Irregular Quadrilateral Pyramids (EdgeBased Formula)by Poggio Tags: edgebased, formula, irregular, pyramids, quadrilateral 

#1
Jan1413, 09:19 AM

P: 1

I have developed a formula that, given eight edgelengths of an irregular quadrilateral pyramid, calculates the pyramid's base diagonals, altitude, etc. The formula converts the eight edgelengths into five quartic coefficients. The four quartic roots yield candidate values for the square of one of the pyramid's base diagonals. The pyramid's altitude can then be easily determined given the eight edgelengths and the one base diagonal.
I'm an amateur. The proof is based on simple solid geometry and basic algebraic manipulation. Using Excel I've studied the permutations of consecutiveinteger irregular pyramids and have applied the formula across very large sets of data. Beyond yielding a precise method, the work shows that any eight edgelengths in a stipulated arrangement will yield from zero to four viable constructable pyramids (in either convex, concave or complex form). A quick example: Of all permutations of the set of edgelengths (3,4,5,6,7,8,9,10) there are many viable pyramids that can be produced. Many stipulated arrangements have no constructable solutions at all. But two stipulated arrangements produce four constructions. Arrangement (3,6,8,9,5,7,10,4) has two convex, one concave and one complex construction. Arrangement (3,7,10,8,5,6,9,4) had three convex and one complex construction. My two questions: Is this work significant at all? Can I find a place to present/publish it? Thanks for any feedback. 


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