**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