2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51792A new mneumonic device is shown to emerge in connection with O(7) numerical tensors exhibiting duality and reflecting the natural 7=(4+3) splitting of 7-dimensional space. Then Desargues' and Pappus' theorems are shown to be connected through a geometry that makes use of octonionic numbers exhibiting this duality. Construction of exceptional Hilbert space based on Jordan algebras and exceptional projective geometries is illustrated. A brief discussion of the Moufang plane and non-Desarguesian geometries is presented.37 pages, 6 figuresHigh Energy Physics - Theorytext