What is Hyperbolic Geometry?
Hyperbolic geometry or Lobachevskian geometry is a type of non-Euclidean geometry where triangles have angles adding up to less than 180 degrees. In this geometry, parallel lines move away from each other and there are no similar triangles. It is based on the hyperbolic plane which has a consistent negative curve.
In Euclidean geometry, parallel lines never meet and the angles of a triangle sum to exactly 180°. However, in hyperbolic geometry, parallel lines can intersect and the sum of angles in a triangle is always less than 180°.
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.