Understanding Longitude, Latitude, and Area Measurement on Google Earth

Many people wonder how Google Earth can display different shapes for longitude and latitude lines, when these spherical geometry lines are supposed to be rectilinear. This confusion often stems from the flat mapping (cartography) used to represent the Earth's surface on a digital grid. In reality, the Earth is an oblate spheroid, and calculus helps reconcile the discrepancy between spherical and linear measurements.

The Earth's Spherical Geometry

The Earth's surface is roughly spherical, though it's actually an oblate spheroid. When we try to represent the Earth on a flat surface, such as a map or a digital grid, distortions inevitably occur. One of the fundamental issues is that the lines of longitude and latitude don't form perfect squares because of the curvature of the Earth.

Flat Maps and Sphericity

Maps are often created using a flat map approach, where the Earth's surface is distorted to fit a flat rectangle. This method can result in areas near the poles being stretched, while areas near the equator are compressed. Consequently, the northern side of a grid square on a flat map will appear shorter than the southern side, an effect known as conformal projection.

Why Square Miles Aren't Perfect Squares

It's a common misunderstanding that area measurements must always be literal squares or rectangles. In reality, square miles (or square kilometers) are simply units of area, and they don't have to be geometrically perfect. Consider a circular area with a one-mile radius; its area would be approximately 3.14 square miles. Similarly, a square mile can be imagined as a large carpet, which can be cut and rearranged into various shapes without changing its area.

Reconciling Spherical Geometry with Area Measurement

The boxes delimited by longitude and latitude lines on Google Earth don't have to be perfect squares because they are representations of a spherical surface on a digital grid. At the poles, the lines of longitude and latitude form triangles rather than squares. This shape discrepancy is due to the curvature of the Earth and the distortions inherent in flat map representations.

Imagine a square mile of carpet. While a square mile is defined as an area of one square mile, it doesn't need to be a geometrically perfect square. By cutting and rearranging the carpet, we can form various shapes that still cover one square mile.

Conclusion

Understanding the principles of spherical geometry and the distortions that occur in flat map representations can help clarify the apparent discrepancies between longitude, latitude, and area measurements on Google Earth. Square miles are simply units of area, and they don't have to be perfect squares. Google Earth, like any digital map, is a representation of a 3D world on a 2D grid, which inevitably introduces some level of distortion.

Keywords: longitude, latitude, square miles