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 POLYOMINOES SET
A polyomino is a collection of connected squares. Two-square polyominoes are called dominoes, and the tetris shapes are four-square polyominoes. All of the artworks here use pentominoes (five squares) and hexominoes (six squares) primarily.
- A Luminiferous Quintessence
- At Fives and Sixes
- Cubic Contragate
- Tesselation Covered the Land as Far as the Eye Could See
- Geometric Krakatoa
1. LUMINIFEROUS QUINTESSENCE. September 4, 2018. 47.5 cm by 61 cm
There are twelve possible pentominoes and in this work there are pentominoes made up of smaller pentominoes on four levels. The twelve pentominoes can be seen in black. The large rectangle is made up of three pentominoes (primarily brown, primarily blue and primarily red) but it is simultaneously made up of the full set of twelve, each outlined in white. Each one of those twelve is itself made up of nine pentominoes. Furthermore, each of those nine have in turn been themselves subdivided into nine smaller pentominoes. One could do this forever.
The pentomino design at the bottom uses all twelve pentominoes. Quintessence was the name of a fifth element theorized by medieval philosophers and scientists who thought there were only five elements. Quinque is a Latin word meaning ‘five’. The quintessence is also sometimes referred to as the luminiferous ether because of its supposed ability to transmit non-terrestrial light waves.
2. AT FIVES AND SIXES. September 6, 2018. 45.7 cm by 61 cm
The expression ‘at fives and sixes’ means being confused. In this case the title refers to the grey pentominoes and the brightly colouredt hexominoes:
Next to that are two rectangles (at the top); the first one is made up of six pentominoes and the second is made up of the other six. Below that are two congruent shapes that are almost rectangular. Again, the first one is made up of six pentominoes and the second is made up of the other six.
These shapes are all surrounded by the twelve giant-sized pentominoes which contain the following varieties of text:
- A variety of curves, numbers, formulae and conjectures
- Numbers, geographic mathematical landmarks, and theorems
- Einsteinian terms, miscellaneous fractions and constants, theorems
- Theorems, constants, mathematicians who died young
- A variety of primes, some unusual numbers
- Numbers, conjectures, polygons, and unusual entities (sieve, necklace, spiral)
- A wide variety of triangles
- A variety of angles, triangles and squares
- The five Platonic Solids, formulae, and a variety of fractals
- Mathematical fiction and important non-fiction, surfaces, and unusual entities (Cantor dust, googolplex etc.)
- Feature films that focus on mathematical concepts and personalities
- Mathematical music
The design on the right side includes all twelve pentominoes.
3. CUBIC CONTRAGATE. September 17, 2018. 45.7 cm by 61 cm
This is an illustration of how the twelve pentominoes can be arranged to cover a set of six squares in the shape of a cross without gaps or overlaps; the mathematical proof of this is in the upper left hand corner. That cross is actually a net for a hexahedron (i.e. a cube) which means that the squares can be folded up to form a cube. Therefore the pentominoes cover the cube; the Iran Contragate affair was a case of the President of the United States, Ronald Reagan, covering up his government’s illegal activities and paying no price for that even when the incident came to light. Hence the title.
All around the central cross is a white border (with blue curves) consisting of the twelve pentominoes. Furthermore, beyond that to fill up the main rectangle, the space is filled with smaller pentominoes.
At the bottom is a demonstration of how the pentominoes can be arranged to exactly cover a rectangle in two different ways. Most of the pentominoes in the first of the two rectangles (the grey ones) remain in place in the second rectangle, but the coloured pentomino cluster is turned upside down yet it still fits into the second rectangle.
4. TESSELATION COVERED THE LAND AS FAR AS THE EYE COULD SEE. September 24, 2018. 45.7 cm by 61 cm
The central image here is that of a staircase formed from hexominoes surrounded by pentominoes. The side panels consist of individual pentominoes positioned to tesselate the plane (that is, cover the plane completely in all directions with no gaps or overlaps). There are six of these, in two different varieties. Here are examples of each of the two:
At the bottom are more pentominoes primaril in blue, green and grey, but also in brown at the very bottom:
Pentomino puzzles have been around for over a century. The text at the top is as follows:
Add a two by two square made up of four smaller squares to the pentomino set. Place, if you can, these thirteen shapes onto a chessboard so that all sixty-four squares are covered. Puzzle 74 in ‘The Canterbury Puzzles’ by Henry Dudeney. 1907.
Dudeney frames the puzle as a broken chessboard that has to be restored. The URL below takes you to a copy of ‘The Canterbury Puzzles’ with the problem presented on page 121 and the solution on page 221. The page numbers are displayed on the right side of the screen. The book is out of copyright:
Gutenberg.org/files/27635/27635-h/27635-h.htm
5. GEOMETRIC KRAKATOA. October 14, 2018. 45.7 cm by 61 cm
This image is reminiscent of a volcanic eruption and one of the most famous and most devastating eruptions historically was the eruption of Krakatoa in the late nineteenth century. Its effects were felt around the world and were still visible nine months later. Almost the entire surface of the art work is covered with pentominoes, the most frequent being the one that resembles a house.
The design at the top is also dominated by pentominoes.
According to The Kidd 