The following problem was proposed by Thomas Ihringer in [1]: are there, for every n@eN, only finitely many possibilities f(n) to dissect a square into n rectangles of equal size? We prove that the answer is 'yes'. We also prove that lim"n"->"~f(n)^1^n exists.
We study the dissection of a square into congruent convex polygons with $q$-vertices. Yuan \emph{et al.} [Dissection the square into five congruent parts, Discrete Math. \textbf{339} (2016) 288-298] posed the question that if the number of tiles is a prime number $\geq 3$, is it true that the polygon must be a rectangle. We conjecture that the same conclusion still holds even if the number of tiles is an odd number $\geq 3$. Our conjecture has been confirmed for triangles in earlier works. We prove that the conjecture holds if either the prototile is a convex $q$-gon with $q\geq 6$ or it is a right-angle trapezoid.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.