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2007 mathematics book by Demaine and O'Rourke
Geometric Folding Algorithms: Linkages, Origami, Polyhedra is a monograph on the mathematics and computational geometry of mechanical linkages, paper folding
Geometric_Folding_Algorithms
origami foldability problems. In 1893, Indian civil servant T. Sundara Row published Geometric Exercises in Paper Folding which used paper folding to demonstrate
Mathematics_of_paper_folding
Theorem about origami
O'Rourke, Joseph (2007), "12.2.2 Flat-Foldable Single-Vertex Mountain–Valley Patterns", Geometric Folding Algorithms, Cambridge University Press, pp. 203–210
Big-little-big_lemma
Computer scientist (b. 1981)
thesis was later incorporated into his book Geometric Folding Algorithms on the mathematics of paper folding published with Joseph O'Rourke in 2007. Demaine
Erik_Demaine
Edge-joined polygon with multiple principle shapes
ISSN 0925-7721. Demaine, Erik D.; O'Rourke, Joseph (2007). Geometric folding algorithms: linkages, origami, polyhedra. Cambridge: Cambridge University
Common_net
List of unsolved computational problems
O'Rourke, Joseph (2007). "24 Geodesics: Lyusternik–Schnirelmann". Geometric folding algorithms: Linkages, origami, polyhedra. Cambridge, England: Cambridge
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Edge-joined polygons which fold into a polyhedron
O'Rourke, Joseph (2007), "Chapter 22. Edge Unfolding of Polyhedra", Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Cambridge University Press, pp
Net_(polyhedron)
Branch of mathematics
formation, and embryonic patterning. Geometric constraints influence processes such as neural tube closure, cortical folding, branching morphogenesis, and craniofacial
Geometry
Flat-sided three-dimensional shape
Erik D.; O'Rourke, Joseph (2007), "23.2 Flexible polyhedra", Geometric Folding Algorithms: Linkages, origami, polyhedra, Cambridge University Press, Cambridge
Polyhedron
Complexity class of problems
O'Rourke, Joseph (2007). "24 Geodesics: Lyusternik–Schnirelmann". Geometric folding algorithms: Linkages, origami, polyhedra. Cambridge: Cambridge University
NP-intermediate
Flexible polyhedron with 14 triangle faces
Erik D.; O'Rourke, Joseph (2007), "23.2 Flexible polyhedra", Geometric Folding Algorithms: Linkages, origami, polyhedra, Cambridge University Press, Cambridge
Steffen's_polyhedron
Net obtained by cutting a polyhedron
Demaine, Erik; O'Rourke, Joseph (2007), "24.3 Star unfolding", Geometric Folding Algorithms, Cambridge University Press, pp. 366–372, ISBN 978-0-521-71522-5
Star_unfolding
World Scientific. Erik D. Demaine; Joseph O'Rourke (2007). Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press.
List of books in computational geometry
List_of_books_in_computational_geometry
Origami math problem
The napkin folding problem is a problem in geometry and the mathematics of paper folding that explores whether folding a square or a rectangular napkin
Napkin_folding_problem
Any finite subset of an algebraic curve has a linkage which traces it
O'Rourke, Joseph (2007), "3.2 Kempe's Universality Theorem", Geometric Folding Algorithms, Cambridge University Press, pp. 31–40, ISBN 978-0-521-71522-5
Kempe's_universality_theorem
1893 book on making polygons with origami
Geometric Exercises in Paper Folding is a book on the mathematics of paper folding. It was written by Indian mathematician T. Sundara Row, first published
Geometric Exercises in Paper Folding
Geometric_Exercises_in_Paper_Folding
British mathematician (1849–1922)
O'Rourke, Joseph (2007), "3.2 Kempe's Universality Theorem", Geometric Folding Algorithms, Cambridge University Press, pp. 31–40, ISBN 978-0-521-71522-5
Alfred_Kempe
quantum algorithms Quantum optimization algorithms: family of quantum algorithms for optimization problems Quantum phase estimation algorithm: estimates
List_of_algorithms
Set of points where the shortest paths from a specific starting point cease to be unique
Demaine, Erik; O'Rourke, Joseph (2007). "24.1.1 Source unfolding". Geometric Folding Algorithms. Cambridge University Press. pp. 359–362. ISBN 978-0-521-71522-5
Cut_locus
Tetrahedron whose faces are all congruent
MR 2341323, S2CID 32897155. Demaine, Erik; O'Rourke, Joseph (2007), Geometric Folding Algorithms, Cambridge University Press, p. 424, ISBN 978-0-521-71522-5.
