## Cosmic Rectangle

I am delighted that a fellow maths educator is about to run a course on Maths and Art for gifted and talented year 9′s and even more delighted that a session will be devoted to the golden rectangle. It is an excuse for me to make my first origami maths video.

which is show an origami method of making a rectangle with the ratio $1:\frac{\sqrt{5}-1}{2}$

### 3 Responses to “Cosmic Rectangle”

1. creativemaths Says:

$\frac{\textup{length of long bit}}{\textup{length of short bit}}=\frac{\textup{length of whole part}}{\textup{length of long part}}\\ \Rightarrow \frac{x}{1-x}=\frac{1}{x}\\ \Rightarrow x\times x\ = 1 \times (1-x)\\ \Rightarrow x^2=1-x\\ \Rightarrow x^2-1+x=0\\ \Rightarrow x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \textup{where } a=1,b=1,c=-1\\ \Rightarrow x= \frac{-1 \pm \sqrt{1^2- 4 \times 1 \times (-1))}}{2 \times 1}\\ \Rightarrow x= \frac{-1 \pm \sqrt{1-(-4)}}{2}\\ \Rightarrow x= \frac{-1 \pm \sqrt{5}}{2}\\ \textup{and since we know that our desired number } x \textup{is between } 0 \textup{ and } 1 \textup{ we can exclude the negative solution so}\\ x= \frac{-1 + \sqrt{5}}{2} = \frac{\sqrt{5}-1}{2}\\=0.61803398874989484820458683436564 \textup{ copied and pasted from windows' calculator} \\$

2. Carlos Says:

:O Interesting :)

3. Ed Says:

I love it. I did think you raced a bit for a non-mathematician like me, I didn’t follow fast enough how the number 5 popped out of Pythagoras until you’d got to the end and I had a chance to think back. Also, just say no to biro! For the sake of video definition stick to your big fat felt tipped friend :-)