What is the width w of the fern with length of its golden rectangle is 1.5 cm?
the golden ratio is ... (1 + √5) / 2 ≈ 1.618
1.5 cm = w * 1.618
The GR is (1+√5)/2
so divide 1.5 by that value
1.5 ÷ (1+√5)/2
= 1.5*2/(1+√5)
= 3/(1+√5) = appr .927
note 1.5/.927 = 1.6181..
and (1+√5)/2 = 1.6180339...
To determine the width w of the fern, we first need to understand what a golden rectangle is. A golden rectangle is a rectangle whose side lengths have a specific ratio, known as the golden ratio. The golden ratio is approximately 1.618.
Given that the length of the golden rectangle is 1.5 cm, we can use this information to find the width w.
To find the width w using the golden ratio, we can set up the following equation:
w / 1.5 = 1.618 / 1
To solve for w, we cross-multiply and divide:
w = (1.5 * 1.618) / 1
Simplifying:
w = 2.427 cm
So, the width w of the fern with a length of its golden rectangle being 1.5 cm is approximately 2.427 cm.