If you have ever seen a tall chimney fall, you will have observed that they break up on the way down. This is because of the effect you have found.

What is even more interesting a cylinder falling in that manner will break into 3 large pieces and some crumbs (about .14 ) so the chimney breaks in to [itex] \pi [/itex] pieces.

Ok, Ok, the chimney is a streach.... Drop a full stick of chalk it will usually break into [itex] \pi [/itex] I have always felt that it was somehow related to the falling chimney

Drop a full piece of chalk, I have done this experiment many times.... With amazing regularity, it will break into 3 large pieces and several smaller fragments + dust, or .14 so it breaks into [itex] \pi [/itex] pieces.

Then what do you mean by "breaks into [itex] \pi [/itex] pieces"? Aren't each of the smaller fragments pieces? How can you have .14 of a piece? When you talk about units, it seems like your defining a unit as (1/pi)*total length, so then it's no surprise that the fragment lengths sum to pi.

No, I am saying that a new piece of chalk will break into 3 large sections and a number of much smaller fragments + dust. Envision the fragments as being a small fraction (approximately of course) ~ .14 of one of the (not exactly equal sized, but of the same magnitude ) larger sections.

Don't over think this, just find a box of chalk and start dropping chalk from several feet. See for yourself.

I've done this accidentally before, it broke into 2 (not 3) big pieces, ~5 small-ish pieces and some very fine dust... but I suppose it matters on the kind of chalk? For example, whether or not it's very thick or pencil-like, or the 'dustless' kind, etc.?

hmmm, is chalk 'ideally brittle' ? If not there would be a size and length effect (the thing of course, different perceptions) + a neat distribution of characteristic parameters.

Chalk breaks when it hits the ground due to the impact - a chimney breaks due to gravitational acceleration causing large internal stresses. They are utterly unrelated.

Chalk will break into any number of pieces based on the specifics of the impact. Try a higher energy impact....

Chimneys/towers break into 2 or more pieces based on their geometry and strength. HERE is one that broke into two pieces.

Are they indeed? That is a pretty strong statement, much stronger then my hunch that they may be related.

Only if you drop the chalk very carefully can you make it hit anyway other then one end first. As soon as one end hits first you have a "falling chimney"

I think your statement is to strong. I would certainly buy " there is some doubt" but not a "utterly unrelated"

EDIT:
I just looked at the pictures in your link. I disagree with you. It appears to me that the break in the 5th pic is a DIFFERENT break then the one in the 6th pic. If you ask me it broke into 3 pieces _+ change! PI!

A piece of chalk will fail when it hits the floor, as a result of shock waves travelling through the chalk at the speed of sound, which cause the brittle chalk to shatter.

A chimney will fail once its foundations removed, by collapse under gravitational fall in whatever manner the steeplejack has intended. I suspect the failure is due to local stress concentrations within the chimney walls exceeding some critical value, where it either snaps (if a 'toppling' fall has been planned), or just collapses in on itself (in a kind of 'telescopic' collapse).

I do think the scenarios are rather different.

In any case, if the chalk thing is true, it's quite a nice little discovery Integral!

Good questions, perhaps the fact that I made my observations some years ago at a single university, it may have been typical of that brand and size of chalk. ...

Actually it was one of profs. can't really remember which, who pointed this out.

Defiantly a fall with rotation is much different from a collapse, that is a very different scenario. Even a hollow chimney would be different from a solid cylinder such as a stick of chalk.

Integral, I presume you meant to claim that a piece of chalk tends to break in a ratio of lengths/mass equal to [itex]1:1:1:(\pi-3)[/itex]. The last proportion tends to further fragment into an indefinite number of pieces. Correct ?

Without a theoretical reason why this should be so (and I can't see one), I cannot accept it. Your assertion in fact reminded me of Buffon's needle, but then there really is a theoretical reason why the probability of an idealised thin needle of unit length intersecting an infinitesimally thin line on lined paper with unit spacing is [itex]\frac{2}{\pi}[/itex]. It's trivial to see that, and I've proved it myself. Your assertion, alas, I cannot see my way to proving.

Ahh, misunderstood what you were saying in the first post. The problem is still that it depends an awful lot on the energy of the impact. If the force is large enough, it'll still shatter the entire piece of chalk.

Hmm... I think that's an optical illusion due to the tower falling away from us, but I'm not sure. I'll look for more pics....

Yes, the specifics of the structure make a big difference. http://www.southcoasttoday.com/daily/05-99/05-30-99/c01lo082.htm [Broken] is one that looks to me like a hybrid between a "toppling" and "telescopic" collapse. It does not appear to break anywhere along the structure, but disintegrates from the bottom up as it falls over. A large building would do the same thing (but less toppling and more telescoping) because structurally they are much weaker than a masonary chimney - they would not be able to support their own weight leaning over even a little bit.

This is actually a fairly common college level dynamics problem (in fact, there is a thread open in college help about it...)

edit: http://www.randyspier61.com/photos1.html [Broken] is another one that appears to fall in 2 pieces.

http://www.www.dykon-explosivedemolition.com/Archives/AthensOhio/AthensOhio.htm [Broken] is a cool video clip of one that also appears to fall in two pieces. Click the index for more videos - most seem to break in two pieces, but there is one that doesn't break and another that crumbles (the 6 smokestacks clip).

Hmm...I wonder if it would depend on the brand of chalk. Dustless chalk is pretty dense and uniform, but more "traditional" chalk is a lot more porous and non-uniform. I wouldn't know how it breaks when you drop it because I'm not sure that in my entire life I've ever gotten a piece that wasn't already broken in two while still in the box, or pre-shattered by the person teaching in the lecture ahead of me, or that I didn't snap in half in my hand after the first few words (I learned to properly press hard on the board with the chalk so it is dark enough for the students to read, but then I end up snapping chalk...nobody was ever nice enough to buy me one of those nifty chalk holders). But, there must be a length requirement, because I'm pretty sure when I've dropped those short pieces, they didn't shatter into three more pieces (+ change). I think more often, just an edge chipped off, but it has been so long since I've had to used chalkboards instead of whiteboards that I'm not sure any more.