Activity for JRN
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #292810 |
My answer is consistent with the one posted here: https://problemcorner.missouristate.edu/AdvSol35.html? (more) |
— | 2 months ago |
| Edit | Post #292810 |
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— | 2 months ago |
| Edit | Post #292810 |
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— | 2 months ago |
| Edit | Post #292810 |
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— | 2 months ago |
| Edit | Post #292810 |
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— | 2 months ago |
| Edit | Post #292810 |
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— | 2 months ago |
| Edit | Post #292810 |
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— | 2 months ago |
| Edit | Post #292810 | Initial revision | — | 2 months ago |
| Answer | — |
A: Area of the surface of revolution of a Reuleaux triangle Shown below is a Reuleaux triangle with the $x$-axis as one of its symmetry axes and the origin as one of its corners. Reuleaux triangle 1 Let points $A$, $B$, and $C$ be the corners of the Reuleaux triangle with width $w=1$ shown below. These are also the corners of the inscribed equilateral t... (more) |
— | 2 months ago |
| Edit | Post #292809 | Initial revision | — | 2 months ago |
| Question | — |
Area of the surface of revolution of a Reuleaux triangle A Reuleaux triangle is "a curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices." What is the area of the surface of revolution of a Reuleaux triangle (with width $w$) through one of its symmetry axes? (more) |
— | 2 months ago |
| Comment | Post #292776 |
My answer is consistent with the one posted here: https://problemcorner.missouristate.edu/AdvSol35.html? (more) |
— | 2 months ago |
| Edit | Post #292776 | Initial revision | — | 2 months ago |
| Answer | — |
A: Volume enclosed by the surface of revolution of a Reuleaux triangle Shown below is a Reuleaux triangle with the $x$-axis as one of its symmetry axes and the origin as one of its corners. Reuleaux triangle 1 Let points $A$, $B$, and $C$ be the corners of the Reuleaux triangle with width $w=1$ shown below. These are also the corners of the inscribed equilateral t... (more) |
— | 2 months ago |
| Edit | Post #292775 | Initial revision | — | 2 months ago |
| Question | — |
Volume enclosed by the surface of revolution of a Reuleaux triangle A Reuleaux triangle is "a curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices." What is the volume enclosed by the surface of revolution of a Reuleaux triangle (with width $w$) through one of its symmetry axes? (more) |
— | 2 months ago |
| Comment | Post #292644 |
Thank you for the reference. I was not aware of it. The MathOverflow problem involves breaking a stick in five randomly chosen points; the problem I mention involves having the lengths of the sticks the same as six randomly chosen points. The two seem different. (more) |
— | 2 months ago |
| Comment | Post #292644 |
Thank you for pointing this out. I have replaced the broken link with a working one. (more) |
— | 2 months ago |
| Edit | Post #292644 |
Post edited: Fixed broken link |
— | 2 months ago |
| Edit | Post #292644 | Initial revision | — | 3 months ago |
| Question | — |
Probability that six random numbers between 0 and 1 are the lengths of a tetrahedron's edges > If six numbers are chosen at random, uniformly and independently, from the interval [0,1], what is the probability that they are the lengths of the edges of a tetrahedron? This is Part 3 of Problem No. 81 of the Missouri State University's Advanced Problem Archive. The website seems to have b... (more) |
— | 3 months ago |
| Comment | Post #286926 |
Do they have to be first order ordinary differential equations? (more) |
— | over 2 years ago |
| Edit | Post #286612 | Initial revision | — | over 2 years ago |
| Question | — |
Notation for nested exponents An expression such as $a^{b^c}$ is usually interpreted as $a^{(b^c)}$ and not as ${(a^b)}^c$. (See, for example, the Wikipedia entry for double exponential function.) Is there a reputable source that states how an expression such as $a^{b^{c^{\cdots^n}}}$ is to be interpreted? (more) |
— | over 2 years ago |
| Comment | Post #285983 |
The handwritten text that you show is not Xi, it is Xi divided by overline Xi (as shown in Peter Taylor's answer). (more) |
— | almost 3 years ago |
| Edit | Post #285018 | Initial revision | — | about 3 years ago |
