Károly Bezdek, Robert Connelly, Balázs Csikós
Abstract. Almost 20 years ago, R. Alexander conjectured that, under an arbitrary contraction of the center points of finitely many congruent disks in the plane, the perimeter of the intersection of...
Flexible suspensions with a hexagonal equator (2009)
Alexandrov, Victor, Connelly, Robert
We construct a flexible (non immersed) suspension with a hexagonal equator in Euclidean 3-space and study its properties related to the Strong Bellows Conjecture which reads as follows: if an...
Instructions in The Independent Euler (2009)
W. U. Behrens, John Nelder, Howard Garns, Robert Connelly, Peter J. Cameron, Cβ Aγ Bα, ...
Sudoku – an alternative history There’s no mathematics involved. Use logic and reasoning to solve the puzzle.
Robert Connelly, Sándor P. Fekete, Tu Braunschweig, Erik D. Demaine, ...
We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid...
Robert Connelly, Erik D. Demaine, Günter Rote
Abstract. Consider a planar linkage, consisting of disjoint polygonal arcs and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another...
Aquino, Wilkins, Connelly, Robert, Earls, Christopher J., Ewert, Eduard, Guan, Y., Guggenberger, Werner, ...
IASS-IACM 2008 Session: Structural Stability -- Session Organizer: Herbert MANG (Technical University of Vienna) -- Plenary Lecture: Abstract, Slides and Video: "Answers to three not quite...
Károly Bezdek, Robert Connelly
Abstract. If a finite set of balls of radius π/2 (hemispheres) in the unit sphere S n is rearranged so that the distance between each pair of centers does not decrease, then the (spherical) volume...
HIGHER ORDER RIGIDITY- WHAT IS THE PROPER DEFINITION? (2008)
Robert Connelly, Herman Servatius
Abstract. We show that there is a bar–and–joint framework G(p) which has a configuration p in the plane such that the component of p in the space of all planar configurations of G has a cusp at...
When is a symmetric pin-jointed framework isostatic? (2008)
Connelly, Robert, Fowler, Patrick, Guest, Simon, Schulze, Bernd, Whiteley, Walter
Maxwell's rule from 1864 gives a necessary condition for a framework to be isostatic in 2D or in 3D. Given a framework with point group symmetry, group representation theory is exploited to provide...
CLASSIFICATION OF FIRST-ORDER FLEXIBLE REGULAR BICYCLE POLYGONS (2008)
Robert Connelly, Balázs Csikós
Abstract. A bicycle (n, k)-gon is an equilateral n-gon whose k-diagonals are equal. S. Tabachnikov proved that a regular n-gon is first-order flexible as a bicycle (n, k)-gon if and only if there is...
gerechte designs, resolutions, affine space, spreads, reguli, and Hamming codes (2008)
R. A. Bailey, Peter J. Cameron, Robert Connelly
The popular Sudoku puzzle was invented, with the name “number place”, by Harold Garns in 1979. The puzzle consists of a 9 × 9 grid partitioned into 3 × 3 subsquares, some of which contain...
ABSTRACT Dedicated to Godfried Toussaint (2008)
Robert Connelly, Erik D. Demaine
We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid...
Stress Matrices and M Matrices (2008)
In [2] a connection is made between what are called “M ” matrices, as used in Colin de Verdière’s theory of graph invariants, and stress matrices as used in rigidity theory in [1]. Following a...
Robert Connelly, Sándor P. Fekete, Tu Braunschweig, Erik D. Demaine, ...
We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid...
gerechte designs, resolutions, affine space, spreads, reguli, and Hamming codes (2008)
R. A. Bailey, Peter J. Cameron, Robert Connelly
Solving a Sudoku puzzle involves putting the symbols 1,..., 9 into the cells of a 9 × 9 grid partitioned into 3 × 3 subsquares, in such a way that each symbol occurs just once in each row, column,...
www.elsevier.com/locate/ejc Rigidity of packings (2008)
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors...
