How tall is the Parthenon

Question

The Parthenon has the rectangular front in the form of a golden rectangle. If the lenght of the front of the Parthenon meaasures 101 feet, how tall is the parthenon?

Answer 1

In geometry, a golden rectangle is a rectangle whose

side lengths are in the golden ratio equal to approximately

1:(1+√5)/2 or 1:1.618.  The golden rectangle is comprised

of a smaller square of sides "a" adjacent to a smaller vertical

rectangle with height "a" and width "b" (common side is "a").  

The golden rectangle's sides can be expressed by....

 

(a+b)/a = a/b ≡ 1.618 where.....

 

"a+b" is the horizontal length of the larger rectangle 

"a" is the vertical height of the larger rectangle

 

With front elevation length equal to 101 ft, then "a+b=101".  So...

(a+b)/a≡1.618

   101/a≡1.618

           a≡101/1.618 

       ∴ a≡62.42 ft

 

The Parthenon's height is approximately 62.42 feet.

 

** Interesting to note that today's popular HD television

screen's aspect ratio of 16:9 come very close to representing

the golden rectangle ratio.