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Euclidean geometry has become closely connected with computational geometry, computer graphics, convex geometry, and some area of combinatorics.

Topology and geometry

The field of topology, which saw massive developement in the 20th century is a technical sense of transformation geometry.

Geometry is used on many other fields of science, like Algebraic geometry.

Types, methodologies, and terminologies of geometry:

Absolute geometry

Affine geometry

Algebraic geometry

Analytic geometry

Archimedes' use of infinitesimals

Birational geometry

Complex geometry

Combinatorial geometry

Computational geometry

Conformal geometry

Constructive solid geometry

Contact geometry

Convex geometry

Descriptive geometry

Differential geometry

Digital geometry

Discrete geometry

Distance geometry

Elliptic geometry

Enumerative geometry

Epipolar geometry

Euclidean geometry

Finite geometry

Geometry of numbers

Hyperbolic geometry

Information geometry

Integral geometry

Inversive geometry

Inversive ring geometry

Klein geometry

Lie sphere geometry

Non-Euclidean geometry

Numerical geometry

Ordered geometry

Parabolic geometry

Plane geometry

Projective geometry

Quantum geometry

Riemannian geometry

Ruppeiner geometry

Spherical geometry

Symplectic geometry

Synthetic geometry

Systolic geometry

Taxicab geometry

Toric geometry

Transformation geometry

Tropical geometry

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Q: What are some real world applications of geometry?
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This is geometry that is based on ordinary space-- space as we normally consider it. This is the ordinary space of 3 dimensions as you can imagine them in the coordinate system. Planes are flat, and parallel lines on any plane never ever meet, parallel planes never meet... you get the point. There are geometries that involve other kinds of space and they are called "non-Euclidean" geometries. Some of these non-Euclidian geometries are very real and not just theoretical in nature. For example, in the relativistic world, the space in and around very strong gravitational forces is distorted. This has been observed and verified in several ways. Euclidean proofs and the methods of analytical geometry do not work without accounting for these spacial distortions.


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