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Ten Equal Tangents 01 02 03
2004
Acrylic on canvas (quadriptych)
38 x 108 inches
© Michael Schultheis
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Ten Equal Tangents 01 02 03
Statement from artist Michael Schultheis
I sit at my studio window and look out across the Puget Sound to the Olympic Mountain. On one
blustery day, a flock of ten birds issued from the top of these snow-capped peaks. At first, they
appeared just like flecks of pepper but, as they approached, they became more like a small storm
cloud. Breaking off and joining up, their cloud-like form soared and twisted and drove through the
street in front of my window, scattering their collective and then, just as easily, picking up where
they left off, a forgotten bed sheet in the wind.
Mesmerized by their synchronity, I found myself lost in thought while they banked to the left,
twirled to the right, and folded onto themselves like a sandwich. Unpredictable tempests and
sudden, they formed a perfect monkey-saddle shape before swarming over my studio and out of
sight.
I blinked in disbelief, and looked out my window: nothing but water, mountains, sky. What
remained were a set of doodles I had made in my notebook while watching the group of ten birds
fly like one. The doodles evolved into this painting titled “Ten Equal Tangents” based on the
observation that when all ten birds shift simultaneously in mid-air, the angles of intersections
(Ψ‘s) of the curves of their wings are all equal: Ten Equal Tangents of Ψ, given by the equation:
tan Ψ1 = tan Ψ1+1
tan Ψ1 = {tan Ψ1 – tan Ψ2}/{1 + tan Ψ1 tan Ψ2}, I = 1, …, 9.
At the end of the day I sat down again at the window. There were no birds. There were no
doodles. There was only this painting hanging on the wall.
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