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References (141)
-
S. Kosslyn (1994)
Image and Brain: The Resolution of the Imagery DebateJournal of Cognitive Neuroscience, 7
-
N. Biggs (1979)
The roots of combinatoricsHistoria Mathematica, 6
-
Axel Conrad, Tanja Hindrichs, Hussein Morsy, I. Wegener (1994)
Solution of the knight's Hamiltonian path problem on chessboardsDiscret. Appl. Math., 50
-
A. Turing (1937)
On Computable Numbers, with an Application to the Entscheidungsproblem.Journal of Symbolic Logic, 2
-
B. Butterworth (1999)
What Counts: How Every Brain is Hardwired for Math -
David Wells (1993)
The Penguin Book of Curious and Interesting Puzzles -
M. Danesi (2002)
The Puzzle Instinct: The Meaning of Puzzles in Human Life -
I. Bashmakova (2019)
Diophantus and Diophantine Equations -
Girolamo Cardano, S. Gould (1961)
The book on games of chance : "liber de ludo aleae" -
Dina Hiele-Geldof, P. Hiele, David Fuys, Dorothy Geddes, R. Tischler (1984)
English Translation of Selected Writings of Dina van Hiele-Geldof and Pierre M. van Hiele. -
Henry Dudeney (1958)
The Canterbury puzzles : and other curious problems -
J. Uexküll
Umwelt und Innenwelt der Tiere [microform] / von J. von Uexküll. -
K. Devlin (2011)
The Man of Numbers: Fibonacci's Arithmetic Revolution -
B. Averbach, O. Chein (1999)
Problem Solving Through Recreational Mathematics -
A. Margalit, M. Bar-Hillel (1983)
Expecting the unexpectedPhilosophia, 13
-
D. Klarner (1998)
Mathematical recreations : a collection in honor of Martin Gardner -
M. Kline (1985)
Mathematics and the Search for Knowledge -
P. Erdös (1934)
A Theorem of Sylvester and SchurJournal of The London Mathematical Society-second Series
-
Robin Wilson (2002)
Four Colors Suffice: How the Map Problem Was Solved -
George Warner, C. Wyatt, R. Dudley, A. Kendall (2010)
The Voyage of Robert Dudley, Afterwards Styled Earl of Warwick and Leicester and Duke of Northumberland, to the West Indies, 1594-1595 -
Laura Taalman (2007)
Taking Sudoku SeriouslyMath Horizons, 15
-
B. Russell (1998)
The Philosophy of Logical Atomism -
R. Roberts (1989)
Serendipity: Accidental Discoveries in Science -
M. Ascher (1990)
A River-Crossing Problem in Cross-Cultural Perspective.Mathematics Magazine, 63
-
M. Gessen (2009)
Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century -
J. Dewey (1927)
Half-Hearted NaturalismThe Journal of Philosophy, 24
-
D. Hudson. (1972)
Lewis Carroll: An Illustrated Biography -
M. Danesi (2003)
Second Language Teaching -
J. Neumann (1959)
The Computer and the Brain -
S. Kosslyn (1994)
Image and Brain -
S. Vajda (1989)
Fibonacci and Lucas Numbers and the Golden Section -
M. Brooke (1969)
150 Puzzles in Crypt-Arithmetic -
R. Gillings (2019)
Mathematics in the Time of the PharaohsMathematics: People · Problems · Results
-
M. Petkovic (2009)
Famous Puzzles of Great Mathematicians -
G. Frege
Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens -
K. Appel, W. Haken (1977)
Every planar map is four colorable. Part I: DischargingIllinois Journal of Mathematics, 21
-
J. Lagarias, T. Hales, Samuel Ferguson (2011)
The Kepler conjecture : the Hales-Ferguson proof by Thomas Hales, Samuel Ferguson -
G. Fauconnier, Mark Turner (2002)
The Way We Think: Conceptual Blending and the Mind''s Hidden Complexities. Basic Books -
D. Benson (1999)
The Moment of Proof: Mathematical Epiphanies -
A. Hinz, S. Klavžar, Uroš Milutinović, C. Petr (2013)
The Tower of Hanoi - Myths and Maths -
R. Thom (1977)
Structural stability and morphogenesis - an outline of a general theory of models -
Yair Neuman (2014)
Introduction to Computational Cultural Psychology -
