How is the ring portion of a disk not identical to a ring of identical dimensions?
“Take a round 2” disk, scribe a cirle 1" in diameter concentric with the outer diameter."
Leaving aside the concept of a disk having an “outer diameter” or even an “outer circumference” I will restate your question:
“How is a ring drawn concentrically on a disk-shaped substrate not identical to a ring of identical dimensions?”
One is a drawing of a ring, the other is a ring.
Try putting a drawing of a ring on your finger.
Try putting a disk on your finger.
Try putting a ring on your finger.
The portion of the disk being heated inside the drawing of the ring on the surface of the disk pushes outward, as does every part of the disk. There is no “inward” space like there is in a ring.
They are physically different and topologically different (those are two different things).
Take a ring. Draw a ring on that ring. How many rings do you have? One. How many drawings of a ring do you have? One.
The map is not the territory.
No, sorry. The ring portion of the disk expands the same whether or not the central portion of the disk is there or not. Not a topological problem, a simple physical one, one with which you (confusingly) agree with the answer.
I tried to be clear. I’ll try to be clearer. What you call “the ring portion of the disk” is a circle drawn on the disk. You could draw the circle anywhere on the disk (i.e. not concentrically) and it would expand.
If the central portion of the disk is not there, you do not have a disk but a ring.
What I’m saying is drawing a circle on a disk doesn’t illustrate the case of a ring.
A ring is not a disk.
A disk without a center portion is not a disk.
A circle scribed on a disk as I described will be in the IDENTICAL position (have the same diameter) as the same-sized hole in the corresponding ring when both are heated to the same degree. Do you disagree?
I will try to be even clearer, but first will note that now you have changed from
“How is the ring portion of a disk not identical to a ring of identical dimensions?”
to
“A circle scribed on a disk as I described will be in the IDENTICAL position (have the same diameter) as the same-sized hole in the corresponding ring when both are heated to the same degree.”
I agree with you that the drawing of the ring would be in the same position as the hypothetical ring. I do not agree that this is a good argument (it’s true, but it’s not a good argument because you open up a possible qualm on the part of the opponent that the expanding matter of the disk inside of the drawing of the ring is pushing the drawing outward, whereas the opponent believes that in the case of an actual ring, the inner circumference will be pushed inward by the expanding material outside the inner circumference.
And a drawing of a ring is still not a ring.
I’ll not take the math or science route. I’m taking the “it worked for me approach”. Long before stainless steel exhaust and cat convertors it was common to need the crossover or Y pipe replaced. It was also common for the studs or bolts to have been rusted to thin to use or the threads were rusted off. We used a torch to heat the ear of the manifold to cherry red and the stud could and would be extracted without breaking. My practical application without explaining all scientifical says it expands.