How to cut a cube into sevenths

 

Blog – How to cut a cube into sevenths?

 

When I graduated from art school last year, an instructor left me these words: try to incorporate science in my art endeavours.  After some rumination, I came up with this: How to cut a cube into sevenths, cardboard, 103 x 81 cm, 2021.

 

I know I shouldn’t be specific when talking about artwork --- better be vague so the viewer can ponder more and stay longer.  But this is also about math, so forgive me for babbling here.

 

The question is: how to cut a cube in sevenths?  It’s rather simple: start from any point on the perimeter of the square (the present artwork starts with a corner), measure 1/7 of the perimeter length, make a mark and repeat.  Then connect the marks to the centre of the square.  Finish.

 

This may not accord with your intuition.  Let’s revisit our secondary school math: how to calculate the area of a triangle?  The area is half x base x height.  Now the height is constant --- half the length of the square.  The base is given and is also constant --- 1/7 of the perimeter length.  (For the corner pieces, consider them as being made up of two triangles, whose height is half the length of square and whose total base length is 1/7 of perimeter.)  Thus, even though the 7 pieces are not all of the same shape, they have the same area.  Since the depth is constant, their volumes are all equal.

 

With the math solved, let’s talk about the artwork.  It’s made from cardboard and no paint has been used.  So you are looking at colours that come naturally with the cardboard.

 

First, the black is intended to give a 3-D effect.

 

I also used some cardboard with non-solid colours.  You will notice the ‘blanks’ sitting at the back of the words and figures on cardboard.  This lets a sense of space and translucence to emerge.  At the same time, each (straight) line you see can be geometrically traced.  Some of the lines are surplus, i.e. more than expected, enabling a hint of the original, uncut cube.  Inadvertently they also produce some ‘flattening’ effect.

 

Now that we’ve revisited old math, let’s attempt this: replace the square (cube) with a rectangle (cuboid).  How would you divide it into sevenths?  [Hint: start from a corner, pick say the long side and mark it into sevenths.  Do the same for the other.  Repeat this for the short sides.] 

 

Boon LEE

8-2-2021

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