Sources page biographical material

5.T. DIVIDING A CAKE FAIRLY
Mittenzwey. 1880. Prob. 200, pp. 37 & 89; 1895?: 225, pp. 41 & 91; 1917: 225, pp. 38 & 88. Family of 4 adults and 4 children. With three cuts, divide a cake so the adults and the children get equal pieces. He makes two perpendicular diametrical cuts and then a circular cut around the middle. He seems to mean the adults get equal pieces and the children get equal pieces, not necessarily the same. But if the circular cut is at 2/2 of the radius, then the areas are all equal. Not clear where this should go -- also entered in 5.Q.

B. Knaster. Sur le problème du partage pragmatique de H. Steinhaus. Annales de la Société Polonaise de Mathématique 19 (1946) 228 230. Says Steinhaus proposed the problem in a 1944 letter to Knaster. Outlines the Banach & Knaster method of one cutting 1/n and each being allowed to diminish it -- last diminisher takes the piece. Also shows that if the valuations are different, then everyone can get > 1/n in his measure. Gives Banach's abstract formulations.

H. Steinhaus. Remarques sur le partage pragmatique. Ibid., 230 231. Says the problem isn't solved for irrational people and that Banach & Knaster's method can form a game.

H. Steinhaus. The problem of fair division. Econometrica 16:1 (Jan 1948) 101 104. This is a report of a paper given on 17 Sep. Gives Banach & Knaster's method.

H. Steinhaus. Sur la division pragmatique. (With English summary) Econometrica 17 (Supplement) (1949) 315 319. Gives Banach & Knaster's method.

Max Black. Critical Thinking. Prentice Hall, Englewood Cliffs, (1946, ??NYS), 2nd ed., 1952. Prob. 12, pp. 12 & 432. Raises the question but only suggests combining two persons.