linguistic:voice_change, stylistic:tone, information:extraction
Construction

Dividing by interior division

Dividing by exterior division

Application examples you can see in the articles Pentagon with a given side length, Decagon with given circumcircle and Decagon with a given side length.

Both of the above displayed different algorithms produce geometric constructions that determine two aligned line segments where the ratio of the longer one to the shorter one is the golden ratio.