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 OCTAHEDRON SET
- Linear Fractal at Zero Degrees Celsius
- Vital Sines and Tangents
- Nothing Bewitching About This
- Escape From Dimension One
- Parabolic Anarchy
- Round the Twist But Ahead of the Curve
- Hearts and Minds and Circles
- Adventures in Curvature
THE PLATONIC SOLIDS SETS
There are five Platonic Solids, all with faces in which all sides and all angles are equal. The five Platonic Solids artwork sets are meant to cover the sides of all five. The tetrahedron has four equilateral triangles for sides so four works were created each of which features an equilateral triangle. The octahedron has eight equilateral triangles for sides, the dodecahedron has twelve pentagons for sides and the icosahedron has twenty equilateral triangles for sides. Originally there were six hexahedron works (a hexahedron is a posh name for a cube) with squares for sides and all six featured rep-tiles (replicating tiles). As I discovered more fascinating rep-tiles I created three sets of six instead of just one, and I’m presently working on a fourth.
1. LINEAR FRACTAL AT ZERO DEGREES CELSIUS. April 27, 2017. 45.7 cm by 61 cm
This is a Snowflake Curve, a fractal based on a curve analysed by Helge von Koch in Sweden in 1904, decades before fractals entered the mainstream consciousness. The border is generated by starting with an equilateral triangle and repeating forever a set of simple procedures called an algorithm. The border detail gets smaller but the shape of the curve stays the same. My central design also gets infinitesimally small. A straight line has one dimension (length), and a square has two (length and width). This curve has 1.26186 dimensions (the natural logarithm of four divided by the natural logarithm of three) and is continuous.
This detail shows how the original image of a fractal is replicated in smaller and smaller versions of itself infinitesimally. This is the bottom left hand corner.
The text at the top:
- SPEAKER ONE: Could you please give me the equation of one of the tangents to the curve.
- SPEAKER TWO: I’m afraid that the Snowflake Curve has no tangents, sir.
- SPEAKER ONE: No tangents you say. How about a nice derivative then?
- SPEAKER TWO: I’m sorry sir, but no tangents, no derivatives.
- SPEAKER ONE: Well never mind, then.
- SPEAKER TWO: The curve does enclose a precise area, however. Will that do, sir instead?
- SPEAKER ONE: Yes, please.
- SPEAKER TWO: The area of the Snowflake Curve, when the perimeter is infinite, is eight-fifths times the area of the generating triangle. In this case the area enclosed by the curve is 753.088 square centimetres.
- SPEAKER ONE: Thank you very much, my dear woman.
2. VITAL SINES AND TANGENTS. April 9, 2017. 45.7 cm by 61 cm
These curves are the graphs of trigpnometric functions. The orange vertical curves are tangent functions. They extend toward positive and negative infinity never reaching their asymptotes, indicated by the dotted lines. The blue and green curves are sine curves pi radians apart. The tangent graphs are similar to the lines you get, going to infinity in opposite directions, if you head off toward the limits of one divided by zero from a negative direction and a positive direction, which is why the fraction one divided by zero is undefined.
3. NOTHING BEWITCHING ABOUT THIS. June 4, 2017. 45.7 cm by 61 cm
Here are two examples (in orange and blue) of a curve known as the witch of Agnesi, first analysed by Maria Agnesi (1718 – 1799), a female mathematician at a time when women were barred from careers in Mathematics. Agnesi was the second prominent female mathematician that we know of, the first being Hypatia, and there were more than 1300 years between Hypatia’s torture and murder and the birth of Agnesi. The backgraound text consists of the names of prominent and important female mathematicians and scientists.
The background text includes the names of Jane Goodall, Mileva Maric, Augusta Ada Noel-King, Maryam Mirzakhan, Joan Clarke, Mary Leakey, Marie Curie, Irene Joliot-Curie, Beatrix Potter, Marie Pasteur, Lise Meitner, Caroline Herschel, Eileen Collin, Rosalyn Yalow, Roberta Bondar, Amelia Earhart and many others. In Galleries 15 and 16, the Dodeahedron set, there are twelve works of art each one examining the work of a prominent female mathematician (e.g. Emmy Noether, Florence Nightingale, Grace Hopper and nine others).
4. ESCAPE FROM DIMENSION ONE – July 15, 2019. 45.7 cm by 61 cm
The main idea this time is the process of getting smaller and smaller.
The central feature here is a space-filling curve, that is one which begins life as a one-dimensional entity but after an infinite number of iterations of its algorithm covers two dimensional space, hence the title. There is a maze here superimposed on the space-filling curve, an island maze inside a larger maze.
These triangles, with angles of thirty, sixty and ninety degrees, can also regress infinitely.
5. PARABOLIC ANARCHY. April 18, 2017. 45.7 cm by 61 cm
This is a fairly unstructured display of parabolic curves drifting upward and to the right. A parabola is one of the four conic sections. In line with the idea of anarchy, one of the curves is intentionally non-parabolic.
6. ROUND THE TWIST BUT AHEAD OF THE CURVE. May 16, 2017. 45.7 cm by 61 cm
Three distinct curves are illustrated here – a normal curve, a cycloid and a catenary. ‘Being driven round the twist’ is a slang expression for being driven out of one’s mind from extreme annoyance or unwelcome surprise. The first curve is the normal curve; the area under the curve is coloured orange and green. It is used extensively in statistics; in probability theory a normal distribution for a real-valued random variable has at its peak in the centre the mean, median and mode of the distribution. The Central Limit Theorem states that the average of many observations of a random variable with finite mean and variance has a distribution that converges to a normal curve as the number of observations increases.
This is a cycloid, which is the curve traced by a point located on the perimeter of a wheel as it moves without slipping along a straight line. It is the curve of fastest descent given constant gravity. The cycloid was discovered in 1503 by Charles de Bovelles.
This is a catenary, the curve that a hanging cable assumes under its own weight when supported by two poles. Though it resembles a parabola, a catenary is the graph of the hyperbolic cosine function. Strssed ribbon bridges follow a catenay curve.
7. ADVENTURES IN CURVATURE. June 18, 2017. 45.7 cm by 61 cm
This is just a simple celebration of circles. There is a logarithmic spiral at the top consisting of ever-shrinking quarter circles. On the top right are Borromean Rings. The red and green rings are quite unconnected. So are the red and black, and so are the green and black. But the entire set are inextricably linked. The dotted line going across the green and orange circle in the upper left divides the image in two precisely. The main feature here are the two sets of circles at the bottom. They represent the solutions to a puzzle Apollonius was challenged to solve centuries ago. He had to find a circle that was tangent to three other circles. He found not one solution but eight.
The text consists of a circular argument, a quotation from Archimedes about circles that got him killed by a Roman soldier, several definitions of circles, a circle paradox, and many examples of circles (e.g. the circle of fifths, a vicious circle, the circle of perpetual occultation, Le Cercle, the Cyrkle, Picadilly Circus, A Perfect Circle, Circle of Steel, the Vienna Circle and circular points at infinity.
8. HEARTS AND MINDS AND CIRCLES. March 25, 2017. 45.7 cm by 61 cm.
A cardioid is the path traced by a point on the circumference of a circle which is moving around the outside of a fixed circle with the same radius. A cardioid is the inverse curve of a parabola with its focus at the centre of inversion. The boundary of the central bulb of the Mandelbrot set is also a cardioid (as illustrated in the art piece entitled ‘The Iterated Functionary’ found in the Mockva Suicide gallery).
According to The Kidd 