T. Hales (2005)
A proof of the Kepler conjectureAnnals of Mathematics, 162
-
A. Cayley
The Collected Mathematical Papers: On the Theory of Groups as depending on the Symbolical Equation θn = 1Philosophical Magazine Series 1, 7
-
A. Schwenk (1991)
Which Rectangular Chessboards Have a Knight's Tour?Mathematics Magazine, 64
-
C. Jung, A. Storr (1983)
The Essential Jung -
D. Hilbert (1931)
Die Grundlegung der elementaren ZahlenlehreMathematische Annalen, 104
-
D. Gale (1979)
The Game of Hex and the Brouwer Fixed-Point TheoremAmerican Mathematical Monthly, 86
-
R. Smullyan (1979)
The Chess Mysteries of Sherlock Holmes -
E. Kasner, J. Newman (1940)
Mathematics and the Imagination -
C. Trigg (1978)
What is Recreational MathematicsMathematics Magazine, 51
-
David Wells (2012)
Games and Mathematics: Subtle Connections -
M. Costello (1988)
The greatest puzzles of all time -
S. Shapiro (1998)
A procedural solution to the unexpected hanging and Sorites paradoxesMind, 107
-
Trina Kershaw, S. Ohlsson (2004)
Multiple causes of difficulty in insight: the case of the nine-dot problem.Journal of experimental psychology. Learning, memory, and cognition, 30 1
-
M. Gardner (1998)
A Quarter-Century of Recreational Mathematics.Scientific American, 279
-
M. Gardner (1994)
My Best Mathematical and Logic Puzzles -
A. Benjamin, G. Chartrand, Ping Zhang (2015)
The Fascinating World of Graph Theory -
L. Simons, O. Neugebauer, A. Sachs, A. Goetze (1946)
Mathematical Cuneiform Texts.American Mathematical Monthly, 53
-
J. Wimp, K. Devlin (2002)
The math gene: How mathematical thinking evolved and why numbers are like gossipThe Mathematical Intelligencer, 24
-
Herrn Cantor
Ueber eine Eigenschaft des Inbegriffs aller reellen algebraischen Zahlen.Journal für die reine und angewandte Mathematik (Crelles Journal), 1874
-
U. Eco (1989)
The Open Work -
J. Conway (1976)
On Numbers and Games -
L. Foulds, D. Johnston (1984)
An Application of Graph Theory and Integer Programming: Chessboard Non-attacking PuzzlesMathematics Magazine, 57
-
T. Machan (1983)
Ethics and the regulation of professional ethicsPhilosophia, 13
-
William Springer (2009)
Review of the traveling salesman problem: a computational study by Applegate, Bixby, Chvátal, and Cook (Princeton University Press)SIGACT News, 40
-
Yair Neuman (2007)
Immune memory, immune oblivion: a lesson from Funes the memorious.Progress in biophysics and molecular biology, 95 1-3
-
S. Kosslyn (1983)
Ghosts in the mind's machine: Creating and using images in the brain -
H. Ayaz, P. Shewokis, M. Izzetoglu, M. Çakır, B. Onaral (2012)
Tangram solved? Prefrontal cortex activation analysis during geometric problem solving2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society
-
L. Clarke (1972)
Fun with Figures -
D. Hofstadter, E. Sander (2013)
Surfaces and Essences: Analogy as the Fuel and Fire of Thinking -
S. Smoliar, D. Hofstadter (1979)
Godel, Escher, Bach: An Eternal Golden BraidComputer Music Journal, 5
-
David Richeson (2008)
Euler's Gem: The Polyhedron Formula and the Birth of Topology -
M. Gardner (1982)
Aha! Gotcha: Paradoxes to Puzzle and Delight -
W. Andrews (2018)
Magic Squares and Cubes -
R. Dunlap (1997)
The Golden Ratio and Fibonacci Numbers -
J. Changeux, L. Garey (2012)
The good, the true, & the beautiful : a neuronal approach -
David Antin (1965)
100 Great Problems of Elementary Mathematics -
I. Stewart (2007)
Taming the Infinite -
Henry Dudeney
Amusements in MathematicsNature, 100
-
F. Schuh (2015)
The Master Book of Mathematical Recreations -
D. Rockmore (2005)
Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers -
R. Kurzweil (2012)
