Talk:Frenet-Serret formulas

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[edit] (Has this been fixed?)

Not to knit pick, but there is a hole in the logic. After the derivation of dB/ds, it is concluded that this is parallel to N, Showing it perpendicular to T, but not B. —The preceding unsigned comment was added by 144.133.97.254 (talk • contribs) 11:06, 20 June 2005.

[edit] History of use of linear algebra and vector notation in the formulas

The Frenet page notes (correctly) that "[h]e wrote six out of the nine formulas, which at that time were not expressed in vector notation, nor using linear algebra." That is, they were written out explicity using coordinates.

There is a textbook, "A treatise on the analytic geometry of three dimensions," by Salmon which uses coordinates exclusively. This book was first published in 1862, but was revised several times. I've been reading the fifth edition published in 1915. It, too, uses coordinates.

Does anyone know when differential geometry matured beyond three dimensions and the use of coordinates? Presumably it was in the early 20th century. Lunch 02:14, 13 August 2006 (UTC)

OK, so Riemann first described more general geometries in the mid 1850s, and by the end of the century this was well-known. So had the use of vector notation and linear algebra been popularized by then? (But Frenet had only published his coordinate-based formulas in 1847...) Lunch 02:23, 13 August 2006 (UTC)