Rational Unfoldings of ±Xk and Their Relation with Geometric Equilibrium Theory


W. Kuyk (in real life, Willem Kuijk - here are a few other of his many works) and Lieven Smits

Bibliographical Reference

Acta Applicandae Mathematicae, volume 19 (1990), pages 87-95.


In this paper, two theorems determine the locus B ('buoyancy locus') of the centre of gravity of the displaced water of a ship with any number of 2n sides, as a function of the arbitrary continuous curves that make up those sides, and that generalize the classical wall-sided case (n = 1). Although the theorems may have interest from the pure geometrical point of view, they have been obtained with a view to simulate processes in biology that, in analogy to the self-righting of ships, are self-regulating, such as the neural control of the body heat and the servo-control of the heart rate.

AMS Subject Classifications (1985)

28A75, 52A10, 26B15.


There are a few reprints left. If your library does not have this particular journal issue, ask for a reprint by emailing me your postal address. Remove "unwanted" from the address below.


  1. Janssens, J. and Kuyk, W., A Set of Integral-differential Equations for the Ventricular Cardiac Suction Pump, in B. Schmidt (ed.), "Proc. 3rd European Simulation Congress," Erlangen 1990, pp. 567-572.
  2. Kuyk, Willem, The Human Thermostat, in G.C. Vansteenkiste (ed.), "Proc. 2nd European Simulation Congress," Antwerp 1986, pp. 713-719.
  3. Kuyk, Willem, Servocontrol of the Heart Rate in Homeothermic Animals, Bull. Math. Biol. 48 (1986), 107-124.
  4. Kuyk, Willem and Smits, Lieven, On the Geometries of the Rational Unfoldings of ±Xk, Acta Applic. Math. 19 (1990), 77-86.
  5. Poston, T. and Stewart, I., "Catastrophe Theory and its Applications," Pitman, London 1978.
  6. Thom, R., "Méthodes mathématiques de la morphogénèse," Edition 10-18, UGE, Paris 1974.
  7. Zeeman, E.C., "Catastrophe Theory: Selected Papers 1972-1977," Addison-Wesley, Reading, Mass. 1977.

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