[phoe-krk]

> The best conceptualization of the concept of number that I've come across is Von Staudt's construction of the rationals using the concept of harmonic tetrads.

Do you have any more material for this? Google seems to give me no good results.

[jacobolus]

From what I understand, Von Staudt and some other geometers were trying to push back against algebra/arithmetic taking over geometry, and against projective geometry invariants like the cross ratio being defined in terms of algebraic relations between Euclidean distances. So he flipped things around and developed arithmetic in terms of basic projective geometry relations instead. (Projective geometry is geometry without circles, angle measures, distances, or parallelism, only straight lines.)

See Coolidge (1934) "The Rise and Fall of Projective Geometry". AMM 41(4), pp. 217-228 https://www.jstor.org/stable/2302023

Google scholar search: https://scholar.google.com/scholar?q=staudt+throws

https://en.wikipedia.org/wiki/Karl_Georg_Christian_von_Staud...

https://en.wikipedia.org/wiki/Cross-ratio

[phoe-krk]

Thanks!