where \([r]_{n}\) means the number \(r\) up to \(n\) decimals. No calculations are needed to show that (a close approximation of) the Pythagorean theorem holds, i.e., \(d^{2}(p,q) + d^{2}(q,r) = d^{2}(p,r)\). Finally, there is an easy explanation why the Weyl problem occurs: it corresponds to the limiting case \(N_{D} = 1\). When \(N_{D} = 1\), then \([\sqrt{2} \cdot N_{D}] = [\sqrt{2}] = 1\), hence \(d(p,r) = N_{L} \cdot 1 = N_{L}\) and Pythagoras’ theorem fails.