# Difference between revisions of "Math"

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==Irrational Numbers== | ==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? | *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). | ||

---- | ---- |

## Revision as of 11:13, 4 December 2021

## Miscellaneous

- Gower Twitter thread on thinking you've found a great result, but you made a mistake (2021).

- Shannon's math camp notes on analysis, etc.

## Math Education

- My StackExchange question on synthetic division and whether it is every useful for anything.

## 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).