Robert Connelly, Erik D. Demaine
The line numbers in the margins should encourage you to quickly report any errors that you spot to the authors. Remarks of any other kind are equally welcome. (If you don't like those numbers,...
Pushing disks apart — the Kneser–Poulsen conjecture in the plane (2007)
Károly Bezdek, Robert Connelly
We give a proof of the planar case of a longstanding conjecture of Kneser (1955) and Poulsen (1954). In fact, we prove more by showing that if a nite set of disks in the plane is rearranged so that...
Instructions in The Independent Euler (2007)
Peter J. Cameron, W. U. Behrens, John Nelder, Howard Garns, Robert Connelly
There’s no mathematics involved. Use logic and reasoning
On the infinitesimal rigidity of weakly convex polyhedra (2006)
Connelly, Robert, Schlenker, Jean-Marc
The main motivation here is a question: whether any polyhedron which can be subdivided into convex pieces without adding a vertex, and which has the same vertices as a convex polyhedron, is...
Locked and Unlocked Chains of Planar Shapes (2006)
Connelly, Robert, Demaine, Erik D., Demaine, Martin L., Fekete, Sandor P., Langerman, Stefan, Mitchell, Joseph S. B., ...
We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid...
Locked and unlocked chains of planar shapes (2006)
Robert Connelly, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Stefan Langerman, ...
We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid...
A polygonal chain in the plane without self-intersections can open expansively until it achieves a convex configuration. What can you add to the chain to insure that the whole object does not...
Review of Convex Polyhedra by A. D. Alexandrov (2006)
This book was first published in Russion in 1950, then translated into German in 1958, and V. A. Zalgaller has updated and substantially increased this English edition with more recent related...
Locked and unlocked chains of planar shapes (2006)
Robert Connelly, Erik D. Demaine, Martin L. Demaine, Sándor Fekete, Stefan Langerman, ...
If we attach to each bar in a polygonal chain a rigid shape whose inward normals all hit the attached bar, and the resulting hinged chain of shapes does not overlap itself, then this chain can always...
J. Computational Physics Manuscript A Linear Programming Algorithm to Test for Jamming in (2003)
Hard-sphere Packings, Ar Donev, Salvatore Torquato, Frank H. Stillinger, Robert Connelly
Jamming in hard-particle packings has been the subject of considerable interest in recent years. In a paper by Torquato and Stillinger [J.Phys.Chem. B, 105 (2001)], a classification scheme of jammed...
A Linear Programming Algorithm to Test for Jamming in Hard-Sphere Packings (2002)
Donev, Aleksandar, Torquato, Salvatore, Stillinger, Frank H., Connelly, Robert
Jamming in hard-particle packings has been the subject of considerable interest in recent years. In a paper by Torquato and Stillinger [J. Phys. Chem. B, 105 (2001)], a classification scheme of...
Infinitesimally locked self-touching linkages with applications to locked trees (2002)
Robert Connelly, Erik D. Demaine, Günter Rote
Abstract. Recently there has been much interest in linkages (bar-and-joint frameworks) that are locked or stuck in the sense that they cannot be moved into some other configuration while preserving...
Infinitesimally Locked Self-Touching Linkages with Applications to Locked Trees (2002)
Robert Connelly, Erik D. Demaine, Günter Rote
Recently there has been much interest in linkages (bar-and-joint frameworks) that are locked or stuck in the sense that they cannot be moved into some other configuration while preserving the bar...
Pushing disks apart - The Kneser-Poulsen conjecture in the plane (2001)
Bezdek, Károly, Connelly, Robert
We give a proof of the planar case of a longstanding conjecture of Kneser (1955) and Poulsen (1954). In fact, we prove more by showing that if a finite set of disks in the plane is rearranged so that...
Straightening polygonal arcs and convexifying polygonal cycles (2000)
Robert Connelly, Erik D. Demaine, Günter Rote
Consider a planar linkage, consisting of disjoint polygonal arcs and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another arc or...
Straightening polygonal arcs and convexifying polygonal cycles (2000)
Robert Connelly, Erik D. Demaine, Günter Rote
Consider a planar linkage, consisting of disjoint polygonal arcs and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another arc or...
