Is There A Mathematician In The House?

[Gennie]

Given that the circumference of a circle is equal to 2?R. Let’s say that this is a rope in a circle around a center point, and it’s equidistant from the center point at any and all points along the circumference

For this discussion, all decimal places are out to four places.

The value for ? is given at 3.1417.

The circumference of our circle is 10,000’. This gives us a radius of 1591.4950’ for the circumference.

If we add 100’ to the circumference of our circle, the length of the rope, or 1/100th of the total length of the rope, would it be possible for a person to stand (or lay down) between the old circumference and the new circumference? Could you even put a stool for the person to sit on (average stool height being 30”)?

The answer is ‘Easily!’ The 1/100th of the total circumference is also 1/100th of the radius, and the additional radius of 15.915’ takes us out to 1607.4100’. So, you could stand between the old circumference and the new one.

Now, lets say our circumference was 1,000,000’! Let’s add the same amount of distance, 100 feet and see what we come up with.

The radius of a circle having a million foot circumference is 159149.5050’. Whereas the 100’ of 1/100th of the 10,000’ rope, 100’ here is 1/10,000th! Will the same thing work here as before?

IF you do the math, it says it will. In fact, it says that it will give you EXACTLY the same distance, 15.9150 feet.

HOW is this possible? I’ve increased my circumference by a factor to 100, but yet, with the addition of the same 100’ of rope to the circumference, anywhere along the circumference, the new circumference has increased the exact same distance? Shouldn’t it, at least, be 1/100th of the distance?

Can you explain this apparent paradox?

Gary

[diaperwerx]

How is this a paradox? It's a linear equation. For every 100 feet in circumference the radius increases by 15.xxxxxxxxx feet.

[Repaid1]

Heck I don't know, I just did it in AutoCad, just for the fun of it Trying to figure out what the heck.

[Gennie]

How is this a paradox? It's a linear equation. For every 100 feet in circumference the radius increases by 15.xxxxxxxxx feet.

You're right, Werx, that it isn't a paradox, but to ME, it seems such, which is why I used that word. I know that my thinking must be flawed somehow, and I'm not sure how.

For each circumference, C, if you add 100' of rope, the radius grows by 15.915'. This is what the math says. So, if I have a 100' circumference, and I add a 100' to it, the radius grows ~15.915'.

I can accept that, almost. What I have a huge amount to trouble accepting is that if I have a 100 million mile circumference, by adding a mere 100' of circumference to it, I'm going to push the radius out by 15'.

My mind doesn't go that way! And I don't know why it seems wrong, but it does!

To ME, it's a paradox. Or, I'm just stupid.

Gary

[Valentine]

Gary, it's not you. I think part of it has to do with the similarity between the formula for area and circumference of a circle

[diaperwerx]

Gary, wasn't implying anything by my previous response. It's a good question. I can vaguely remember talking about the peculiarities of pi in one of my math classes and this was mentioned.

It's been far too long since I was even remotely tolerable at proofs and number theory. However here's how I broke this down: The distance between the circle circumferences' increase linearly as the circumference increases.

Or try thinking of it this way:

A circle of circumference 1,000,000 relates to a circle of 1,000,100 as a ratio of

1,000,000 / 1,000,100 or approx 0.999 right?

A circle of circumference of 10000 relates to circle of 10100 as a ratio of 10000/10100 or approx. 0.9900

A circle of circumference of 1000 relates to circle of 1100 as a ratio of 1000/1100 or approx. 0.909

The ratio approaches but never exceeds 1. As the circumference increases so does the number of significant digits. Therefore the variance appears to stabilize at 15.xxx at values over three significant digits, ie distances greater than 10,000 units in circumference.

[DiaperedRacer]

my head hurts just looking at it

[DollyDiaper]

I've got 10 fingers and 10 toes last time I counted. Would you like to borrow them?

D lly

[diaperwerx]

My point is that if you are the person chosen to stand between two cylinders one with a million ft circumference and one with one million one hundred feet circumference you can know that there will be at LEAST 15ft clearance between the circles so you won't be squashed. Unless you move of course...

[MyNameIsDee]

HoW sHuD i KnOw I oNlY 2

[Sunshine2585]

Lol Dee.

[diaperwerx]

A two year old wouldn't be reading this particular forum...however since they are then as x approaches infinity y becomes absolute. LOL

[MyNameIsDee]

DoEs ThAt MeAn I cAn Go AnD PlAy ThEn?