25 What are the Types of Numbers?
 R  C
Real vs. Imaginary, Rational vs. Irrational 
31 Twodimensional Looped Space
 R  C
A 2D looped space is limited in area but has no boundary. 
32 finite area
 R  C
In a 2D space there are two directions normal to each other at any point. In a looped space the path lengths along the two directions are finite.
So the area of the 2D looped space is finite because it is not greater than the product of the two lengths. 
42 finite volume
 R  C
In a 3D space there are three directions normal to each other at any point. In a looped space the path lengths along the three directions are finite. So the volume of the 3D looped space is finite because it is not greater than the product of the three le 

21 Looped Space
 R  C
Suppose a space as follows:
(1) At any point, if you go straight in any direction, you will get to the starting point.
(2) At any point, you can get to any other point by going straight. 
22 Onedimensional Looped Space
 R  C
In a 1D space, there's only one direction and hence 'going straight' means 'going'. In a 1D looped space, there's only one route and hence 'all the points in the route' means 'all the points in the space'. 
23 finite length, no end
 R  C
A 1D looped space is limited in length but has no end. 
The Poincare Conjecture
 R  C
In the early 1900s mathematicians and physicists were very interested in the shape of space. New experiments and theories were being developed that would ultimately create relativity theory and change our entire view of the universe. 
