File:FS HC dia.png
FS_HC_dia.png (680 × 425 pixels, file size: 20 KB, MIME type: image/png)
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Summary
[edit]DescriptionFS HC dia.png |
English: Largest circle in a semicircle
Deutsch: Größter Kreis in einem Halbkreis |
Date | |
Source | Own work |
Author | Hans G. Oberlack |
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![](https://upload.wikimedia.org/wikipedia/commons/thumb/5/5e/FS_HC_dia.png/220px-FS_HC_dia.png)
The semicircle as base element. And the largest inscribed circle.
General case
[edit]Segments in the general case
[edit]0) The radius of the semicircle:
1) The radius of the inscribed circle:
Perimeters in the general case
[edit]0) Perimeter of base semicircle:
1) Perimeter of inscribed circle:
Areas in the general case
[edit]0) Area of the base semicircle
1) Area of the inscribed circle
Centroids in the general case
[edit]0) By definition the centroid point of a base shape is
1) The centroid of the inscribed circle relative to the base centroid is: , see Calculation 1
Normalised case
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/3/34/FS_HC.png/220px-FS_HC.png)
In the normalised case the area of the base semicircle is set to 1.
So
Segments in the normalised case
[edit]0) Radius of the base semicircle
1) Radius of the inscribed circle
Perimeter in the normalised case
[edit]0) Perimeter of base semicircle:
1) Perimeter of inscribed circle:
S) Sum of perimeters:
Area in the normalised case
[edit]0) Area of the base semicircle is by definition
1) Area of the base semicircle
Centroids in the normalised case
[edit]0)
1)
Distances of centroids
[edit]The distance between the centroid of the base semicircle and the centroid of the circle is:
Sum of distances:
Identifying number
[edit]Apart of the base element there is only 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]
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 22:01, 21 May 2022 | ![]() | 680 × 425 (20 KB) | Hans G. Oberlack (talk | contribs) | new version |
16:51, 21 May 2022 | ![]() | 680 × 425 (22 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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