Research Information System
DEMONSTRATIO MATHEMATICA, vol.46, no.4, pp.795-808, 2013 (ESCI)
G. Chen [ 1] developed Chinese checker metric for the plane on the question " how to develop a metric which would be similar to the movement made by playing Chinese checker" by E. F. Krause [ 13]. Tian [ 17] developed alpha-metric which is defined by d(alpha) ( P 1,P 2) = m a x {vertical bar x(1)-x(2)vertical bar; { vertical bar y(1)-y(2) vertical bar} + ( sec alpha-tan alpha) min{ vertical bar x(1)-x(2)vertical bar} {vertical bar y(1)-y(2)vertical bar } where P 1 = ( x(1),y(1)) and P 2 = ( x(2)-y(2)) are two points in analytical plane, and alpha is an element of[ 0; parallel to/4] : Stewart's theorem yields a relation between lengths of the sides of a triangle and the length of a cevian of the triangle. A taxicab and Chinese checkers analogues of Stewart's theorem are given in [ 12] and [ 9], respectively. In this work, we give an alpha-analog of the theorem of Stewart by using the base line concept and we give a alpha-analog of formulae for the medians which is the application of Stewart's theorem.