Artwork
Summary
Imagine It and Build
It by Kate Jones explores the remarkable combinative diversity
that can emerge from just five geometric pieces called octiamond shapes
composed of eight equilateral triangles. By rearranging these five identical
building blocks, the artist creates recognizable forms such as birds, animals,
and human figures. The result is a visual representation for the imagination,
and constraint, where mathematical structure becomes a source of creativity
rather than limitation.
Art Replication
To replicate Imagine
It and Build It, I focused on the underlying mathematics of, geometry,
and transformation by physically constructing and rearranging five
octiamonds. Each octiamond is composed of eight equilateral triangles, and the
mathematical challenge lies in exploring how many recognizable forms can emerge
under strict constraint, using the same five pieces, without overlap, and with
very limited opportunities for symmetry. I used the free resources and diagrams
from MathPuzzle.com (https://www.mathpuzzle.com/octiamond.html) to support my understanding of the octiamond and this site also showed me more possibilities
to use these shapes with.
To create the pieces,
I printed triangular graph paper from Incompetech and used this tool to set the
parameters for the size of the triangular graph paper.
 https://incompetech.com/graphpaper/triangle/)
I then used different
colours of paper to assemble each octiamond making it more visible during
construction. I began placing and gluing them together mimicking the five
shapes used in the original artwork. Having the opportunity to work with
physical materials made the mathematics tangible: through trial and error plus
the shapes did not turn out perfectly.  After constructing the octiamonds, I attempted to assemble them into figures that resembled those shown in the artwork. This process highlighted how constraint generates creativity, recognizable forms emerged not in spite of the limitations, but because of them. The activity reinforced that mathematical structure does not limit imagination; instead, it invites play, experimentation, and problem solving.
 This was called the
Sampan Ride  Elephant  Hen and Egg   Disco Dancer This task also lends itself naturally to classroom use. Students could construct equilateral triangles using a compass and straightedge, emphasizing precision and geometric reasoning before moving into combinatorial exploration. A clear demonstration of how to construct equilateral triangles with a compass can be found here: https://www.youtube.com/watch?v=XBgwGROzzzk. From there, students could build octiamonds, investigate symmetry and transformation, and explore how many figures can be created from the same fixed set of shapes. In this way, the activity bridges geometry, art, and inquiry, making mathematics both visible and meaningful | ||||
These are very lovely art pieces. I don't know if this is disparaging to squares, but triangles give art so much life, so to say. It feels like your art has so much movement to it, movement that squares wouldn't be able to accomplish.
ReplyDeleteI love these! I will be making a note to incorporate this activity in my classes. I also know this is a task my son would really enjoy. That disco dancer is so fun!
ReplyDeleteYour comment “constraint generates creativity” really stuck out to me. At MTS PD day a few years ago, Nat Banting ran a session based on that idea and it impacted my approach to teaching and problem-posing. He has a collection of activities titled “Menu Math” that use this approach. I have used them in my classroom a number of times and they have resulted in great problem solving, productive mathematical discourse and lots of play! https://natbanting.com/menu-math/