[math-fun] Isn't it odd that when you flex a circular wafer,
it fails along a diameter--the widest point? Presumably, sufficient elongation parallel to that diameter will bifurcate the line of probable failure. E.g., is there a shape that half the time breaks 1:2 and half 2:1? Convex? Could it be an ellipse? Is there a shape where the crack might be uniformly anywhere? --rwg
How do you define flex? Hold diametrically opposite points on the edge and try to fold it in two? Or something else? And . . . what kind of material are you thinking of? --Dan
On Nov 21, 2014, at 2:30 PM, Bill Gosper <billgosper@gmail.com> wrote:
it fails along a diameter--the widest point? Presumably, sufficient elongation parallel to that diameter will bifurcate the line of probable failure. E.g., is there a shape that half the time breaks 1:2 and half 2:1? Convex? Could it be an ellipse? Is there a shape where the crack might be uniformly anywhere? --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I am unable to find a combination of search words that will dig up anything about the well-known phenomenon of a spaghetti noodle breaking into 3 parts. Hold each end, bend until broken. Find 3 pieces. If unconvinced, do it again. Hilarie
Date: Fri, 21 Nov 2014 14:30:20 -0800 From: Bill Gosper <billgosper@gmail.com>
it fails along a diameter--the widest point? Presumably, sufficient elongation parallel to that diameter will bifurcate the line of probable failure. E.g., is there a shape that half the time breaks 1:2 and half 2:1? Convex? Could it be an ellipse? Is there a shape where the crack might be uniformly anywhere? --rwg
In about 2005, I read in Science News about work done by Andrew Belmonte at Penn State on this very question. It's getting late, so I'll let others Google it and dig up info, but this should get you started. Bob --- Hilarie Orman wrote:
I am unable to find a combination of search words that will dig up anything about the well-known phenomenon of a spaghetti noodle breaking into 3 parts. Hold each end, bend until broken. Find 3 pieces. If unconvinced, do it again.
Hilarie
Date: Fri, 21 Nov 2014 14:30:20 -0800 From: Bill Gosper <billgosper@gmail.com>
it fails along a diameter--the widest point? Presumably, sufficient elongation parallel to that diameter will bifurcate the line of probable failure. E.g., is there a shape that half the time breaks 1:2 and half 2:1? Convex? Could it be an ellipse? Is there a shape where the crack might be uniformly anywhere? --rwg
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At 06:42 PM 11/21/2014, Hilarie Orman wrote:
I am unable to find a combination of search words that will dig up anything about the well-known phenomenon of a spaghetti noodle breaking into 3 parts. Hold each end, bend until broken. Find 3 pieces. If unconvinced, do it again.
New Scientist "Last Word" (questions column), Dec 2, 2006 Pasta puzzle If you bend a piece of dried spaghetti it breaks into three pieces with the middle piece flying out. Why does this happen? (Continued) This question has for a long time perplexed The Last Word and its readers. Some theories were proposed in our 12 December 1998 issue, but nothing had been verified until Basile Audoly and Sebastien Neukirch published their paper "Fragmentation of rods by cascading cracks: Why spaghetti does not break in half" in Physical Review Letters last year (vol 95, p 95505), which won them the 2006 Ig Nobel Prize for Physics. A précis follows - Ed While an Ig Nobel might have been the most Audoly and Neukirch could expect for their work with pasta, the same question intrigued a man from the other end of the research spectrum. Physics Nobel laureate Richard Feynman frequently presented house guests with strands of dried spaghetti and challenged them to explain the way it broke. Audoly and Neukirch broke dried strands of spaghetti of varying thicknesses and lengths by clamping one end and then bending it from the other. They found that the unexpected three-part breakage occurs because of "flexural waves". When the curvature of the spaghetti reaches a critical point, the first break appears. The shock of this causes a flexural wave to ripple down each of the two resulting lengths at high speed and amplitude. The two halves do not have time to relax and straighten before being hit by the flexural wave, which causes them to curve even further and suffer more breaks, leading to a cascade of cracks in the pasta. Often, more than three pieces are created when this happens. A video of the process can be seen at <http://www.lmm.jussieu.fr/spaghetti/index.html>www.lmm.jussieu.fr/spaghetti/index.html. While snapping spaghetti is, in itself, a rather mindless if fun pastime, Audoly and Neukirch's work also provides important information about failures in other elongated, brittle structures, including human bones and bridge spans.
Applying an ideal planar bending to an almost-ideal spaghetto, maybe it starts to look roughly like some shape of isosceles triangle, with two symmetrical local minima of the curvature. Because a real spaghettus won't be perfectly symmetrical, one of those local maxes will reach its breaking point before the other. Which would release the larger portion to snap back in the opposite direction. As the middle piece then tries to snap back toward straight, the already weakened local max is just too stressed out and falls apart. I'd like to see a espal-emit movie of this happening, which might clear a lot of stuff up. --Dan
On Nov 21, 2014, at 6:42 PM, Hilarie Orman <ho@alum.mit.edu> wrote:
I am unable to find a combination of search words that will dig up anything about the well-known phenomenon of a spaghetti noodle breaking into 3 parts. Hold each end, bend until broken. Find 3 pieces. If unconvinced, do it again.
Hilarie
Date: Fri, 21 Nov 2014 14:30:20 -0800 From: Bill Gosper <billgosper@gmail.com>
it fails along a diameter--the widest point? Presumably, sufficient elongation parallel to that diameter will bifurcate the line of probable failure. E.g., is there a shape that half the time breaks 1:2 and half 2:1? Convex? Could it be an ellipse? Is there a shape where the crack might be uniformly anywhere? --rwg
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Where of course "minima" means "maxima".
On Nov 21, 2014, at 10:33 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Applying an ideal planar bending to an almost-ideal spaghetto, maybe it starts to look roughly like some shape of isosceles triangle, with two symmetrical local minima of the curvature
Ask and ye shall get. Cf. this: < https://www.youtube.com/watch?v=8GutricnMNc >. --Dan
On Nov 21, 2014, at 10:33 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Applying an ideal planar bending to an almost-ideal spaghetto, maybe it starts to look roughly like some shape of isosceles triangle, with two symmetrical local minima of the curvature.
Because a real spaghettus won't be perfectly symmetrical, one of those local maxes will reach its breaking point before the other. Which would release the larger portion to snap back in the opposite direction.
As the middle piece then tries to snap back toward straight, the already weakened local max is just too stressed out and falls apart.
I'd like to see a espal-emit movie of this happening, which might clear a lot of stuff up.
--Dan
On Nov 21, 2014, at 6:42 PM, Hilarie Orman <ho@alum.mit.edu> wrote:
I am unable to find a combination of search words that will dig up anything about the well-known phenomenon of a spaghetti noodle breaking into 3 parts. Hold each end, bend until broken. Find 3 pieces. If unconvinced, do it again.
Hilarie
Date: Fri, 21 Nov 2014 14:30:20 -0800 From: Bill Gosper <billgosper@gmail.com>
it fails along a diameter--the widest point? Presumably, sufficient elongation parallel to that diameter will bifurcate the line of probable failure. E.g., is there a shape that half the time breaks 1:2 and half 2:1? Convex? Could it be an ellipse? Is there a shape where the crack might be uniformly anywhere? --rwg
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participants (5)
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Robert Baillie