To calculate the golden rectangle, you need to understand its proportions, specifically the golden ratio (approximately 1.618). The golden rectangle's length to width ratio adheres to this golden ratio. Based on the reference, one way to visualize and calculate the dimensions involves assigning a value to a component and using that to determine the overall ratio.
Here's a breakdown based on the provided reference:
The reference suggests a scenario where a section of the golden rectangle has a length of 1. Based on this:
- Length of the Golden Rectangle: 1 + √5
- Width of the Golden Rectangle: 2
Calculating the Length-to-Width Ratio
The length-to-width ratio of the golden rectangle can then be calculated as:
(1 + √5) / 2 ≈ 1.618
This value is the golden ratio, often represented by the Greek letter phi (φ).
Therefore, to construct a golden rectangle, you simply need to ensure that the ratio of its length to its width is approximately 1.618.
Practical Insights:
- If you have a given width, multiply it by 1.618 to find the required length.
- If you have a given length, divide it by 1.618 to find the required width.
Example:
If you want to create a golden rectangle with a width of 5 units:
Length = Width 1.618 = 5 1.618 ≈ 8.09 units.
