# Math

## Irrational Numbers

• I read that Kronecker opposed the use of irrational numbers because they can't be constructed from integers by a finite number of steps. But you can construct pi as the ratio not only as an infinite series, but as the ratio of circumference to diameter. What's wrong with that?

## Line Integrals

I should set up a latex file in a rasmapedia directory to explain line integrals.

They are really "curve integrals".

1. You want to integrate x^2 over all points between 2 and 6.

2. You want to integrate x^2 + y^2 over all points between y=0, x in [2,6].

3. You want to integrate x^2 + y^2 over all points on the straight line between (2,2) and (6,6) (not intervals now--- vectors).

4. You want to integrate x^2 + y^2 over all points on the curve y = x^3 between (2,8) and 3,27). This is the real stuff.

5. You want to integrate x^2 + y^2 over all points in the area bounded by (0,0) and (0,2) and (2,0) and (2,2).

6. You want to integrate x^2 + y^2 over all points in the area bounded by y = x^3 and y = log x (or some two curves that cross).