Nine Point Circle

Opus 6: Nine Point Circle

“Opus 6: Nine Point Circle!. There is no circle in this image but it was created because of a shearing effect determined by two of the points in “the Nine Point Circle” that can be found in every triangle.

Nine Point Circle

There is no circle visible in this work but the shearing of the triangle was made using two of the points from the nine point circle.

The Circle Explanation:

The nine point circle is a mathematical phenomenon sometimes referred to as Feuerbach’s Circle, Euler’s circle, Terquem’s circle. Every Triangle has within it and through it a nine point circle.

The nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant concyclic points defined from the triangle. These nine points are:

  • The midpoint of each side of the triangle.
  • The foot of each altitude.
  • The midpoint of the line segment from each vertex of the triangle to the orthocenter (where the three altitudes meet; these line segments lie on their respective altitudes).200px-Triangle.NinePointCircle.svg

                     Feuerbach’s Circle

Not being a mathematician that’s the best I can do with the technical explanation. The  following are my thoughts on making the work.

My thoughts that gave birth to the work:

“The cradle rocks above an abyss, and common sense tells us that our existence is but a brief crack of light between two extremities of darkness” this is the opening sentence from Vladimir Nabokov‘s book “Speak, Memory”.

Two paradox’s of my comprehension gave birth to this work and others in the “Opus” series. The first is the idea that the infinite behind me is the same as the infinite in front of me as I move from one to the other and the second is that as some scientists think time did not exist before the “Big Bang”, although theories change all the time. No pun intended!

The two extremities of darkness for me are both infinite, and the small crack of light that is my life I am moving through, so the infinity behind me should be getting bigger and the one in front of me smaller but I am told that the infinite is always the same so can the one behind me remains the same as I get further away from it, no matter how miniscule in the universal eternity that may be.

I am vaguely aware that some scientists say before the “Big Bang” time did not exist but I can’t comprehend that, before the “Big Bang” the entire matter that makes up the universe was supposedly the size of a pea, and in my mind no matter how small anything is it needs space to exist and if it exists there must be duration and so there was always what I would consider time.

Now at this stage many scientist’s and cosmologist’s will be tearing their hair out at my ramblings but these thought whether right or wrong give rise to my thoughts and imaginings and the universe is realized through the thoughts and imaginings of  humanity.

These paradox made me wonder therefore if the “Nine Point Circle” existed before the Big Bang or was the theoretical phenomenon of life born with the physical. In my mind they must always have existed, but then my mind doesn’t half come up with some strange and wild imaginings every now and then, so reader beware!

So here is the simple premise for the work, I created a random triangle which can still be seen, created the nine point circle and using two of the nine points sheared the triangle on those points and then moving out created the pattern which  I then painted. The spacing and colour in the work apart from the shearing distance are completely intuitive and so that aspect of the work mirrors the idea of the universe being imagined by humanity, whilst the pattern is the creation of something that has always existed  imagined by myself.

Colour and Shape

Flight

Colours and shape:

The universe and world around us is imagined entirely by humanity, the colours we see around us are as a result of the cones at the back of the eye, cats who have fewer cones and more rods see a very different greyer world but this helps them to hunt at dawn and dusk in poor light when their vision give them a sharper view of the world around them.

cat-color-vision

Bats can see fruit bats have quite good eyesight but some species especially those that use echo location or ‘sonar have poorer eyesight, when you research this information you find people saying bats use the echo location to create a ‘visual image’, but do they or is that just us describing this system as visual, a term we understand, because we cannot comprehend or imagine the world as the bat does.

There may be experts out there who would question the voracity of my explanation but what I am exploring is how light which is similar to radio waves is revealed to humanity as colour simply because we have cones which perceive light waves as such. The amount of light, the angle of the sun, our position, the frequency of the light reflected from objects all combine to provide a colour map and with this map and shape combined we produce a three dimensional imager of the world around us.

Here a though, if the only form of life with this vision system is on the earth there may be no colour anywhere else in the universe.

This is the primary reason I stared making my series of geometric paintings they explore a system that allows us to position ourselves within a space, in addition to this it positions us in the present because seeing is an immediate experience.

Hans Ulrich Gumbrecht explores this phenomenon in his work and writing, in today’s world where the past continues to invade present because everything is recorded on social media and stored almost permanently it is harder to forget it, and concerns over things like terrorism, global warming and energy shortages brings the future ever closer to us and so today it is harder to live in the present.

Making these paintings is an act which keeps me in the present, I start with a drawing which intuitively develops from a simple shape or form, this is then transferred to a canvas and the first layer of colour is created using masking tape, I have for some reason never been happy with the edge I get using tape and so once the tape is removed I go over the edge with a clean brush with white spirit to give and edge I like. This process is entirely personal and I cannot explain the preference. The colour is then built up in layers to create varied and graduated shapes of colour which reflect the complex seeing process rather than areas of flat colour, but after the first layer of colour much of the work is done without the aid of tape which requires considerable concentration and this concentration keeps me in the present, which I enjoy, but also gives the work a handmade feel which on close inspection reveals the imperfections in my ability to follow freehand a straight line.

The first of these works ‘Laths l’ can be seen in the previous post.

‘We are who we say we are’

mon-01

The title of this piece is a CS Lewis quote, it is made from found pieces by myself, my wife and my father and assembled with bought components. The meaning we give to things like pendulums, steps and random shapes fascinate me.

There are two more pieces like this in the pipeline but today I am working on a series of abstract paintings.