This Way Up

Which way would you hang (or wear) this art?

ThisWayUp, digital image

The orientation of the image is important. To ensure maximum viewing pleasure place this side (with the image on it) so that it faces the audience. Placing the art so the image faces away from the viewer may make it difficult to see.

Available as prints, apparel and other formats from Society6 and RedBubble.

Too many winters

I am in the midst of my 53rd Winter. So far I have experienced 50 Autumns and 48 Springs, but only 47 Summers. How old am I? Why am I procrastinating Summer?

The seasons I have met (pie chart)
The seasons I have met (pie chart), digital image

One of the benefits of international travel is that I can spend time in different hemispheres, experiencing the different food, culture and people of the world. I grew up in the Southern Hemisphere where Christmas is in Summer and the school year matches the calendar year. But, 14 and a bit years ago I moved to the Northern Hemisphere for work and a different lifestyle. I now get a real Winter Christmas and the academic year spans two calendar years with a long break in the Northern Hemisphere Summer/Southern Hemisphere Winter.

One of the drawbacks of living on the other side of the equator from family and friends is the opposite seasons. With my immediate family in school, our local long Summer break is the only practical time for us to visit our antipodean whanau, who are then in the midst of their Winter.   

The seasons I have met (stacked)
The seasons I have met (stacked), digital image

Unseasonal days experienced during the season have not been counted, only prolonged exposure to the season experienced by the rest of the hemisphere at that time. 

For the purposes of my calculations, a season is counted if I was in a hemisphere experiencing any part of that season at the time. If I visit an opposite season and return before the end of the original season, the original season is only counted once – for example, I left the Northern Hemisphere Summer in June 2016, had four weeks of Southern Hemisphere Winter and returned to experience the remainder of the Northern Hemisphere Summer; earlier/later in the year I had another whole Northern Hemisphere Winter. I have only counted a season if I experienced it for at least one week – I do not remember any of the 21.5 hours of the summer of my birth.     

I am using the Meteorological definition of seasons:
Southern Autumn / Northern Spring: 1 March to 31 May
Southern Winter / Northern Summer: 1 June to 31 August
Southern Spring / Northern Autumn: 1 September to 30 November 
Southern Summer / Northern Winter: 1 December to 28 (29 in leap years) February


No. Digits

Can you solve these simple equations and find the pattern?

No. Digits (Just Equations)
No. Digits (Just Equations). Digital Image

This was the question I posed to friends on Facebook. Thanks to them I found some missing brackets and corrected the above image, representing digits as equations.

From this, I created a simple book reminiscent of a child’s counting book or math exercise book with a number represented on each page by its equation. If you include the answers to the equations (left as an exercise for the reader), each statement has all of the digits from zero to nine appearing only once. I created the book from a school desktop flip calendar, giving it a distressed old school look by painting the pages with a mixture of gouache and acrylic house paint. Letting the wet pages stick together before separating and applying a second coat produced the rough surface for the equations in pastel, sharpie and pencil.  

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The title of this work No. Digits is a play on the idea that “Number” is often abbreviated as “No.” and for each equation there is no digit for that specific number until you solve the equation.

Approximately Φ

Acrylic and Gouache on Lack Coffee Table, 90x55 cm
Approximately Phi, Acrylic and Gouache on Ikea Lack Coffee Table, 90×55 cm


Approximately Phi, Acrylic and Gouache on Ikea Lack Coffee Table.
Approximately Phi, Acrylic and Gouache on Ikea Lack Coffee Table.

The mathematics of the golden ratio [phi (ɸ) ~1.61803399] and of the Fibonacci sequence [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …] are intimately interconnected.

At 90 x 55 cm, the dimensions of the Ikea Lack Coffee Table are close to two consecutive terms of the Fibonacci series, and give a ratio of 1.63636363636 which is only 0.01832964761 or 1.1328% more than phi. Our coffee table was in need of refurbishment and so I painted it with this exaggerated approximation of the fibonacci series / golden ratio spiral.



3 dominates π

3 dominates π, digital image

This work attempts to show the significance of the starting digits of pi. [Zoom in hundreds of times on the SVG image above to see all nine of the circles]. Over short distances, it is the 3 that dominates.

C = π2r

So for a small circle you can roughly approximate the relationship between the circumference and the diameter (2r) as three. You will be wrong, but only .14159265359… wrong. Round it to 3.1 and you are less wrong (.04159265359… wrong).

Pi is irrational, not like a two year old having a tantrum, but in the mathematical sense where it cannot be represented by a ratio (fraction) because it has a infinite non-repeating decimal expansion. With infinite digits after the decimal point, the best we can do is approximate pi to the number of digits we know. [Currently pi to about 12 trillion digits has been calculated].

For calculating the distances and sizes of far off galaxies, the decimals of pi take on more significance and more precise estimates of pi are needed.

So how much pi is necessary? In Scientific American’s blog: How Much Pi Do You Need?, the answer is 32 significant digits for use with the fundamental constants of the universe and 15 or 16 for everyday things like space station and GPS navigation.

Happy pi day!