Disphenoid
O'Rourke, Joseph (2007). "Chapter 22. Edge Unfolding of Polyhedra". Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press. pp
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
2018 book by Michael Friedman
History of Folding in Mathematics: Mathematizing the Margins is a book in the history of mathematics on the mathematics of paper folding. It was written
A History of Folding in Mathematics
A_History_of_Folding_in_Mathematics
Description of flat one-vertex origami
15: Single-vertex crease patterns", Course Notes for 6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Massachusetts Institute of Technology
Kawasaki's_theorem
3-dimensional geometric figure
Erik D.; O'Rourke, Joseph (2007), "23.2 Flexible polyhedra", Geometric Folding Algorithms: Linkages, origami, polyhedra, Cambridge University Press, Cambridge
Flexible_polyhedron
Polygon with four crossed edges of two lengths
antiparallelogram linkage. Demaine, Erik; O'Rourke, Joseph (2007), Geometric Folding Algorithms, Cambridge University Press, pp. 32–33, doi:10.1017/CBO9780511735172
Antiparallelogram
American computer scientist
Goodman and Csaba Tóth. 3rd Ed. (2017). ISBN 978-1-49871-139-5 [3] Geometric Folding Algorithms: Linkages, Origami, Polyhedra, with Erik D. Demaine (2007).
Joseph_O'Rourke_(professor)
Japanese art of paper folding
to fold, and "kami", meaning paper. Until recently, not all forms of paper folding were grouped under the word origami. Before that, paper folding for
Origami
Geometric pattern characteristic of Muslim art
that such constructions are in effect algorithms, making Islamic geometric patterns forerunners of modern algorithmic art. The circle symbolizes unity and
Islamic_geometric_patterns
Computational problem
problems can be solved with grid-based algorithms that overlay a grid on top of configuration space, or geometric algorithms that compute the shape and connectivity
Motion_planning
Optimization algorithm
optimization algorithm for the 2D HP protein folding problem[dead link]," Proceedings of the 3rd International Workshop on Ant Algorithms/ANTS 2002, Lecture
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Existence of geodesic circles on surfaces
O'Rourke, Joseph (2007), "24 Geodesics: Lyusternik–Schnirelmann", Geometric folding algorithms: Linkages, origami, polyhedra, Cambridge: Cambridge University
Theorem of the three geodesics
Theorem_of_the_three_geodesics
Press. 2nd ed., 1991. Demaine, Erik; O'Rourke, Joseph (2007). Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press. Deza
List_of_books_about_polyhedra
Python module
algorithms of graph-tool are implemented in C++, making extensive use of metaprogramming, based heavily on the Boost Graph Library. Many algorithms are
Graph-tool
separator itself) is small. When a geometric separator exists, it can be used for building divide-and-conquer algorithms for solving various problems in
Geometric_separator
Self-crossing 8-sided flexible polyhedron
Erik D.; O'Rourke, Joseph (2007), "23.2 Flexible polyhedra", Geometric Folding Algorithms: Linkages, origami, polyhedra, Cambridge University Press, Cambridge
Bricard_octahedron
Growth of quantities at rate proportional to the current amount
time t. So exponentially complex algorithms are most often impractical, and the search for more efficient algorithms is one of the central goals of computer
Exponential_growth
Demaine, Erik; O'Rourke, Joseph (2007), "24.1.1 Source unfolding", Geometric Folding Algorithms, Cambridge University Press, pp. 359–362, ISBN 978-0-521-71522-5
Source_unfolding
Method in geometry for representing a polygon by a topological skeleton
decompose complex geometric domains for hydrodynamic and shallow-water modeling. By analyzing the wavefront propagation layers, algorithms can automatically
Straight_skeleton
Branch of mathematics
of these items either by using or improving one of these algorithms, or by finding algorithms whose complexity is singly exponential in the number of the
Algebraic_geometry
Producing images of 3D scenes
