326 Constructions with the golden section
Proof.SupposeABhas unit length. ThenCD=
√
√^3 andEG=EF=
2. LetHbe the orthogonal projection ofEon the lineAB. Since
HA=^12 , andHG^2 =EG^2 −EH^2 =2−^34 =^54 ,wehaveAG=
HG−HA=^12 (
√
5 −1). This shows thatGdividesABin the golden
section.
Remark.The other intersectionG′ofC 4 and the lineABis such that
G′A:AB=^12 (