How to Create a Mind: The Secret of Human Thought Revealed -
Alfred Posamentier, I. Lehmann (2007)
The Fabulous Fibonacci Numbers -
G. Pólya (1921)
Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im StraßennetzMathematische Annalen, 84
-
David Wells (2005)
Prime Numbers: The Most Mysterious Figures in Math -
L. Zadeh (1996)
Fuzzy sets -
(2013)
How Humans Learn to Think Mathematically: University Mathematics and Beyond -
G. Bohning, Jody Althouse (1997)
Using tangrams to teach geometry to young childrenEarly Childhood Education Journal, 24
-
M. Clark (2002)
Paradoxes from A to Z -
E. Goldberg, L. Costa (1981)
Hemisphere differences in the acquisition and use of descriptive systemsBrain and Language, 14
-
L. Carroll (2006)
The Game of Logic -
J. Strohmeier, P. Westbrook (1999)
Divine Harmony: The Life and Teachings of Pythagoras -
D. Bor (2012)
The Ravenous Brain: How the New Science of Consciousness Explains Our Insatiable Search for Meaning -
A. Olson (1993)
The Eight Queens Problem.The Journal of Computers in Mathematics and Science Teaching, 12
-
S. Collings (1970)
The Eighth Book of TanThe Mathematical Gazette, 54
-
A. Borovkov (1998)
Probability Theory -
T. Hales, Samuel Ferguson (1998)
A Formulation of the Kepler ConjectureDiscrete & Computational Geometry, 36
-
A. Wiles (1995)
Modular Elliptic Curves and Fermat′s Last Theorem(抜粋) (フェルマ-予想がついに解けた!?), 34
-
B. Mazur, P. Pesic, K. Sabbagh (2003)
"Imagining Numbers" (Particularly the Square Root of Minus Fifteen)@@@"Abel's Proof": An Essay on the Sources and Meaning of Mathematical Unsolvability@@@"The Riemann Hypothesis": The Greatest Unsolved Problem in MathematicsAmerican Mathematical Monthly, 111
-
G. Lakoff, R. Núñez (2002)
Where mathematics comes from : how the embodied mind brings mathematics into beingAmerican Mathematical Monthly, 109
-
(1987)
Mind Tools: The Five Levels of Mathematical Reality -
R. Smullyan (1997)
The riddle of Scheherazade and other amazing puzzles, ancient & modern -
R. Banks (1999)
Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics -
Jo-Anne Hadley, D. Singmaster (1992)
Problems to sharpen the youngThe Mathematical Gazette, 76
-
R. Sternberg (1984)
Beyond IQ: A Triarchic Theory of Human Intelligence -
K. Appel, W. Haken (1978)
The Four-Color Problem -
Véronique Izard, Pierre Pica, E. Spelke, S. Dehaene (2011)
Flexible intuitions of Euclidean geometry in an Amazonian indigene groupProceedings of the National Academy of Sciences, 108
-
Frank Swetz, T. Kao (1977)
Was Pythagoras Chinese? An Examination of Right Triangle Theory in Ancient China. The Pennsylvania State University Studies No. 40. -
C. Ogilvy (1994)
Excursions in Mathematics -
D. Klarner (1967)
Cell Growth ProblemsCanadian Journal of Mathematics, 19
-
R. Merton, Elinor Barber (2004)
The Travels and Adventures of Serendipity: A Study in Sociological Semantics and the Sociology of Science -
P. Gerdes (1994)
On mathematics in the history of Sub-Saharan AfricaHistoria Mathematica, 21
-
Thomas Tymoczko (1979)
The Four-color Problem and Its Philosophical SignificanceThe Journal of Philosophy, 76
-
M. Livio (2002)
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number -
L. Smolin (2013)
Time Reborn: From the Crisis in Physics to the Future of the Universe -
R. Bert (2013)
\IThe King of Infinite Space: Euclid and His\N Elements By David Berlinski. New York City: Basic Books, 2013Civil Engineering, 83
-
K. Sigmund (2004)
Kepler’s conjecture: How some of the greatest minds in history helped solve one of the oldest math problems in the worldThe Mathematical Intelligencer, 26
-
E. Bono (1970)
Lateral thinking: Creativity Step by Step -
