MASALAH SUDUT DAN KEORTOGONALAN S PADA GEOMETRI TAKSI - FONIZON (NIM : 90111303), ALTIVO
Taxicab geometry is built based on specific norm, T x , called taxicab norm, or equivalently based on taxicab metric (formula). Distance between two points and measure of angle between two lines are two fundamental measures in any geometry. In taxicab geometry, distance between points are naturally measured using provided metric, i.e. taxicab metric. Angle in inner-product space can be measured based well-known identity , cos (formula) . Therefore existence of inner-product is crucial in taxicab geometry to introduce a notion of angle. However, the inner product has to be compatible with the existing norm. Here, we investigate the existence of such inner-product. It is shown that there is no such inner-product. We also show that Pythagoras, Isosceles, Birkhoff, and Roberts notions of orthogonality does not hold in taxicab geometry.