blonde poker forum

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?

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 ???

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

Step aside boys, MereGeek is on thread.

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

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

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?

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.

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...

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

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".

make sense?

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"

Bugger got the square right and the circle wrong  ;djinn;

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

Red face here.
Sorry, as pointed out above, the square would be 23ft by 23ft so 92ft in "length".
Oh dear, silly me.

In fact, I got the radius of the circle wrong too so you can ignore ALL the numbers in my response.

i make the smaller sq 92 foot....the square is obv 23x23x23x23 because its a foot inside all the way round. thats just in my head. kids running round destroying stuff but will do you the cicle in a moment coz dad comes first

My Maths is rusty but I think this is wrong, this would only give 0.5ft of space between the inner and outer square.

Red Dog, I meant inner circle is 1.7xxxxft longer than inner square

Kinboshi thinks the square is inside the circle.....

should copy someone who's got it right next time imo

cicle is 93.7 imo sq 92

i worked out the diameter of circle coz circum = 100 so circum is 22/7x diameter so 100x 7/22 = diameter of 31.18 (odd) therfore inner circle is 29.18 odd multiplly this by 22/7 again to get 93.7

which is what starwars put str8 away and chip prince illustrated nicely

Yup, can't even rely on geeks these days.

Yeah, sorry misread.  Thought you said a circle inside a square (100ft) compared to a square inside a circle (100ft).  Serves me right for trying to do that and work at the same time :(

there is some shocking maths here from old school guys who are meant to be able to at least work out pot odds..delete this thread imo before the young guys all wake up at tea time and rip the piss out of you on a basic maths problem.

I was triple range-merging.

I was setting a trap for you - worked a treat.

lol mere and tony. perfect answers

pmsl... just read the thread again. wtf is tom on about it only being shorter at the corners. kids just come in  from the garden asking why are  you crying daddy

Guys... you really need to do something more productive with yourselves during the day... :)

Of course it's only shorter at the corners. Thinking outside the box won't help you here.

There's a box as well?

You didn't mention that - how big is it and where should I put it*

*I've chipped it over...

logic dictates SQUARE shorter. the corners are were the inner rope is further inside the square by roughly 5 inch at each corner which is why the square rope is shorter.

Sorry, I dont care 8)

Then why would you start the thread ffs?!

Isn't that what I said?

yes you are right. suns burnt of most of the cloud so am off up the park with the 3 boys for some football

no thats not what you said tom. complete opposite. dont play the alzheimers card now.  right utd are goona whoop chelsea now

No, you're right. What I mean is I meant what I said the first time.

But if Coke is better than Pepsi, why is Pepsi Max better than Coke Zero?

Oh, hang on, wrong thread.

depends if the field is flat, as unless you have a perfect flat table the measurements will change as they will have to go over rocks, down dips and over those pesky mole hills

also, that crafty Reddog didn't specify how thick the rope was .... and are all ropes the same thickness


Tom for RSQ quizmaster next week  ;D

So if you were to move halfway towards something at a speed of 10,000 miles an hour, then stop for a billionth of a second, and then move halfway towards it again and so on, would that mean you were constantly moving towards something but never getting there?  

Yes I know you keep stopping, but so does the part of your car tyre that touches the road, but that still gets there along with the rest of your motor....

Holy shit, this is the last thread I should have looked at after a bottle of wine  ;carlocitrone;

no need for the pauses. google zeno's dichotomy paradox. you can also check out his arrow paradox to show that you can't move towards wherever it was you were going at all

and while you're there check out achiles and the tortoise which I'd forgotten about to see that no matter how fast you're going you can't catch a tortoise

In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise


Yes. that illustrates exactly what I was trying to say. We think alike, me an ole Zeno.

Or radioisotopes and their half lives.

All ropes are 100ft long...  Therefore.. None is longer than the other..!!