The Editor
New Zealand Journal of Forestry Science
Forest Research Institute
Rotorua

Pine needles and tree stems

Editor,

J.C. Grace (1987) showed that the projection of a sector of a circle, averaged over all directions, is 1/p times the perimeter. In fact, by a theorem of Cauchy (Matérn 1956), this is true for any convex figure. The same theorem ensures that the expected diameter obtained by calipering a tree from a random direction equals that obtained with a diameter tape, regardless of the shape of the stem cross-section.

References:

Grace, J. C. 1987: Theoretical ratio between ``one-sided'' and total surface area for pine needles. New Zealand Journal of Forestry Science 17: 292-6.

Matérn, B. 1956: On the geometry of the cross-section of a stem. Meddelanden frän Statens Skogsforskningsinstitut Vol. 46, No. 11.

Oscar García
Forest Research Institute
Rotorua