The Golden Rectangle

Aloha Fibonacho muchachos! In the previous post I talked about the golden ratio and the fibonacci sequence, and before y'all forget, we should review what we have learnt in the last post! :)

The golden ratio Phi (), is a special number approximately equal to 1.618033897...so on. Drawing the golden rectangle from at the golden ratio is very easy. Here is the formula! 

Ex.)  The square is 1x1. 

 = 1/2 + √5/2  (This will be the length of the other corner up top in the rectangle) 

you can see in the diagram that at the 1/2 mark, the line is extended to another corner. That length is  √5/2. 

Then you align that line so it lies on the same horizon as the square, and you have an extended length! 

 = (1+√5)/2 

Draw a square place a 1/2 way dot, where they meet, and you have a golden rectangle! 

and finally...THE GOLDEN RECTANGLE ITSELF! 

The golden rectangle is a visual representation of the Fibonacci sequence. Because we know that a square with a golden ratio and the dimensions of 1x1 has a formula of 

 = 1/2 + √5/2  

 = 1+√5/2

The golden rectangle can be cut off or sectioned into squares using the formula above,  and the end result would look like: 

we can see the squares created here are basically successive fibonacci sequence numbers! Cool huh? The spiral created while forming this rectangle is also called the golden spiral. I'm so honoured that a lot of buildings today are 'inspired' by this formula and is considered a symbol of beauty in nature.

See you soon! Bye! Have a fantastic day, my Fibonachos!

Sources: 

http://mathforum.org/dr.math/faq/faq.golden.ratio.html
https://www.mathsisfun.com/numbers/golden-ratio.html