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Abstract.We show the first unified description of some of the oldest known geometries such as the Pappus' theorem with more modern ones like Desargues' theorem, Monge's theorem and Ceva's theorem, through octonions, the highest normed division algebra in eight dimensions. We also show important applications in hadronic physics, giving a full description of the algebra of color applicable to quark physics, and comment on further applications. IntroductionIn mid sixties Miyazawa, in a series of papers [1] , extended the SU (6) group to the supergroup SU (6/21) that could be generated by constituent quarks and diquarks that could be transformed to each other. In particular, he found the following: (a) A general definition of SU (m/n) superalgebras, expressing the symmetry between m bosons and n fermions, with Grassman-valued parameters. (b) A derivation of the super-Jacobi identity. (c) The relation of the baryon mass splitting to the meson mass splitting through the new mass formulae.This work contained the first classification of superalgebras (later rediscovered by mathematicians in the seventies). Because of the field-theoretic prejudice against SU (6), Miyazawa's work was generally ignored. Supersymmetry was, of course, rediscovered in the seventies within the dual resonance model by Ramond [2] , and Neveu and Schwarz [3] . Golfand and Likhtman [4] , and independently Volkov and Akulov [5] , proposed the extension of the Poincaré group to the super-Poincaré group. Examples of supersymmetric field theories were given and the general method based on the super-Poincaré group was discovered by Wess and Zumino [6] . The super-Poincaré group allowed transformations between fields associated with different spins 0,