u/Effective-Bunch5689

The document is ~60 Mb, 233 pages, written in collaboration among four other civil engineering students. It contains everything I've learned in the last 4 years: differential equations, Euler beam theory, Cramer's rule in matrix algebra, finite elements, geometric series convergence, Cauchy sequence generating functions, and a massive mathematical proof that took me two months to fix. All of that so we could design a hypothetical building up to code.

The reason I ask is because I figured it out while working on my capstone project, and I have only found one practical application for it: designing concentric lateral bracing of a multi-story building. These reaction forces, R_{n-k}, ideally solve for the deflection of the statically indeterminate multi-supported cantilever beam.

The governing equation that does this requires that a certain theorem be true, which I conjectured using an algorithm in Maplesoft and later proved using matrix determinant identities: that a finite array of "n" equidistant supports of spacing "h" subjected to a uniformly distributed load "w" each experience a force equal to w*h*n times their unique rational number, say, R_{n-k}=whn*(N_{n-k}/d_n).

These integer numerators N_{n-k} and denominators d_n form sequences, and by superposing exponential regressions onto them, they have slopes exactly equal to that of the sequence, A001835. That is, 2+√3. Hence, these numerators and denominators can be expressed in terms of sequence generators in the form of ceiling functions of 2+√3.

However, if we had an infinite number of floors, the theorem cannot apply because these rational numbers, (N_{n-k}/d_n), become irrational. For example, the infinite-story building's top-floor resistances, R_n and R_{n-1}, have the irrational ratio, R_{n-1} / R_n = 6(4-√3)/(3+√3), and thus R_{n-k} cannot be solved by sequence generators. Instead, R_{n-k} becomes a product of 1-\frac{\left(-1\right)^{k}}{2}e^{-k\cosh^{-1}\left(2\right)}.

I typed 22 pages deriving it all in latex, and with every surprising feature comes a rabbit hole of splendors further beckoning exploration that would easily take 6 more months to discover. Idk it seems useless and not publishable despite whatever mathematical merit it has.