Constructing The Golden Triangle From A Straight Edge & Compass
The Golden Triangle is a special type of isosceles triangle. Any isosceles triangle has two equal sides and two equal angles. In the case of the Golden Triangle, the two equal angles = 72o and the apex angle = 36o.
Constructing With Straight Edge ad Compass
Draw line AB any convenient length, which is the length of the Golden Triangle's two longer sides. Be sure to extend the line segment AB beyond point B, as shown on right.
Next, draw line BC perpendicular to line AB, so that the two lines share the point B. Have BC = AB.
Now bisect line AB in half, at O. Place the pivot end of the compass at O and the pencil end at point C. Draw an arc from point C to where it intersects the extended base line at point E. Line BE = the base of the Golden Triangle.
Measure line BC (or AB) with the compass. Place the pivot end of the compass at point B and draw an arc over base BE. Then place the pivot end of the compass at point E and again extend the arc over base BE. The two arcs intersect at the apex of the Golden Triangle.
That's it. You're done!
Figuring Phi = 1.618034
Phi, the Golden Ratio, cannot be expressed as a simple fraction because it's an irrational number. But the figure 1.618 represents a reasonably close approximation.
Given that line OB = 1 and line BC = 2, then the hypotenuse OC must = the square root of 5 = 2.236068. That means the Base BE = 2.236068 - 1 = 1.236068.
The longer side of the Golden Triangle/the base of the Golden Triangle = 2/1.236068 = 1.618034 = Phi, the Golden Ratio
copyright 2013 by Bruce McClure