The Origin of the 11d World Membrane as a Pascal Conic Section of Six 1d Strings in a 5d Projective Space

known ever since then simply as Pascal’s theorem. Which basically (as defined by Wikipedia) states that if an arbitrary hexagon is inscribed in any conic section, where the opposite sides are extended until they meet, the three intersection points will lie on a straight, so-called ‘Pascal, line’ of that configuration.

Though this simple description verbally suffices, it might fail to convey the fuller, and more truly ‘mystic,’ aspects that earn the Pascal theorem and configuration the distinction of being regarded as the most centrally fundamental construct in projective geometry. And while diagrams would certainly help clarify things, especially the following descriptions, its hard enough re-formatting these articles content from the preferred notebook text to accommodate the differing formats of the web’s various e-magazines or article distribution services. In any case, it’s no coincidence that I not only made the Pascal conic the cover figure for my text covering projective and its subgeometries, but include a frontispiece of various 6-element conics relevant to all, including the Brianchon projective dual to Pascal’s. So any interested readers can go to the resource box and pull up at least the Pascal cover figure, if not the frontispiece.

Anyway, the text’s cover figure illustrates Pascal’s theorem represented on a simple hexagon formed by mutually inscribing a complete 6-point (15 line) and complete 6-line (15 point) representing the respective plane sections of a complete six-dimensional 6-line-at-a-point and a complete 3-dimensional 6-plane derived by recurrently sectioning a complete five-dimensional 6-point {being the simplest representation as a maximal spatially-extended

Pages: 1 2 3 4 5 6 7