Geometry Wonderland
Geometric Art, Kadon's GAMEPUZZLES™, KaleidoscopesPentominoes, SOMA Cube, Tangram, Tilings & Patterns, and more...
Kadon Enterprises
GAMEPUZZLES™Kadon Enterprises
(in the Curiosity Shoppe Collection)
Arc Anglespentagon universeKate Jones
Archimedes Squaretilings and designsaka Stomachion c. 260 B.C.
Marasco, J., Jones, K., & Streif, A. (2018). Tricolor stomachion monograph..
Collidescapepentagon universegolden triangles
Hexmozaixedge-matchingCharles Butler
Iamond Hexessential polyformsKate Jones
Kite Mosaicpentagon universeKate Jones
MiniTouch-Iedgematchingstyled by Elijah Allen
Over the past 38 years, Kadon Enterprises has mindfully created an encyclopedic collection of geometrical GAMEPUZZLES™. Their puzzles & games beckon to a broad audience that yearns for creativity and deep order: children, artists, teachers, recreational & professional mathematicians.
Just when you come to believe you have mind-mined all the beauty their puzzles have to reveal, you can revisit their puzzles or again dip into their whirlpool of a catalog and observe like Michael Corleone in the Godfather: "Just when I thought I was out, they pull me back in".
From the Kadon Enterprises website
"To create beauty. To capture a spark of cosmic truthwithin a model you can hold in your eye, your mind, your hand...and move it about at will. To transmute chaos into orderand define that order in a myriad of lovely ways.To start from a singularityand build to those levels of complexity that most enchant you.To weave diversity into the sweetest harmony.To explore roads as yet not dreamed of,perchance to create beauty."
Just when you come to believe you have mind-mined all the beauty their puzzles have to reveal, you can revisit their puzzles or again dip into their whirlpool of a catalog and observe like Michael Corleone in the Godfather: "Just when I thought I was out, they pull me back in".
From the Kadon Enterprises website
"To create beauty. To capture a spark of cosmic truthwithin a model you can hold in your eye, your mind, your hand...and move it about at will. To transmute chaos into orderand define that order in a myriad of lovely ways.To start from a singularityand build to those levels of complexity that most enchant you.To weave diversity into the sweetest harmony.To explore roads as yet not dreamed of,perchance to create beauty."
Kate Jones, President of Kadon Enterprises
I'm delighted to provide an itinerary of progressive discoveries for your [Curiosity Shoppe] students. How's this list for exploring reality from the singularity to infinity:
Poly-5 the foundation of all combinatorial insights
Sextillionsclimbing higher mountains
Quintillionsinto the 3rd dimension
Hexnut Jr.plane-filling with hexagons
Iamond Ringfrom singularity to level 7, tiling with triangles
Rombixdissections and recombinations of rhombs
MiniMatch-Idelightful introduction to edge-matching; the philosophy of neighborly cooperation
Trifoliagrowing complexity in diversity accommodation
L-Sixteenintegrating multiple goals
Arc Anglesthe golden ratio plus connective issues
Kite Mosaikintroduction to inflation by the golden ratio
Hexdominoesmath as art, the combinatorics of color and shape, the limits of mapping
Intarsiabillions and billions of symmetries, a philosophical capsule of complexity and artistic creation
This baker's dozen should give you a good cross-section of types and challenge levels, serving also as stepping stones for building a philosophy of questing and questioning the real world of materials and thought. In teen parlance, these are the coolest. Thank you for this opportunity to introduce our work to the next generation.
more about polyominoes and polycubes
Jones, K. (2004). Combinatorial philosophy. In B. Cipra, E. D. Demaine, M. L. Demaine, & T. Rogers (Eds), Tribute to a mathemagician. Boca Raton, FL: CRC Press.
Rombixessential polyformsAlan Schoen'Games 100' 1993
Roundominoesessential polyformsKate Jones
Snowflake Super Squareedge-matching
Other Kadon Puzzles
Other Kadon Puzzles
Escape the PlagueKate JonesIPP 34 Exchange GiftLondon, UK
Put-Together/Pattern(Route-Building)
Put-Together/Pattern(Route-Building)
Escape the plague includes continuous path
and closed-loop challenges
Let Them Eat CakeKate JonesIPP37 Exchange GiftParis, France
Solving Let Them Eat Cake is like constructing and solving a 5x5 Strimko puzzle that has pentomino 'streams'.
