Thanks!

gAr · 2011-02-16 15:23:13

Hi phrontister,

Geogebra is really good for geometry. It has many features, even I'm not aware of all.
But you can master it easily if you have some time to spend, there are many tutorials.
For some random examples, google:- filetype:ggb

After opening the ggb file, in geogebra, go to: View -> Construction protocol , for the steps.

bobbym · 2011-02-16 17:16:10

Hi phrontister;

I do not think it is too advanced for you. Also it is a lot of fun.

phrontister · 2011-02-18 04:26:11

Thanks, Bobby and gAr.

I'll check it out.

bobbym · 2011-02-18 07:11:42

Hi phrontister;

Let me know how and what you are doing with it, if you like it.

bobbym · 2011-02-18 18:13:28

Captain Eric Finlander is in command of a destroyer armed with anti submarine rockets. They have a range of 2.07 miles. He has positioned himself on a cartesian grid at the origin. An enemy sub is steaming around like a drunken ocean liner following a path that is exactly y = x^2 - 6. Each tick on the cartesian grid is a mile. So (0,1) is one mile from Finlanders missiles. At what position ( x,y ) will the submarine be in range of his missiles?

Our distinguished experts are eating so you are on your own!

gAr · 2011-02-18 19:09:53

Hi bobbym,

Last edited by gAr (2011-02-18 19:14:35)

bobbym · 2011-02-18 20:29:44

Hi gAr;

bobbym · 2011-02-19 09:28:20

New problem.
A parallelogram has 2 adjacent sides of 19 inches and 16 inches. If the diagonals have integral lengths, what is the sum of the diagonals length?

A says) 31
B says) That is not right.
C says) Beautifully done A! Would you teach my kid?
D says) Impossible to determine! I am suprised the A did not say that first.
A says) Sorry, I forgot! Yes it is impossible to determine. Here is why:

Let G be a metric...

Had to chop off the rest of A's 291 page proof. What do you think?

gAr · 2011-02-20 00:58:45

Hi bobbym,

Math Is Fun Forum

#551 2011-02-14 01:14:25

Re: What do you think?

#552 2011-02-14 22:19:23

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#553 2011-02-15 05:09:01

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