computer graphics used geometric algorithms or ray casting to remove the hidden portions of shapes, or used the painter's algorithm, which sorts shapes by
Rendering_(computer_graphics)
American artist and mathematician
diseases", Boston Globe. Demaine, Erik (2009), "Algorithms Meet Art, Puzzles and Magic", Proc. Algorithms and Data Structures Symposium (WADS 2009), Banff
Martin_Demaine
AI research laboratory
cases. The sorting algorithm was accepted into the C++ Standard Library sorting algorithms, and was the first change to those algorithms in more than a decade
Google_DeepMind
Mapping arbitrary data to fixed-size values
keys into fixed-length (usually machine-word-length or less) values, by folding them by words or other units using a parity-preserving operator like ADD
Hash_function
Algorithms for calculating square roots
Square root algorithms compute the non-negative square root S {\displaystyle {\sqrt {S}}} of a positive real number S {\displaystyle S} . Since all square
Square_root_algorithms
zero matrix Algorithms for matrix multiplication: Strassen algorithm Coppersmith–Winograd algorithm Cannon's algorithm — a distributed algorithm, especially
List of numerical analysis topics
List_of_numerical_analysis_topics
Rational design of new protein molecules
algorithms have been developed specifically for the protein design problem. These algorithms can be divided into two broad classes: exact algorithms,
Protein_design
Protein folding hypothesis
The folding funnel hypothesis is a specific version of the energy landscape theory of protein folding, which assumes that a protein's native state corresponds
Folding_funnel
Mathematical optimization problem restricted to integers
Branch and bound algorithms have a number of advantages over algorithms that only use cutting planes. One advantage is that the algorithms can be terminated
Integer_programming
Canadian computer scientist (1944–2019)
polygons in 3D: a survey", in Physical Knots: Knotting, Linking, and Folding Geometric Objects in R3, AMS Special Session on Physical Knotting, Linking,
Godfried_Toussaint
S2CID 12629688. Hofacker IL, Stadler PF (May 2006). "Memory efficient folding algorithms for circular RNA secondary structures". Bioinformatics. 22 (10): 1172–1176
List of RNA structure prediction software
List_of_RNA_structure_prediction_software
Mathematics of number-placement puzzle
often be solved in practice by methods that include the dancing links algorithm. The answer to the question 'How many Sudoku grids are there?' depends
Mathematics_of_Sudoku
Measure of algorithmic complexity
any other algorithm up to an additive constant that depends on the algorithms, but not on the strings themselves. Solomonoff used this algorithm and the
Kolmogorov_complexity
Numerical methods for matrix eigenvalue calculation
is designing efficient and stable algorithms for finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors. Given an
Eigenvalue_algorithm
Method of drawing geometric objects
Monthly 95 (1988), no. 3, 185-194. Row, T. Sundara (1966). Geometric Exercises in Paper Folding. New York: Dover. Conway, John H. and Richard Guy: The Book
Straightedge and compass construction
Straightedge_and_compass_construction
Generative process for base sequences
computationally expensive than the energy minimization algorithms needed for thermodynamic or geometrical modeling, and being easier to implement, but at the
Nucleic_acid_design
Canadian computer scientist
Lubiw, Anna (1999), "Folding and one straight cut suffice", Proceedings of the Tenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '99), pp. 891–892
Anna_Lubiw
Base pairs in molecular genetics
secondary structural blocks which aid the folding of RNA complexes and three dimensional structures. The overall folded RNA is stabilized by the tertiary and
Non-canonical_base_pairing
Research institute in computer science
computer science with a focus on algorithms and their applications in a broad sense. It hosts fundamental research (algorithms and complexity, programming
Max Planck Institute for Informatics
