Golden Gnomon
Closely related to the golden triangle is the golden gnomon, which is the obtuse isosceles triangle in which the ratio of the length of the equal (shorter) sides to the length of the third side is the reciprocal of the golden ratio. The golden gnomon is also uniquely identified as a triangle having its three angles in 1:1:3 proportion. The acute angle is 36 degrees, which is the same as the apex of the golden triangle.
The distance of AD and BD are both equal to φ, as seen in the figure. "The golden triangle has a ratio of base length to side length equal to the golden section φ, whereas the golden gnomon has the ratio of side length to base length equal to the golden section φ."
A golden triangle can be bisected into a golden triangle and a golden gnomon. The same is true for a golden gnomon. A golden gnomon and a golden triangle with their equal sides matching each other in length, are also referred to as the obtuse and acute Robinson triangles. These isosceles triangles can be used to produce Penrose tilings. Penrose tiles are made from kites and darts. A kite is made from the golden triangle, and a dart is made from two gnomons.
Read more about this topic: Golden Triangle (mathematics)
Famous quotes containing the words golden and/or gnomon:
“Ah, Hope! what would life be, stripped of thy encouraging smiles, that teach us to look behind the dark clouds of to-day, for the golden beams that are to gild the morrow.”
—Susanna Moodie (1803–1885)
“Like to the Artick needle, that doth guide
The wand’ring shade by his magnetick pow’r,
And leaves his silken Gnomon to decide
The question of the controverted houre;”
—Francis Quarles (1592–1644)