Geometry's Parts
Prepared by:
Joseph Malkevitch
Department of Mathematics and Computer Studies
York College (CUNY)
Jamaica, New York
email:
malkevitch@york.cuny.edu
web page:
http://www.york.cuny.edu/~malk/
To see the vast landscape that geometry occupies within mathematics it is an interesting exercise to wrote down the different parts of geometry. Of course these parts are not totally independent of one another but there are scholars who spend their whole research careers devoted to essentially one line in this list.
1. Axiomatics
2. Finite geometries
3. Geometric transformations
4. Symmetry
5. Tilings
6. Lattice point problems
7. Graph theory
8. Taxicab geometry
9. Convexity
10. Discrete geometry
11. Geometry of surfaces
12. Polyhedra
13. Equidecomposability
14. Differential geometry
15. Computational geometry
16. Packing and covering problems
17. Geometric probability
18. Digital geometry
19. Rigidity theory
20. Knots
21. Isoperimetric problems
22. Cartography
23. Geometric extremal problems
24. Geometric games
25. Plane curves
26. Distances
27. Coordinate systems
28. Geodesy
29. Algebraic geometry
30. Groups
31. Linear and integer programming
32. Conic sections
33. Polygons
34. Arrangements of lines and hyperplanes
35. N-dimensional geometry
36. Space-time geometry
37. Display of data
38. Image processing
39. Linkages
40. Computer vision
41. Fractal geometry
42. Geometric constructions
43. Geometric puzzles
44. Pythagorean theorem
45. Geometric inequalities
46. Integral geometry
47. Inversive geometry
48. Solid modeling
49. VLSI design
50. Error-correcting codes
51. Cellular automata
52. Optical illusions and moire patterns
53. Robotics
54. Crystallography
55. Dynamical systems
56. Shape grammars
57. Catastrophe theory
58. Geometry of complex numbers
59. Paper folding and origami
60. Geometric Ramsey theory
61. Geometry, art and architecture
62. Computer graphics
63. Geometry and physics
64. Descriptive geometry
65. Geometry of fabrics
66. Teaching geometry
67. Oriented matroids
68. History of geometry
69. Voronoi diagrams
70. Polyominoes, polyiamonds, and polyhexes
71. Pseudolines