Golden Section in Two Equilateral Triangles

Quang Tuan Bui

November 6, 2011

ABC and AMN are two equilateral triangles where M is midpoint of side BC. Arc 60° centered at B passing through A, C intersects side MN by golden ratio.

For a proof, construct

  • D as symmetry of A in M,
  • E as symmetry of A in N,
  • Q as symmetry of P in M.

By George Odom, NM/MQ = φ; therefore MN/MP = φ.

(There is another proof for the same construction.)

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