Construct the Vecten figure of the equilateral ABC and show that the equilateral triangle LMN is in ratio [sqrt(3)+1] to the original one (ratio their sides).
Triangles ACF and NMB are similar, thus their side-ratio is equal to CF/MB = CF/BL etc. ...
![[alogo]](alogo.png){kind=small}
Vecten diagram of an equilateral triangle ![[0_0]](Vecten_Equilateral_files/Vecten_Equilateral_0_0_0.png)
![[0_1]](Vecten_Equilateral_files/Vecten_Equilateral_0_0_1.png)
![[0_2]](Vecten_Equilateral_files/Vecten_Equilateral_0_0_2.png)
![[0_3]](Vecten_Equilateral_files/Vecten_Equilateral_0_0_3.png)
![[1_0]](Vecten_Equilateral_files/Vecten_Equilateral_0_1_0.png)
![[1_1]](Vecten_Equilateral_files/Vecten_Equilateral_0_1_1.png)
![[1_2]](Vecten_Equilateral_files/Vecten_Equilateral_0_1_2.png)
![[1_3]](Vecten_Equilateral_files/Vecten_Equilateral_0_1_3.png)