Brainteasers B 201: Strange painting, Quantum (May/June 1997) 13 (A. Spivak)
Strange painting. There is a painting on the wall of Dr. Smile's waiting
room. The unusual thing about this painting is the way it's hung. Dr. Smile
hammered two nails (instead of one) into the wall. He says that he wound
the picture wire around these nails in such a way that the painting would
fall if either the nail were pulled out. How did he do it?
SOLUTION:
We have a left (L) and the right (R) nail.
XXXXX is the wall. (o) goes down to the picture.
(Viewing from the top)
X o
XLL\LLLL|L <- left nail
X | \ |
X | \ |
X | \ |
XR|RRRR\RR <- right nail
X o
The Borromean rings give a solution to this problem (Werner Schw\"arzler).
Therefore a three nail configuration is possible too.
References:
- H. Brunn;
Ueber Verkettung,
Sitzungsbericht der Bayerischen Akademie der Wissenschaft Mathematisch
Naturwissenschaftliche Abteilung 22 (1892) 77-99
JFM 24.0507.01
(Borromean rings and their generalizations)
- Walter Lietzmann;
Anschauliche Topologie,
R. Oldenbourg Verlag, M\"unchen, 1955
- I.VI.12 Verkettungen (p80-83)
(Borromean rings and their generalizations)
- Rob Scharein;
Brunnian Links, (KnotPlot Site)
http://www.cs.ubc.ca/nest/imager/contributions/scharein/brunnian/brunnian.html
- A. Spivak
Brainteasers B 201: Strange painting,
Quantum (May/June 1997) p13, p60 figure 5
- the two nail problem
- Ian Stewart;
Game, Set and Math, 1989
- Chapter 7: Parity Piece, p103-106
Borromean rings and their generalizations
Borromean Rings:
- H.S.M. Coxeter;
Symmetrical combinations of three or four hollow triangles,
Math. Intelligencer 16, 3 (1994), 25-30.
- Martin Gardner;
The Unexpected Hanging and Other Mathematical Diversions
Simon & Schuster (1968)
- Chapter 2: 2 Knots and Borromean Rings
- Slavik V. Jablan;
Are Borromean links so rare?
http://members.tripod.com/vismath5/bor/
(Borromean rings and their generalizations)
- B. Lindstr\"om and H.O.Zetterstr\"om;
Borromean circles are impossible,
American Mathematical Monthly 98 (1991), 340-341.
- ???
Borromean Squares,
American Mathematical Monthly 99:4 (1992) 377
- no realization possible with euklidean circles
--
http://www.mathematik.uni-bielefeld.de/~sillke/
mailto:Torsten.Sillke@uni-bielefeld.de