Little math problems July 2019

[John Keith]

Brute-force program for the diagonal case, odd sizes only. Exact mode for symbolic results:

Code:


\<< \-> n
  \<< n DUP NEG SWAP
    FOR x n DUP NEG SWAP
      FOR y x SQ y SQ + \v/
      NEXT
    NEXT n 2 * 1 + SQ \->LIST \GSLIST EVAL 2 * EVAL
  \>>
\>>

First few results:

3: '8+8*√2' ~19.314
5: '24+24*√2+16*√5' ~93.718
7: '48+48*√2+(16+16*√2)*√5+16*√13' ~259.94
9: '160+80*√2+(48+16*√2)*√5+16*√13+16*√17' ~554.72


I will leave it to the "big brains" here to derive a general formula.