| Answer | — |
A: Intuitively, why can $a, b$ cycle in ${\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}$? "what's the intuition why a,b can swap places, whilst c remains in the numerator?" It's called the commutative property of multiplication. If $ab=c$ leads to $b=c/a$, then $ba=c$ leads to $a=c/b$. (more) |
— | about 3 years ago |
| Comment | Post #284723 |
"*In fact, subtracting the additive inverse of $b$ to $a$ still counts as using the addition operator.*" If so, then your proposed method "$(a\times b)-(b-a)$" would involve addition, because it is just $a\times b-b+a$. (more) |
— | about 3 years ago |
| Comment | Post #283252 |
From the words in the text "by putting the cutoff for a positive result at a very low level (purple dashed line), you may capture all positive samples, and so the test is very sensitive." and the words in the image "To increase sensitivity, shift to the left (blue line)," it can be concluded that the... (more) |
— | over 3 years ago |
| Comment | Post #283945 |
You say "Solve all operations" but it seems that you mean "perform all operations." Instead of "equation solving," it seems that you are interested in "expression evaluation." For example, when you evaluate the expression "4(3+2)" as "20," you are not solving any equations (the expression does not ... (more) |
— | over 3 years ago |
| Edit | Post #283388 |
Post edited: Fixed formatting |
— | over 3 years ago |
| Edit | Post #283638 | Post undeleted | — | over 3 years ago |
| Edit | Post #283638 |
Post edited: Fixed error |
— | over 3 years ago |
| Edit | Post #283638 |
Post edited: Fixed error |
— | over 3 years ago |
| Edit | Post #283638 | Post deleted | — | over 3 years ago |
| Edit | Post #283638 | Initial revision | — | over 3 years ago |
| Answer | — |
A: Is $r \times \frac{d}{dt} mv=\frac{d}{dt} (r \times mv)$ In equations 1.9 and 1.10, the quantities $\mathbf{r}$, $\mathbf{F}$, $\mathbf{N}$, and $\mathbf{v}$ are vectors, and the symbol $\times$ denotes a vector cross product operation. The product rule of differential calculus also applies to the vector cross product. That is, $\frac{\mathrm{d}}{\ma... (more) |
— | over 3 years ago |
| Comment | Post #283633 |
What is the result of a vector crossed with itself? (more) |
— | over 3 years ago |
| Comment | Post #283593 |
@#53922 A function can be a continuous function and yet still have a discontinuity at a point, as long as that point is not in its domain. (more) |
— | over 3 years ago |
| Comment | Post #283593 |
The graph of Desmos is correct. But the function is still a continuous function. Desmos "doesn't say" it is a continuous function, but it "doesn't say" that it is not a continuous function, either. (more) |
— | over 3 years ago |
| Comment | Post #283593 |
More specifically, while $f(x)=\frac{1}{x-1}$ is discontinuous at $x=1$, it is a continuous function because of what @r~~ said. (more) |
— | over 3 years ago |
| Suggested Edit | Post #283388 |
Suggested edit: Fixed formatting (more) |
helpful | over 3 years ago |
| Comment | Post #283317 |
@#54138 means the exponent must be zero, so it should be k (which is equal to zero) and it should not be k+1 (which is equal to one). (more) |
— | over 3 years ago |
| Comment | Post #283281 |
A line has length but it has no thickness. When you say "measure a perimeter," that means measuring its length. You don't need to measure its "thickness" because the "thickness" of a line is zero. I suggest that you edit your question to say that you are interested in the "thickness" because the t... (more) |
— | over 3 years ago |
| Comment | Post #283281 |
Based on your comments, it seems that you are asking about the "thickness" of the perimeter, and not its length. Is that correct? Are you basically asking how "thick" a line is? (more) |
— | over 3 years ago |
| Edit | Post #282998 |
Post edited: OP says they meant to say "variable," not "function." |
— | over 3 years ago |
| Suggested Edit | Post #282998 |
Suggested edit: OP says they meant to say "variable," not "function." (more) |
helpful | over 3 years ago |
| Comment | Post #283086 |
This is the first link that comes up when I use DuckDuckGo to search for "integration under integral sign": https://mathworld.wolfram.com/IntegrationUndertheIntegralSign.html (more) |
— | over 3 years ago |
| Comment | Post #282998 |
Please edit your question to use the correct term. (more) |
— | over 3 years ago |
| Edit | Post #283023 | Initial revision | — | over 3 years ago |