During the course of the Discovering Mathematics module, I have grown to have a more active awareness and somewhat alertness about the Golden Ratio…

1.61803398875

It appears as a number we may dismiss, but its essence is something astonishing and that is, the Golden Ratio is a measurement buildings and other objects use to be proportioned and it is suggested and perhaps proven that if something is proportioned in accordance to the Golden Ratio, it appears more attractive. 
The Golden Ratio primarily is the Fibonacci Sequence in practice, if you like. Fibonacci was an Italian Mathematician and the Fibonacci Sequence a theory of numbers, sequencing and ratio, used in architecture, buildings, as well as seen in nature (have look at pine cones). The sequence…

1, 1, 2, 3, 5, 8, 13, 21…

It is simple, arguably, to continue the sequence when you understand the theory behind it:
1+1 = 2
1+2 = 3
2+3 = 5
3+5 = 8
8+13 = 21…
Shown here is the sequence and continuation of calculations which construct the Fibonacci Sequence. Each number is put into the next calculation and so on.

This takes us onto the Fibonacci Spiral.

(Picture from: http://i.stack.imgur.com/eHWK9.png)

This is the Fibonacci Spiral drawn out and this is where the connections may make sense between maths ans beauty. Buildings, flowers, paintings and other art works are proportioned based on this mathematical concept and theory that using this ratio and scale will make things appear more attractive.

Here is a link if you would like to look further into the beauty and the art of maths and design:
Dynamical Systems by BBC News – http://news.bbc.co.uk/1/hi/sci/tech/7617191.stm

References

Bourne, M. (2015) The Math Behind the Beauty. Available at: http://www.intmath.com/numbers/math-of-beauty.php. Last Accessed: Dec 5 2015.

Image from – http://i.stack.imgur.com/eHWK9.png