Curvatures 01 02
acrylic on canvas (diptych)
48 x 72 inches
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
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 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.