ARTWORK by Murray Young
Most of these works are mathematical, dealing with fascinating, important and useful concepts; my hope is that these works stimulate an interest in those concepts yet can also be enjoyed by anyone who has no interest in Mathematics whatsoever. The artistic quality here is mediocre at best; I have known at least four people who are better artists than I am so this is not false modesty. The best part of these works are the ideas they play with, ideas to do with music, imagination, culture and philosophy as well as mathematics.
THE CH’I CH’IAO SET
- Infinite Ch’i Ch’iao T’u
- Before Pythagoras There Was Baudhayana
- 2318 Ingenious Pieces
- Thirteen Convex Pieces
- Infinitesimal Ch’i Ch’iao T’u
SEVEN INGENIOUS PIECES
These works are based on the most popular of the dissection puzzles – tangrams. A dissection puzzle is a set of pieces which can be rearranged in various challenging ways and some go back centuries. Tangrams were devised near the beginning of the nineteenth century in China and they were originally called ‘Seven Ingenious Pieces’ (‘Ch’i Ch’iao T’u’ in Chinese), each new piece now referred to as a tan. Their popularity is considerable in part because the shapes and sizes of the pieces lend themselves beautifully to play-based mathematical education. A set of tangrams consists of two small triangles of area a, a square, parallelogram, and triangle all of area 2a, and two triangles of area 4a. These shapes can be put together to form well over a thousand shapes including letters and numbers, and many elaborate tangram sets have been successfully marketed in various forms.
1. INFINITE CH’I CH’IAO T’U. October 31, 2015. 30.4 cm by 30.4 cm
One of my earliest pieces, this is based on the idea that all seven tans as a group can be rearranged into the shape of each individual tan. Therefore one can start with a set of large tans and take each tan and subdivide it into seven smaller tans. One can do this with each of the new smaller tans as well, and keep going making the tans as small as one wants. Notice too that the two largest triangles have been subdivided in two different ways.
The inventor of tangrams is unknown as she or he went by the pseudonym Yang-cho-chu-shih which means dim-witted recluse. It has been reported that Lewis Carroll, Napoleon, and Edgar Allen Poe are all known to have had tangram sets.
2. BEFORE THERE WAS PYTHAGORAS THERE WAS BAUDHAYANA. October 23, 2018. 45.7 cm by 61 cm.
The Baudhayana sutras are a collection of Vedic Sanskrit texts from India which date from the eighth to the sixth century BCE. They contain everything from information about daily rituals to a statement of the Pythagorean Theorem for an isosceles right-angled triangle (Pythagoras wasn’t born until 570 BCE). Tangrams have also been used to geometrically prove the Pythagorean Theorem for isosceles triangles, as demonstrated here, with the proof at the bottom.
3. 2318 INGENIOUS TANS. October 26, 2018. 45.7 cm by 61 cm
The title of this work is a play on the original Chinese name of the tangram set (i.e. ‘Seven Ingenious Pieces’) and yes there actually are 2318 tans in this work. One ingenious aspect of the tans is that they can be rearranged to form a triangle, parallelogram or pentagon (rectangle, trapezium and others) as well as a square, as illustrated here:
4. THIRTEEN INGENIOUS CONVEX SHAPES. December 10, 2018. 45.7 cm by 61 cm
In 1942 Fu Traing Wang and Chuan-Chin Hsiung proved that there are only thirteen convex tangram configurations. Those thirteen are used here. These configurations have been carefully arranged so that they form a rectangle half of which is a mirror image of the other half.
Around the outside of this work is a lengthy tale of the use of tangrams in history by actual and well-known historical figures. It ends with the appearance of a tangram set observed by members of the first Canadian temporal cohort as they met with Weena Kanna, the head of the Terran Science Academy in the year 802861. This is a friendly nod to ‘The Time Machine’ by H.G. Wells and it reveals the fact that everything previously was possibly a fabrication. As it turns out everything that went before is historically accurate except for the details concerning tangram sets. Those details were made up out of whole cloth and I have no idea whether any of them are true or not as they are beyond the realm of fact-checking due to their triviality. At the end a warning is given to always check primary sources before believing detailed and sincere sounding reports of historical events.
Within the confines of the convex tangram configuration itself is the following narrative:
The six incurious disciples and their leader Jori Boggle-Gore came from across the world carrying their sacred tangram shapes convinced that if they all brought them together to form a trapezium the universe would quietly vanish and they would all ascend to paradise. In secrecy these obedient men met under the Azerbaijan moon at midnight beside the medieval walls protecting the palace of the Shirvanshahs in Baku. With trembling hands they brought the treasured shapes together to form a trapezium ignoring its wonderful mathematical properties. Nothing happened of course. The universe was still intact and yet their faith remained strong.
The tale is a confirmation of a famous 1956 study conducted by Leon Festinger which examined what happened when an apocalyptic cult gathered in anticipation of the end of the world predicted by their religion. When nothing happened counter-intuitively these followers did not abandon the cult when the prediction failed even though they had sold all their worldly possessions, said good-bye to family and friends, and prepared themselves psychologically for the end of the world. Afterwards they clung to the tenets of their failed religion more intensely than before.
5. INFINITESIMAL CH’A CH’IAO T’U. October 20, 2018. 45.7 cm by 61 cm
This is a new, larger and considerably more detailed version of the work Infinite Ch’i Ch’iao T’u completed in 2015, almost exactly three years earlier to the day. See the description of that work earlier in the Gallery.
According to The Kidd 