Timeline for Cutting a Circular Pizza Vertically
Current License: CC BY-SA 4.0
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25 events
| when toggle format | what | by | license | comment | |
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| Aug 18, 2023 at 15:13 | answer | added | Yousername | timeline score: 0 | |
| Aug 16, 2023 at 18:59 | comment | added | The Empty String Photographer | @Neil please remember to ping me next time. In this case, the anti derivative does have a formula, one which is \$\dfrac{x\sqrt{10000-x^2}}{2}+5000\arcsin\left(\dfrac{x}{100}\right)\$. | |
| Aug 16, 2023 at 15:13 | comment | added | Neil |
"inverse of" isn't a formula. (Even ∫ can't be called a formula in some cases, e.g. for the Normal distribution.)
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| Aug 16, 2023 at 12:31 | comment | added | The Empty String Photographer | @Neil there technically is a direct formula. Here is the formula to work out the first item in the list (with \$f(x) = \sqrt{10000-x^2}\$, \$F(x) = \int f(x) dx\$, \$F^{-1}(x) = \text{inverse of} F(x)\$ and \$z=\text{number of slices}\$): $$\operatorname {abs}\left(F^{-1}\left(\frac{10000\pi}{z}+F(0)\right)-100\right)$$ | |
| Aug 16, 2023 at 10:28 | comment | added | The Empty String Photographer | Sorry my bad, change the upper number of the last integral to 200. | |
| Aug 15, 2023 at 16:03 | comment | added | The Empty String Photographer | Just solve for (0-indexed) array \$a\$ with length \$n\$ where $$\int_{0}^{a_0}\sqrt{10000-x^2}dx = \int_{a_0}^{a_1}\sqrt{10000-x^2}dx = ... = \int_{a_{n-1}}^{100}\sqrt{10000-x^2}dx$$ and the solution shall follow. Oh, and in case it helps, the indefinite integral of \$\sqrt{10000-x^2}\$ is $$\dfrac{x\sqrt{10000-x^2}}{2}+5000\arcsin\left(\dfrac{x}{100}\right)$$ | |
| Aug 14, 2023 at 9:54 | answer | added | Dominic van Essen | timeline score: 3 | |
| Aug 14, 2023 at 7:23 | answer | added | Damian Pavlyshyn | timeline score: 6 | |
| Aug 14, 2023 at 7:06 | comment | added | Damian Pavlyshyn | Another issue is that rounding to the nearest integer is not a consistent measure of precision, since it requires much more precise estimates for values that are close to n + 0.5 for an integer n. Allowing for off-by-one errors is much closer to the more intuitive "estimate must be within 1 of the true value" | |
| Aug 13, 2023 at 23:06 | answer | added | matteo_c | timeline score: 1 | |
| Aug 12, 2023 at 18:43 | answer | added | Kjetil S | timeline score: 1 | |
| Aug 12, 2023 at 12:21 | history | edited | Yousername | CC BY-SA 4.0 |
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| Aug 12, 2023 at 12:09 | history | edited | Yousername | CC BY-SA 4.0 |
added 713 characters in body
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| Aug 12, 2023 at 12:08 | comment | added | Yousername | Never mind, it looks like there are a few cases where that happens. I'll add those as test cases. | |
| Aug 12, 2023 at 8:32 | answer | added | bsoelch | timeline score: 3 | |
| Aug 12, 2023 at 7:35 | comment | added | xnor | It seems though that the integer making a slice area closest to the desired area isn't necessary the same as the true real value rounded to the nearest integer. If there's any inputs where this distinction matters, it would be good to have test cases for them. | |
| Aug 12, 2023 at 7:10 | answer | added | Neil | timeline score: 2 | |
| Aug 12, 2023 at 6:37 | history | became hot network question | |||
| Aug 12, 2023 at 1:41 | answer | added | l4m2 | timeline score: 2 | |
| Aug 11, 2023 at 23:52 | answer | added | Arnauld | timeline score: 5 | |
| Aug 11, 2023 at 23:37 | comment | added | Yousername | The intended solution is to loop over the integers 0-100 and see which will make the slice area closest to the desired area, or to use some method to approach the real answer over time. | |
| Aug 11, 2023 at 23:31 | comment | added | Neil |
There is no direct formula for these. The values for an input of 4 are known from the Quarter-Tank Problem which can be looked up on e.g. Wolfram MathWorld.
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| Aug 11, 2023 at 23:12 | comment | added | Yousername | @Arnauld The results should match the test cases. | |
| Aug 11, 2023 at 23:11 | comment | added | Arnauld | Is a \$\pm 1\$ error on some values acceptable? Or should we use enough precision to get exactly the results shown here? | |
| Aug 11, 2023 at 22:31 | history | asked | Yousername | CC BY-SA 4.0 |