Question for the maths whizziz.

[RED-DOG]

I was running around a field when this question occurred to me.

If I had a rope that was 100ft long and I laid it out in a circle, and then I got another 100ft rope and laid it out in a square, and then I got another rope and laid it out so that it was exactly one foot inside the circle all the way around, and then I got another rope and laid it out so that it was exactly one foot inside the square on all sides...

Which of the inner ropes would be the longest and by how much?

[Boba Fett]

The circle by slightly around 1.7ft?

[RED-DOG]

The circle by slightly around 1.7ft?

I honestly have no idea Bobba, and I don't know how to work it out.

Logic seems to dictate that the circle would be shorter, because the square is only short at the corners whereas the circle is short all the way around

[RED-DOG]

The circle by slightly around 1.7ft?

Is that 1.7ft shorter than the outer circle, or the inner square?

[tikay]

Step aside boys, MereGeek is on thread.

PS - What price he answers the question WITH a question?

"Well, it depends, you see......"

[Dino]

I make the square 4'10" shorter,but my maths is a bit rusty.

[RED-DOG]

I make the square 4'10" shorter,but my maths is a bit rusty.

I need clarification here, shorter than the outer, or shorter than the other inner?

[MereNovice]

Step aside boys, MereGeek is on thread.

PS - What price he answers the question WITH a question?

"Well, it depends, you see......"

The problem seems to have been clearly expressed so I don't see any need for a "it depends ...".

The smaller square is 96ft in length.

The circumference of a circle is expressed as 2 * pi * radius.
The radius of a circle with circumference of 100ft is 16ft (and a bit).
Therefore we need to know the circumference of a circle with radius 15ft (and a bit).
The circumference of the smaller circle is 93.76ft roughly.
So the smaller circle is smaller by about 2 1/4 foot.

For those that don't know, the radius of a circle is the distance from the centre to the edge.

[kinboshi]

The rope making the square inside the circle is a lot longer (from my calculations).

The square that is 100ft of rope, has sides of 25ft.  That means the circle inside has a diameter of 23 feet, as it's a foot from each side of the square.

23π = 72.25ft = length of the rope for the circle.


The circle that's 100ft of rope has a diameter that is = 100/π = 31.83ft.

A diagonal going from corner to corner of the square will be 29.83ft (as each corner is a foot away from the circle). This 29.83 is the hypotenuse of a right-angled triangle, and the other two sides are the same length.  So 29.83^2=2(x^2), and so x=21ft (approx).  This is one side of the square, so 21 x 4 = 84ft.

Square inside the circle is 84ft of rope, the circle in the square = 72ft of rope (approx).  Unless my calculations are wrong...

[tikay]

Step aside boys, MereGeek is on thread.

PS - What price he answers the question WITH a question?

"Well, it depends, you see......"

The problem seems to have been clearly expressed so I don't see any need for a "it depends ...".

The smaller square is 96ft in length.

The circumference of a circle is expressed as 2 * pi * radius.
The radius of a circle with circumference of 100ft is 16ft (and a bit).
Therefore we need to know the circumference of a circle with radius 15ft (and a bit).
The circumference of the smaller circle is 93.76ft roughly.
So the smaller circle is smaller by about 2 1/4 foot.

For those that don't know, the radius of a circle is the distance from the centre to the edge.

I was going to reply precisely the same, you saved me a job.

[Dino]

Shorter than the other inner,each leg of the inner square is 23',making 92'.
The diameter of a 100' rope is 31.8'
the circumference of rope with the diameter 30.8' is 96'10".

[TheChipPrince]

make sense?

[gatso]

The circle by slightly around 1.7ft?

this

square 1 25"x25"
circle 1 r=15.92"

square 2 23"x23" so total length 92" long
circle 2 r=14.92" so total length 93.7"

[Dino]

Bugger got the square right and the circle wrong  

[gatso]

except put foot notation instead of the inches that I've inexplicably used