Question

In a sunflower seed head, there are 100 spirals going left. How many spirals are going right if the ratio of spirals is close to the golden ratio?91 spirals62 spirals54 spirals78 spirals47 spirals

Answer 1

Solution:

Given that:

In a sunflower seed head, there are 100 spirals going left.

Applying the golden ratio, i.e.

$\begin{gathered} \varphi=\frac{100}{a} \\ Where\text{ a is the number of spirals going right} \\ \varphi=1.6180\text{ \lparen four decimal places\rparen} \end{gathered}$

Substitute the value of the golden ratio to find the number of spirals going right, a.

$\begin{gathered} \varphi=\frac{100}{a} \\ 1.6180=\frac{100}{a} \\ Crossmultiply \\ 1.6180a=100 \\ Divide\text{ both sides by 1.6180} \\ \frac{1.6180a}{1.6180}=\frac{100}{1.6180} \\ a=61.80469 \\ a=62\text{ spirals \lparen nearest whole number\rparen} \end{gathered}$

Hence, the answer is 62 spirals (nearest whole number)