14-billion-years-later: The Inherent Beauty of GeometryTo me geometry is absolutely beautiful, I find small mathematical quirks such as the relation of volume to surface area of a sphere (simple derivation of the formula) to be astounding but the following is just extraordinary.The above pentagram is pretty cool, it’s set inside a pentagon and makes up a series of isosceles triangles using sets of parallel lines (marked b) all the while making a second, inverted regular pentagon in the middle, but it gets better. The pentagram includes the golden ratio in every aspect of its design: the ratio of the length of a to b is equal to the golden ratio ((1+√5)/2 ≈ 1.618). However it doesn’t stop there, similarly the ratios b:c and c:d are also golden. To summarize: a:b = b:c = c:d =  (1+√5)/2, the golden ratio. 

14-billion-years-later:

The Inherent Beauty of Geometry

To me geometry is absolutely beautiful, I find small mathematical quirks such as the relation of volume to surface area of a sphere (simple derivation of the formula) to be astounding but the following is just extraordinary.

The above pentagram is pretty cool, it’s set inside a pentagon and makes up a series of isosceles triangles using sets of parallel lines (marked b) all the while making a second, inverted regular pentagon in the middle, but it gets better. The pentagram includes the golden ratio in every aspect of its design: the ratio of the length of a to b is equal to the golden ratio ((1+√5)/2 ≈ 1.618). However it doesn’t stop there, similarly the ratios b:c and c:d are also golden.

To summarize: a:b = b:c = c:d =  (1+√5)/2, the golden ratio. 

(via 14-billion-years-later)

Tags: geometry golden ratio