Lombard LoopsKate JonesIPP29 Exchange GiftSan Francisco, USA
Put-Together/Pattern(Route-Building)
Put-Together/Pattern(Route-Building)
Oskar's DiscsOskar van DeventerInterlocking Solid
Perplexing PyramidPut-Together(Assembly/(Puzzle Pyramids)
Warp-30™proposed by Len Gordondesigned byKate Jones
The Warp-30 story
The Warp-30 story
Study of irrationality & Disorder with Rhombi by Jaakko JokelainenBridges 2018 Conference Short Film Festival
See also Kadon's Poly-5 and Quintillions(and catalog of many other polyform creations)
Picciotto, H. (2013). Working with pentominoes.
Golomb, S. W. (1994). Polyominoes: puzzles, patterns, problems, and packings.
PentominoesCreative Crafthouse
HeptominoesJean-Claude Constantin
PathwordsThinkFunhybrid word search & pentominoes game
White ChocolateHanayamalevel 6
Milk ChocolateHanayamalevel 7
Black ChocolateHanayamalevel 8
Soma CubeCreative Crafthouse
Block by Blockaka Soma CubeThinkFun
Carson, G. S. (1973, November)), Soma cubes. Mathematics Teacher, pp. 583-592.
Frederickson, G. (2013). Artfully folding hexagons, dodecagons, and dodecagrams. In George W. Hart, & Reza Sarhangi (Eds.), Proceedings of Bridges 2013: Mathematics, art, music, architecture, education, culture (pp. 63-70). Phoenix, AZ: Tesselations Publishing. Retrieved from http://archive.bridgesmathart.org/2017/bridges2017-63.pdf
Spector, D. (1982, May), Soma: A unique object for mathematical study. Mathematics Teacher, pp. 404-407.
Thatcher, D. H. (2001, March). The tangram conundrum. Mathematics Teaching in the Middle School, 6(7), pp. 394-399.
Tian, Xiaoxi (2012). The art and mathematics of tangrams. In R. Bosch, D. McKenna, & R. Sarhangi (Eds.), Proceedings of Bridges 2012: Mathematics, art, music, architecture, education, culture (pp. 553-556). Phoenix, AZ: Tesselations Publishing. Retrieved from: http://archive.bridgesmathart.org/2015/bridges2015-573.pdf
Slocum, J., Botermans, J., Gebhardt, D., Ma, M., Ma, X., Raizer, H., et. al. (2004). The tangram book: The story of the Chinese puzzle with over 2000 puzzles to solve.
TangramCreative Crafthouse
Tangoesw/expansion decks 2-4
On The LineBrainwright
Rectangling of Triangles (Revisited)Vladimir Krasnoukhove
Frederickson, G. N. (1997). Dissections: Plane & fancy.
Coffin, S. (1991). The puzzling world of polyhedral dissections: Hundreds of 3-D puzzles to build and solve. (free online)
4 Tricky Two-Way PuzzlesMathArtFun
The pieces of 4 squares are rearranged to form 4 different geometric shape.
The pieces of 4 squares are rearranged to form 4 different geometric shape.
4 Tricky Two-Way Star PuzzlesMathArtFun
The pieces of 4 squares are rearranged to form 4 different star shapes.
The pieces of 4 squares are rearranged to form 4 different star shapes.
Puzzle Bookleta2 +b2 = c2Puzzle Master
An example of Farkas Bolyai's proof that any 2 polygons with the same area can be dissected into each other
From the Peter Gal puzzle booklet series.
An example of Farkas Bolyai's proof that any 2 polygons with the same area can be dissected into each other
From the Peter Gal puzzle booklet series.
Greek CrossPuzzle & Craft Factory
Morph Square PuzzlePuzzle & Craft Factory
3 Inch Square PuzzlePuzzle & Craft Factory
Trapezoid PuzzlePuzzle & Craft Factory
Pyramid Puzzle(2 pieces)Creative Crafthouse
a site created by David Bailey
a site created by Dr. Robert Fathauer
Tilings & Patterns
see also Kadon's GAMEPUZZLESGAMEPUZZLES™Tilings & Patterns
a site created by Gary Meisner
a site created by Dr. Robert Fathauer
Anthony, H., & Hackenberg, A. (2005, November). Making quilts without sewing: Investigating planar symmetries in southern quilts. Mathematics Teacher, 99(4), pp. 270-276.
