Timeline for number of integer points inside a triangle and its area
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Aug 29, 2020 at 15:35 | vote | accept | Johnny T. | ||
| Aug 29, 2020 at 5:00 | comment | added | fedja | Better upper bound on the deviation from the area? Certainly not: if you move $\beta$ and $\gamma$ by almost $1$ from some integer plus epsilon to the next integer minus epsilon, the number of integer points does not change but the area changes pretty much by the sum of the sides that is your current bound. Perhaps you wanted to ask something else or I misunderstood the question? | |
| Aug 28, 2020 at 17:31 | comment | added | Fedor Petrov | The question reduces to estimates of the sums $\sum_{k=1}^n \{\gamma k\}$. For fixed irrational $\gamma$ and large $n$ this is about $n/2$. | |
| Aug 28, 2020 at 14:20 | answer | added | Iosif Pinelis | timeline score: 5 | |
| Aug 28, 2020 at 11:59 | comment | added | Stanley Yao Xiao | In general I don't think you can do much better. Consider the triangle with end points $(1,1), (n,1), (n,(n+1)/n), n \in \mathbb{N}$ for example. The area is equal to $1/2$, but there are $n$ integral points on the boundary. This is essentially the worst case though. | |
| S Aug 28, 2020 at 11:28 | history | edited | Johnny T. |
retagging the question
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| S Aug 28, 2020 at 11:28 | history | suggested | vidyarthi | CC BY-SA 4.0 |
retagging the question
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| Aug 28, 2020 at 9:44 | review | Suggested edits | |||
| S Aug 28, 2020 at 11:28 | |||||
| Aug 28, 2020 at 8:31 | history | edited | Johnny T. | CC BY-SA 4.0 |
added 2 characters in body
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| Aug 28, 2020 at 7:57 | history | edited | Johnny T. | CC BY-SA 4.0 |
added 22 characters in body
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| Aug 28, 2020 at 7:52 | history | asked | Johnny T. | CC BY-SA 4.0 |