J. Newman (1952)
The Rhind PapyrusScientific American, 187
-
I. Pressman, D. Singmaster (1989)
The jealous husbands and The missionaries and cannibalsThe Mathematical Gazette, 73
-
K. Appel, W. Haken (2019)
Every Planar Map Is Four ColorableMathematical Solitaires & Games
-
T. Kuhn (1964)
The Structure of Scientific Revolutions.The Philosophical Quarterly, 14
-
M. Gardner (1997)
The last recreations : hydras, eggs, and other mathematical mystifications -
K. Appel, W. Haken (1977)
The Solution of the Four-Color-Map ProblemScientific American, 237
-
L. Fortnow (2013)
The Golden Ticket: P, NP, and the Search for the Impossible -
R. Hersh, S. Dehaene (1998)
The Number Sense: How the Mind Creates Mathematics.American Mathematical Monthly, 105
-
B. Visser, M. Ashton, P. Vernon (2006)
g and the measurement of Multiple Intelligences: A response to GardnerIntelligence, 34
-
G. Bruno, A. Genovese, G. Improta (2011)
Routing problems: a historical perspectiveBSHM Bulletin: Journal of the British Society for the History of Mathematics, 26
-
The Ascent of ManNature, 120
-
I. Pohl (1967)
A method for finding Hamilton paths and Knight's toursCommunications of the ACM, 10
-
Richard Taylor, A. Wiles (1995)
Ring-Theoretic Properties of Certain Hecke AlgebrasAnnals of Mathematics, 141
-
P. Auble, J. Franks, S. Soraci (1979)
Effort toward comprehension: Elaboration or “aha”?Memory & Cognition, 7
-
K. Gödel (1931)
Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme IMonatshefte für Mathematik, 149
-
Ophir Nave, Yair Neuman, L. Perlovsky, N. Howard (2014)
How much information should we drop to become intelligent?Appl. Math. Comput., 245
-
M. Danesi (2003)
Second Language Teaching: A View from the Right Side of the Brain -
J. Adam (2003)
Mathematics in Nature: Modeling Patterns in the Natural World -
T. Bergin, M. Fisch (1949)
The New Science of Giambattista Vico -
A. Chace (1979)
The Rhind mathematical papyrus : free translation and commentary with selected photographs, transcriptions, transliterations, and literal translations -
R. Hersh (1998)
What is Mathematics, Really?Mitteilungen der Deutschen Mathematiker-Vereinigung, 6
-
T. Hales (1994)
The status of the kepler conjectureThe Mathematical Intelligencer, 16
- Publisher
- Springer International Publishing
- Copyright
- © Springer International Publishing AG, part of Springer Nature 2018
- ISBN
- 978-3-319-93253-8
- Pages
- 105 –125
- DOI
- 10.1007/978-3-319-93254-5_4
- Publisher site
- See Chapter on Publisher Site
Abstract
[A main tenet of this book is that the idea-structure for many puzzles typically originates in the imagination (a right-hemispheric function) and then migrates, via a cognitive flow, to embed itself into the reasoning and generalizing part of the brain (a left-hemispheric function). The imagination defies a precise definition; that is, we cannot pin it down to a clear semantic explication. One of its most basic functions is to conjure up images in the mind and connect them in some meaningful way to allow people to accomplish particular tasks, such as solving problems in geometry. This primary level of imagination now comes under the rubric of “spatial reasoning,” a term that can be traced to Howard Gardner’s work on what he called “multiple intelligences” in 1983, in contrast to the idea of a single general form of intelligence. Gardner identified eight intelligences:Musical-rhythmicVisual-spatialVerbal-linguisticLogical-mathematicalBodily kinestheticInterpersonalIntrapersonalNaturalistic]
Published: Aug 12, 2018
Keywords: Spatial Reasoning; Cognitive Flow; Polyominoes; assemblyAssembly; geometryGeometry