Naylor, M., & Hart, V. (2011). Human geometry workshop. In R. Sarhangi. & C. H. Sequin (Eds.), Proceedings of Bridges 2011: Mathematics, art, music, architecture, education, culture (pp. 649-656). Phoenix, AZ: Tesselations Publishing. Retrieved from: http://archive.bridgesmathart.org/2011/bridges2011-649.pdf
Rosco, M. B., & Zephrs, J. (2016, August). Quilt block symmetries. Mathematics Teaching in the Middle School 22(1), pp. 18-27.
Soto-Johnson, H., & Bechthold, D.(2004, March). Tessellating the sphere with regular polygons. Mathematics Teacher, 97(3), pp. 165-167.
Tennant, R. (2003). Islamic constructions: The geometry needed by craftsmen. In J. Barrallo, N. Friedman, J. A. Maldonado, J. Martinez-Aroza, R. Sarhangi, & C. Sequin. Mathematics, art, music, architecture, education, culture (pp. 459-464). Phoenix, AZ: Tessellations Publishing. Retrieved from http://archive.bridgesmathart.org/2003/bridges2003-459.pdf
Grunbaum, B., & Shephard, G. C. (2016). Tilings and Patterns (2nd ed.)
Bellos, A. (2016). Visions of the universe: A coloring journey through math's great mysteries.
IzziThinkFun
Izzi 2ThinkFun
Beyer, J. (1999). Designing tessellations: The secrets of interlocking patterns.
Seymour, D. (1997). Tessellation teacher masters.
Sutton, D., & Brand (2007). Islamic design: A genius for geometry.
Field, R. (1999). Geometric patterns from churches & cathedrals.
Field, R. (1999). Geometric patterns from Islamic art & architecture.
Field, R. (1999). Geometric patterns from patchwork quilts.
Field, R. (2017). Geometric Patterns from Roman mosaics (and how to draw them) (2nd Ed.).
Field, R. (1999). Geometric Patterns from Tiles and Brickwork
Ippolito, D. (1999, April). The mathematics of the spirograph. Mathematics Teacher, 92(4), pp. 354-358.
site dedicated to Spirograph, Wild Gears and other spiro tools
Hypotrochoid Art SetNPW
Spirograph Deluxe Design Set
HypnoGraphThinkFunCreate complex epicycloid drawings. Parts can be configured differently to create drawings using the 13 interchangeable gears of varying sizes. Used guided setups or rearrange the gears to create unique designs.
instructions
instructions
Full Page Gear SetWild GearsThe Full Page Gear Set V3 is cut from a 15x15 inch sheet of clear acrylic and contains 28 gears ranging in size from 12 to 210 teeth. This gear set was designed specifically to make designs that fill a standard sheet of paper. although <1 to >20 inch designs are possible. This gear set includes two triangular gears and a square gear.
Hart, G., & Heathfield, E. (2017). Making math visible. In D. Swart, C. H. Sequin, & K. Fenyvesi (Eds.), Proceedings of Bridges 2017: Mathematics, art, music, architecture, education, culture (pp. 63-70). Phoenix, AZ: Tesselations Publishing. Retrieved from http://archive.bridgesmathart.org/2017/bridges2017-63.pdf
Hart, G. (2006). Sculpture puzzles. In R. Sarhangi. & J. Sharp (Eds.), Proceedings of Bridges 2011: Mathematics, art, music, architecture, education, culture (pp. 195-202). Phoenix, AZ: Tesselations Publishing. Retrieved from: http://archive.bridgesmathart.org/2006/bridges2006-195.pdf
Hart, G. (2011). Symmetric Stick Puzzles. In R. Sarhangi. & C. H. Sequin (Eds.), Proceedings of Bridges 2011: Mathematics, art, music, architecture, education, culture (pp. 357-364). Phoenix, AZ: Tesselations Publishing. Retrieved from: http://archive.bridgesmathart.org/2011/bridges2011-357.pdf
Free 3D-printable art files form thingiverse.com
Free and inexpensive 3D-printable Math Art files fro cgtrader.com
dragonfliesGeorge Hartnestorgames
KeltikicdodecaDoug EngelsPuzzleAtomic
KeltikicosaDoug EngelsPuzzleAtomic
Roger von Oech's Star-BallUS Games
Roger von Oech's X-BallCreative Whack Company
Roger von Oech's Y-BallCreative Whack Company
Geometricks Educational Series
GeomeTricks is a series of 2D and 3D geometry project books for students in middle school and high school, based on free SketchUp Make software.
GeomeTricks projects are hands-on, step-by-step exercises that produce colorful and interesting geometric models.
