Notes for
“Complete Quadrangle” construction:
-Start with Segment AC
-Construct point B on AC
-Mark point P at random, not collinear with AC
-Construct PA and PB
-Draw a ray that passes at random through PA and PB (though not through P, A, or B
-Label points of intersection Q and R
-Construct AR and BQ
-Label their intersection S
-Construct ray PS
-Where PS intersects AC, draw point D
-AD/BD = AC/BC; harmonic division
Used in artistic landscapes:
Aerial view
My view
Cross-ratio or Anharmonic ratio:
-Ratio (ABCD) = (AC/AD)/(BC/BD)
-This ratio
is equal to -1 if ABCD is harmonic