Construct a logarithmic spiral using golden rectangles with sides measuring 4 units 

To construct a logarithmic spiral using golden rectangles where the initial rectangle has sides measuring 4 units, you can follow these steps:

### Step 1: Define the Golden Ratio
The golden ratio (denoted by \( \phi \)) is approximately 1.618. This value governs the relationship between the lengths of the sides of a golden rectangle. Specifically, the ratio between the longer side (denoted as \( l \)) and the shorter side (denoted as \( s \)) of a golden rectangle is:

\[
\frac{l}{s} = \phi
\]

### Step 2: Construct the Initial Golden Rectangle
Given that one side of the rectangle measures 4 units, let's call this side \( s = 4 \). Using the golden ratio, the other side of the rectangle, \( l \), can be calculated as:

\[
l = \phi \cdot s = 1.618 \cdot 4 = 6.472 \, \text{units}
\]

So, the dimensions of the initial golden rectangle are 4 units by 6.472 units.

### Step 3: Subdivide the Rectangle into Smaller Golden Rectangles
Inside the original rectangle, you can draw a square with sides equal to the shorter side of the rectangle (4 units). This will leave a smaller golden rectangle inside, with dimensions 4 units by approximately 2.472 units (since

Construct a logarithmic spiral using golden rectangles with sides measuring 4 units.

Explore the step-by-step process of constructing a logarithmic spiral using golden rectangles. Starting with a rectangle with sides of 4 units and applying the golden ratio, this guide covers geometry, logarithmic spirals, and related formulas. Suitable for high school students in Grades 10-12.

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