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Expanded Similar Triangles Poem

The Ancient Dual

2009
Digital
The Ancient Dual, 2009 - the equation written across a cracked granite boulder
The Ancient Dual, 2009 — digital
The poem The Sun  =  The Lion (The Moon + The Snake) ⁄ The Bull  −  The Eagle

The value of the sun is to the value of the moon as the value of the eagle is to the value of the snake as the value of the lion is to the value of the bull.

Where the equation comes from

An expanded similar triangles poem sets three ratios equal — a ⁄ b = c ⁄ d = e ⁄ f — and then adds two of them, numerator with numerator and denominator with denominator. The proportion survives the operation. Solving what is left for one term gives the equation on the piece.

The three ratiosThe Sun ⁄ The Moon  =  The Eagle ⁄ The Snake  =  The Lion ⁄ The Bull
Add the first two(The Sun + The Eagle) ⁄ (The Moon + The Snake)  =  The Lion ⁄ The Bull
Solved for The SunThe Sun  =  The Lion (The Moon + The Snake) ⁄ The Bull  −  The Eagle

What the expansion buys is a poem about a difference or a sum rather than a quantity — two terms held apart, and the gap between them standing in fixed ratio to a third.

How the form works The simpler form