Answer to Question #137068 in Geometry for jay nerves

Question

Let’s draw a rectangle with the Golden Ratio:

1. Draw a square of size "1"
2. Place a dot half way along one side
3. Draw a line from that point to an opposite corner
4. golden ratio construction
5. Now turn that line so that it runs along the square's side
6. Then you can extend the square to be a rectangle with the Golden Ratio!

Answer 1

1. Draw a square of size "1"

2. Place a dot half way along one side

3. Draw a line from that point to an opposite corner

4. golden ratio construction

5. Now turn that line so that it runs along the square's side

6. Then you can extend the square to be a rectangle with the Golden Ratio!

$$1^2+(\dfrac{1}{2})^2=\dfrac{5}{4}=(\dfrac{\sqrt{5}}{2})^2$$

That rectangle above shows us a simple formula for the Golden Ratio.

When the short side is $1,$ the long side is $\dfrac{1}{2}+\dfrac{\sqrt{5}}{2},$ so:

$$\varphi=\dfrac{1}{2}+\dfrac{\sqrt{5}}{2}$$