Google Maps and Navigation
Consider traveling across a large round planet. The common Mercator map distorts land near the poles making Greenland seem larger than Africa which is not true. Hyperbolic geometry provides a solution to this distortion.
- Conformal Maps: Hyperbolic space can be mapped onto a flat surface while keeping angles the same. This ability allows for the creation of maps that accurately represent the shapes and positions of large areas like continents or the whole Earth. Mathematicians use a model of hyperbolic geometry called the Poincaré disk to create “conformal maps.” These concepts are crucial for highly accurate navigation systems and the scientific representation of planetary surfaces Whereas it not used in every phone app.
Real Life Applications of Hyperbolic Geometry
Euclidean geometry is known for its perfect circles and lines that never cross and it has long been the foundation of our understanding of space. Hyperbolic geometry is a seemingly abstract branch of mathematics that becomes valuable for understanding complexities beyond Euclidean geometry in the real world.
In hyperbolic geometry, circles can include countless points and parallel lines can spread apart endlessly. Although hyperbolic geometry might seem unrelated to daily life, it has surprising applications in various fields such as theoretical physics and Google Maps.