Straightening polygonal arcs and convexifying polygonal cycles (2000)
Robert Connelly, Erik D. Demaine, Gunter Rote
Consider a planar linkage, consisting of disjoint polygonal arcs and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another arc or...
Second-order rigidity and prestress stability for tensegrity frameworks (1996)
Robert Connelly, Walter Whiteley
Abstract. This paper defines two concepts of rigidity for tensegrity frameworks (frameworks with cables, bars, and struts): prestress stability and second-order rigidity. We demonstrate a hierarchy...
Covering a Triangle with Disks Centered on its Boundary (1991)
Connelly, Robert, Freimer, Robert
Let $\cal P$ be a triangle and $\cal D_{1}, \cal D_{2}$ be disks centered on the boundary of $\cal P$ with radii $r_{1}$, $r}_{2}$. The disks are chosen so that $\cal D_{1}$ $\cup$ $\cal D$$_{2}$...
Covering a Triangle with Disks Centered on its Boundary (1991)
Connelly, Robert, Freimer, Robert
Let $\cal P$ be a triangle and $\cal D_{1}, \cal D_{2}$ be disks centered on the boundary of $\cal P$ with radii $r_{1}$, $r}_{2}$. The disks are chosen so that $\cal D_{1}$ $\cup$ $\cal D$$_{2}$...
Rigid Circle and Sphere Packings. Part II: Infinite Packings with Finite Motion (1990)
Une juxtaposition P de cercles dans le plan est dite n-stable pour n = 1,2, . . . si tout ensemble de n cercles est tenu fixe par les autres. Pest destabilité finie si elle est n-stable pour tou t n...
Rigid Circle and Sphere Packings. Part II: Infinite Packings with Finite Motion (1990)
Une juxtaposition P de cercles dans le plan est dite n-stable pour n = 1,2, . . . si tout ensemble de n cercles est tenu fixe par les autres. Pest destabilité finie si elle est n-stable pour tou t n...
Rigid Circle and Sphere Packings. Part II: Infinite Packings with Finite Motion (1990)
Une juxtaposition P de cercles dans le plan est dite n-stable pour n = 1,2, . . . si tout ensemble de n cercles est tenu fixe par les autres. Pest destabilité finie si elle est n-stable pour tou t n...
Rigid Circle and Sphere Packings. Part I: Finite Packings (1988)
On montre qu'une juxtaposition P de cercles (ou de sphères) dans un polygone plan (ou un polyhèdre) est localement maximalement dense si, et seulement si, il existe une sousjuxtaposition qui...
Rigid Circle and Sphere Packings. Part I: Finite Packings (1988)
On montre qu'une juxtaposition P de cercles (ou de sphères) dans un polygone plan (ou un polyhèdre) est localement maximalement dense si, et seulement si, il existe une sousjuxtaposition qui...
Rigid Circle and Sphere Packings. Part I: Finite Packings (1988)
On montre qu'une juxtaposition P de cercles (ou de sphères) dans un polygone plan (ou un polyhèdre) est localement maximalement dense si, et seulement si, il existe une sousjuxtaposition qui...
Suppose one holds two sticks in the form of a cross in one hand, and places a rubber band in tension around the four ends. When it is released, it comes to rest in the shape of a convex quadrilateral...
When is a triangulated polyhedral surface rigid? In 1813 Cauchy]4] showed the following: THEOREM C. If each natural face of a convex polyhedral surface is held rigid, then the whole surface is rigid.
On graphs with a constant link, II (1975)
Brown, Morton B., Connelly, Robert
We study the following problem: For which finite graphs L do there exist graphs G such that the link (i.e., the neighborhood subgraph) of each vertex of G is isomorphic to L? We give a complete...
On the infinitesimal rigidity of weakly convex polyhedra
Robert Connelly, Jean-marc Schlenker
The main motivation here is a question: whether any polyhedron which can be subdivided into convex pieces without adding a vertex, and which has the same vertices as a convex polyhedron, is...