In article ,
Richard Cline wrote:
In article ,
s wrote:

the hole isn't part of the metal. it's where the metal isn't. look at
it like this: say you have a piece of wire. you heat it, it expands
and gets longer. now say you bend it into a circle. you heat it, it
gets longer. the corcle gets bigger, both inside and outside diameters

Yea but when you heat the wire, it gets thicker. That means one side
would move toward the center of the circle.

Wrong! counter-intuitive as it may be, that is *NOT* what happens.

Simple disproof:
Consider a _square_ of metal.
With a square hole in the middle of it

When the sides of the square expand, the top/bottom move further apart.
The part of the sides that are against the top/bottom, expand exactly
as much as the top/bottom do. The part of the sides against the hole
_also_ expand.
When the top/bottom of the square expand, the sides move further apart.
The part of the top/bottom that are against the sides, expand exactly
as much as the sides do. The part of the top/bottom against the hole
_also_ expand.


There's another simple proof:

take a _solid_ chunk of material and draw a circle on it, to "represent"
the 'hole'. Now heat it up. what happens to the size of the drawn circle?

Now, for the_hard_ question:
Does it make any difference if you cut along that drawn line,
before or after you heat the material?

Just cut along the line, leave both pieces where they are, and heat.
Hmmm. the center circle gets bigger. yet it still fits in the outer
piece. The hole _must_ get larger, too. grin