F.33 Euclidean (m, n) Generators — Folios¶
Archival manuscript scans and diplomatic transcriptions from seelig’s notebooks for F.33 (Euclidean (m, n) Generators) (SeeligNotebooks).
Folio 0223 (Page 1 of 1): Euclidean (m, n) Pythagorean Triple Table¶
[Folio 0223]
Folio 0223 (original scan 0223.jpg) from resources/seelig/33_m-n.¶
Diplomatic Mathematical & Geometric Transcription
Diplomatic Transcription — Folio 0223 (0223.jpg, Sheet 1 of 1):
Tabulates \((m, n, m^2-n^2, 2mn, m^2+n^2)\) for 11 coprime pairs of opposite parity from \((2,1)\mapsto(3,4,5)\) to \((7,6)\mapsto(13,84,85)\).
\[a = m^2 - n^2, \qquad b = 2 m n, \qquad c = m^2 + n^2, \qquad a^2 + b^2 = (m^2 + n^2)^2 = c^2\]