Diagrams are for Sketchup Make 2014 (or later).
Kaleidoscopes
Kaleidoscopes
Kaplan, G., Gross, R., & McComas, K. (2015). Mathematics throught the lense of a kaleidoscope: A student-centered approach to building bridges between mathematics and art. In K. Delp, C. S. Kaplan, D. McKenna, & R. Sarhangi (Eds.), Proceedings of Bridges 2015: Mathematics, art, music, architecture, education, culture (pp. 573--580). Phoenix, AZ: Tesselations Publishing. Retrieved from: http://archive.bridgesmathart.org/2015/bridges2015-573.pdf
Brewster Kaleidoscope Society An organization for the creators, sellers, and collectors of kaleidoscopes. The site includes in-depth information on the history and collecting of kaleidoscopes.
Baker, C. (1999). Kaleidoscopes: Wonders of wonders.
Newlin, G. (1999). Simple kaleidoscopes: 24 spectacular scopes to make.
Classic Tin Kaleidoscope
Old World KaleidoscopeToysmith
G. W. Schleidt KS135-40B
Nestorgames
Geometric-Themed GamesNestorgames
Books
Geometry ExplorationBooks
An online version of the thirteen books of Euclid's 'Elements' created by David Joyce with static images and/or java applet simulations illustrating the text.
Abbott, E. A. (2008). 'Flatland: A romance of many dimensions. Originally published in 1884.
Annotated edition by Ian Stewart. There are at least 20 editions of this classic Victorian work -- this one is top notch.
Flatland (wikipedia)
Annotated edition by Ian Stewart. There are at least 20 editions of this classic Victorian work -- this one is top notch.
Flatland (wikipedia)
Anderson, R., & Princko, J. A. (2011, March). What if we lived in Flatland? Mathematics Teaching in the Middle School, 16(7), pp. 400-406.
Flatland: The Movie Home Edition: $19.95School Site $149.95*
*includes teacher notes & worksheets
Comments: 'Flatland: The Movie' is a loose adaption of E. A. Abbott's book. It engages spatial imagination as the viewer travels to lands in which the residents are points, lines, 2D, and 3D shapes -- and teases the audience with the existence of a 4-dimensional world.
'Flatland 2: Sphereland', an adaption of a sequel not written by E. A. Abbot, is not as coherent or engaging as the original award-winning movie.
*includes teacher notes & worksheets
Comments: 'Flatland: The Movie' is a loose adaption of E. A. Abbott's book. It engages spatial imagination as the viewer travels to lands in which the residents are points, lines, 2D, and 3D shapes -- and teases the audience with the existence of a 4-dimensional world.
'Flatland 2: Sphereland', an adaption of a sequel not written by E. A. Abbot, is not as coherent or engaging as the original award-winning movie.
Flatland: The Game of Many DimensionsWishlessness
Ages: 6+, 2-4 players, 15 mins. A game inspired by the Victorian novel Flatland. Players put together their hands of geometric character shapes - custom etched into a set of twelve dice. The strength of each piece is determined by the number of sides and the figure's dimensionality. This is strategy rather than a math game.
Flatland - Video Tutorial
Ages: 6+, 2-4 players, 15 mins. A game inspired by the Victorian novel Flatland. Players put together their hands of geometric character shapes - custom etched into a set of twelve dice. The strength of each piece is determined by the number of sides and the figure's dimensionality. This is strategy rather than a math game.
Flatland - Video Tutorial
Stewart, I. (2002). Flatterland: Like flatland, only more so.
Imaginative sequel to Flat Land that extends the imaginative exploration of space from 0-3 to modern geometries (up to 10 dimensions).
Imaginative sequel to Flat Land that extends the imaginative exploration of space from 0-3 to modern geometries (up to 10 dimensions).
Allen, J. (2012). Making geometry: Exploring three dimensional forms.
Hidetoshi, F., & Rothman, T. (2008). Sacred mathematics: Japanese temple geometry.
Olsen, S. (2006). The golden section: Nature’s greatest secret.
Posamentier, A., & Lehmann, I. (2012). The secrets of triangles: A mathematical journey.
Southall, E. (2017). Geometry snacks: Bite size problems and multiple ways to solve them.
Southall, E. (2018). More geometry snacks: Bite size problems and multiple ways to solve them.
Sutton, D.(2009). Ruler and compass: Practical geometric constructions.
Wells, D. (1992). The Penguin dictionary of curious and interesting geometry.