Max_Planck_Institute_for_Informatics
American mathematician
24, 2008) was a mathematician known for his seminal contributions to geometric group theory and 3-manifold topology. Stallings was a Professor Emeritus
John_R._Stallings
Geometric shape formed from squares
Currently, the most effective algorithms belong to the transfer-matrix paradigm. They may be called transfer matrix algorithms (TMAs) for short. Andrew Conway
Polyomino
Number, approximately 3.14
simple spigot algorithm in 1995. Its speed is comparable to arctan algorithms, but not as fast as iterative algorithms. Another spigot algorithm, the BBP digit
Pi
Python library for graphs and networks
NetworkX provides various layout algorithms for visualizing graphs in two-dimensional space. These layout algorithms determine the positions of nodes
NetworkX
under extension. These algorithms preserve area but do not, in general, preserve line length. Restoration using this type of algorithm can be carried out
Section_restoration
One-dimensional approximation to a shape
Zhang-Suen Thinning Algorithm Skeletonization algorithms can sometimes create unwanted branches on the output skeletons. Pruning algorithms are often used
Topological_skeleton
Study of the properties of codes and their fitness
science practice; cryptographic algorithms are designed around computational hardness assumptions, making such algorithms hard to break in practice by any
Coding_theory
Graphics languages
logic and circuits.ee Entity–relationship diagrams – er Polygon folding diagrams – folding Graph drawing with automatic layout options – graphdrawing L-system
PGF/TikZ
Property in graph theory
dynamic programming algorithms". In Chan, Timothy M. (ed.). Proceedings of the Thirtieth Annual ACM–SIAM Symposium on Discrete Algorithms, SODA 2019, San
Cutwidth
Japanese origamist (born 1982)
interdisciplinary perspective, combining approaches from the mathematics of paper folding, structural rigidity, computational geometry, architecture, and materials
Tomohiro_Tachi
Calculus of vector-valued functions
not generalize to higher dimensions, but the alternative approach of geometric algebra, which uses the exterior product, does (see § Generalizations
Vector_calculus
Measurement process
Seismic migration is the process by which seismic events are geometrically re-located in either space or time to the location the event occurred in the
Seismic_migration
Unique positive real number which when multiplied by itself gives 2
There are many algorithms for approximating 2 {\displaystyle {\sqrt {2}}} as a ratio of integers or as a decimal. The most common algorithm for this, which
Square_root_of_2
Straight path on a curved surface or a Riemannian manifold
g_{S}} are metrics on N {\displaystyle N} and S {\displaystyle S} . While geometric in nature, the idea of a shortest path is so general that it easily finds
Geodesic
Homotopic map of a graph
In the mathematical subject of geometric group theory, a train track map is a continuous map f from a finite connected graph to itself which is a homotopy
Train_track_map
(DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. In most IGS, one starts construction
List of interactive geometry software
List_of_interactive_geometry_software
Puzzles solved by mechanical manipulation
Self-reference Mechanical Combination Disentanglement Lock Go problems Folding Stick Tiling Tour Sliding Chess Maze (Logic maze) Word and Number Crossword
Combination_puzzle
Theorem in group theory
One sees that the folding moves do not increase complexity but they do decrease the number of edges in Zj. Therefore, the folding process must terminate
Grushko_theorem
Belgian computer scientist and mathematician
structures, and recreational mathematics. He is professor and co-head of the algorithms research group at the Université libre de Bruxelles (ULB) with Jean Cardinal
Stefan_Langerman
American computer scientist (1925–1999)
Coding. Retrieved June 17, 2011. Haeberli, Paul (November 1996). "Geometric Paper Folding: Dr. David Huffman". GRAFICA Obscura. Retrieved June 17, 2011.
