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? | ||
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| + | ---- | ||
| + | ==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). | ||
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Revision as of 10:13, 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).
