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Curvatures 01 02
2004
acrylic on canvas (diptych)
48 x 102 inches
© Michael Schultheis
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Curvatures 01 02
Statement from artist Michael Schultheis
Lao Tsu, the philosopher and poet who lived in the 6th century B.C. China, described the “genius
in seeing things in the seed.” One botanical seed that has always intrigued me is that of the Vine
Maple Tree (Aceraceae circinatum), which is indigenous to the Pacific Northwest where these
paintings were created.
As many of us have seen as children, the Vine Maple Tree produces seed pods with propeller-
like wings allowing them to fall through the air like a helicopter. Early in the seed development,
the two propeller wings are fused together and slowly open in preparation for flight. This fugitive
moment of separating is visually analogous to progressing from a 2-cusped to a 3-cusped
hypocycloid.
The Persian astronomer and mathematician Nasir Al-Din al-Tusi (1201 – 1274) studied the 2-
cusped hypocycloid. Called the Tusi couple, this line segment results from rolling a circle of
radius b inside a circle of radius 2b. The ratio of inside circle to outside circle is
a/b=2
A 3-cusped hypocycloid, called a deltoid, has a ratio
a/b = 3
These paintings chronicle my thoughts on the visually curious and precarious moment just before
two tangent curves separate, when the Tusi couple becomes a deltoid, and the maple seed
opens.
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