David_A._Huffman
Geometric partition where pieces are connected by "hinged" points
known as a swing-hinged dissection or Dudeney dissection, is a kind of geometric dissection in which all of the pieces are connected into a chain by "hinged"
Hinged_dissection
Bioinformatics subfield
macromolecular 3D structures such as comparisons of overall folds and local motifs, principles of molecular folding, evolution, binding interactions, and structure/function
Structural_bioinformatics
The study of geometric morphometrics in anthropology has made a major impact on the field of morphometrics by aiding in some of the technological and
Geometric morphometrics in anthropology
Geometric_morphometrics_in_anthropology
Application of computer graphics to create or contribute to images
could depict only objects consisting of planar polygons. Advances in algorithms and electronics in flight simulator visual systems and CGI in the 1970s
Computer-generated_imagery
Branch of biology
Darwin: Malthus argued that growth would be exponential (he uses the word "geometric") while resources (the environment's carrying capacity) could only grow
Mathematical and theoretical biology
Mathematical_and_theoretical_biology
Arrangement of amino acid sequence
collection of such methods. The algorithms are classified according to the type of input they require. Sequence-based algorithms require only the sequence of
Circular permutation in proteins
Circular_permutation_in_proteins
or tilings. Paper-folding was used in 1893 by T. Sundara Rao in his Geometric Exercises in Paper Folding to demonstrate geometrical proofs. The mathematics
Mathematics_and_art
Mathematical model used in music theory
represents human perceptions of pitches, chords, and keys in the same geometric space. It was proposed in 2000 by Elaine Chew in her MIT doctoral thesis
Spiral_array_model
Company logo
difference in the logo is the change in the typeface. It switched to a modern, geometric sans-serif typeface called Product Sans, created in-house at Google (which
Google_logo
The packing constant of a geometric body is the largest average density achieved by packing arrangements of congruent copies of the body. For most bodies
List of shapes with known packing constant
List_of_shapes_with_known_packing_constant
of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures List of data structures List of derivatives
List_of_theorems
Branch of mathematics
search capable of escaping from local minima Evolutionary algorithms (e.g., genetic algorithms and evolution strategies) Differential evolution, a method
Global_optimization
Branch of mathematical analysis
Chen, YangQuan; Li, Changpin; Ding, Hengfei (22 May 2014). "High-Order Algorithms for Riesz Derivative and Their Applications". Abstract and Applied Analysis
Fractional_calculus
Study of mathematical knots
knots. Algorithms exist to solve this problem, with the first given by Wolfgang Haken in the late 1960s (Hass 1998). Nonetheless, these algorithms can be
Knot_theory
Array of numbers
impractical matrix multiplication algorithms have been developed, as have speedups to this problem using parallel algorithms or distributed computation systems
Matrix_(mathematics)
Polynomial equation of degree 3
theorem.) geometrically: using Omar Khayyam's method. trigonometrically numerical approximations of the roots can be found using root-finding algorithms such
Cubic_equation
Branch of mathematics
instance, the underlying set of the symmetry group of a geometric object is made up of geometric transformations, such as rotations, under which the object
Algebra
1962), German-Swiss expert on graph theory, randomized algorithms, and approximation algorithms Irene Stegun (1919–2008), American mathematician who edited
List_of_women_in_mathematics
Indian-American computer scientist
research publications include work on algorithms for finding dense subgraphs,[A] a version of the algorithmic Lovász local lemma for large numbers of
Barna_Saha
American computer scientist
developed algorithms for time-division multiple access (used in cell-phone technology). For her doctorate she developed flow-control algorithms for handling
Jeannine_Mosely
the best probable output with specific algorithms. However, with NMT, the approach employs dynamic algorithms to achieve better translations based on
Applications of artificial intelligence
Applications_of_artificial_intelligence
The main idea of these methods is to capture the connectivity of a geometrically complex high-dimensional space by constructing a graph of local paths
Stochastic_roadmap_simulation
GEOMETRIC FOLDING-ALGORITHMS
GEOMETRIC FOLDING-ALGORITHMS
GEOMETRIC FOLDING-ALGORITHMS
GEOMETRIC FOLDING-ALGORITHMS
GEOMETRIC FOLDING-ALGORITHMS
GEOMETRIC FOLDING-ALGORITHMS
GEOMETRIC FOLDING-ALGORITHMS
GEOMETRIC FOLDING-ALGORITHMS
GEOMETRIC FOLDING-ALGORITHMS