File:FS VR dia.png
![File:FS VR dia.png](https://upload.wikimedia.org/wikipedia/commons/thumb/c/c7/FS_VR_dia.png/550px-FS_VR_dia.png?20220504212456)
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Captions
Captions
Summary
[edit]DescriptionFS VR dia.png |
English: Largest right triangle in a quarter circle
Deutsch: Größtes rechtwinkliges Dreieck in einem Viertelkreis |
Date | |
Source | Own work |
Author | Hans G. Oberlack |
![](https://upload.wikimedia.org/wikipedia/commons/thumb/c/c7/FS_VR_dia.png/220px-FS_VR_dia.png)
The quarter circle as base element. Inscribed is the largest right triangle.
General case
[edit]Segments in the general case
[edit]0) The radius of the quarter circle
1) Side length of the inscribed triangle: , since
Perimeters in the general case
[edit]0) Perimeter of base quarter circle:
1) Perimeter of the inscribed triangle:
S) Sum of perimeters:
Areas in the general case
[edit]0) Area of the base quarter circle
1) Area of the inscribed triangle:
Centroids in the general case
[edit]0) Centroid position of the quarter circle:
1) Centroid position of the inscribed triangle: , see calculation 1
Normalised case
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/0/04/FS_VR.png/220px-FS_VR.png)
In the normalised case the area of the base quarter circle is set to 1.
So
Segments in the normalised case
[edit]0) Radius of the base quarter circle
1) Side length of the inscribed triangle:
Perimeters in the normalised case
[edit]0) Perimeter of base quarter circle
1) Perimeter of the inscribed triangle
S) Sum of perimeters:
Areas in the normalised case
[edit]0) Area of the base quarter circle is by definition
1) Area of the inscribed triangle:
Centroids in the normalised case
[edit]0) Centroid position of the quarter circle:
1) Centroid position of the inscribed triangle:
Distances of centroids
[edit]The distance between the centroid of the base element and the centroid of the triangle is:
Identifying number
[edit]Apart of the base element there is one shape allocated. Therefore the integer part of the identifying number is 1.
The decimal part of the identifying number is the decimal part of the sum of the perimeters and the distances of the centroids in the normalised case.
So the identifying number is:
Calculations
[edit]Calculation 1
[edit]Position of the point A:
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Licensing
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File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 21:24, 4 May 2022 | ![]() | 878 × 957 (32 KB) | Hans G. Oberlack (talk | contribs) | Uploaded own work with UploadWizard |
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Horizontal resolution | 59.06 dpc |
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Vertical resolution | 59.06 dpc |
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