The **Stereographic Polar Zenithal Projection** is a type of **azimuthal projection** that maps the surface of a sphere (such as the Earth) onto a flat plane. In this projection, a light source is conceptually placed at the opposite pole from the one being mapped. For example, if mapping the North Pole, the projection is created as if the light source were at the South Pole. This unique perspective allows lines of latitude to appear as concentric circles and meridians (lines of longitude) to radiate outward as straight lines from the central point—the pole.

This projection is known for preserving **angles** and local shapes accurately, making it a **conformal projection**. However, it introduces increasing distortion in **area and distance** as one moves farther from the center (pole) toward the equator.

## Construction

**Question:** Construct a **Stereographic Polar Zenithal Projection** for the **North Pole** at a **scale of 1:300,000,000** with **meridian intervals of 30°** and **parallels at 45°, 60°, and 75°N**.

**Solution: **

**Calculate the Radius of the Globe on the Given Scale:**- $$\text{Radius of the Globe} = \frac{6400 \times 1,00,000}{300,000,000} = 2.1 \, \text{cm}$$
- Thus, the radius of the globe on the scale of 1:300,000,000 is
**2.1 cm**.

**Draw the Globe Circle:**- Draw a
**circle**with a**radius of 2.1 cm**. This circle represents the Earth on the given scale.

- Draw a
**Draw the Polar and Equatorial Diameters:**- Draw two
**perpendicular diameters**passing through the centre**O**of the circle: **NS**for the**polar diameter**.**WE**for the**equatorial diameter**(perpendicular to NS).

- Draw two
**Set Up the Projection Plane:**- Place the
**projection plane (XY)**at the**North Pole (N)**, perpendicular to the polar diameter (NS).

- Place the
**Draw Radii Corresponding to Parallels (45°, 60°, 75°):**- From the centre
**O**, draw lines making**45°, 60°, and 75°**angles with the equatorial diameter**OE**using a**protractor**. - These lines meet the
**circle NWSE**at points**c’, b’, and a’**respectively.

- From the centre
**Draw lines from the periphery**- From point
**S**extend lines such that they intersect from points**c’, b’, and a’**and fall on line**XY**at points**c, b and a’**respectively.

- From point
**Draw the Parallels:**- Use the
**North Pole (N)**as the centre on the projection plane. - Draw
**concentric circles**with radii corresponding to the intersections of the projection plane:**Na**= 75°N**Nb**= 60°N**Nc**= 45°N

- Since the
**equator**lies far from the North Pole, it won’t appear on the projection.

- Use the
**Draw Meridians at 30° Intervals:**- From the centre
**N**, draw**straight lines at 30° intervals**using a**protractor**: **0° meridian,****180° meridian**opposite to it.**90°E**and**90°W**at right angles.

- From the centre
**Final Diagram:**- The resulting projection will show
**the North Pole at the centre**. **Meridians at 30° intervals**radiate outward.**Parallels**at**45°, 60°, and 75°N**are represented as**concentric circles**around the pole.

- The resulting projection will show