File:FS QHC dia.png
![File:FS QHC dia.png](https://upload.wikimedia.org/wikipedia/commons/thumb/2/2d/FS_QHC_dia.png/629px-FS_QHC_dia.png?20211231224940)
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Captions
Captions
Summary
[edit]DescriptionFS QHC dia.png |
English: FS QHC 2.1953234 dia Largest circle in a QH sangaku |
Date | |
Source | Own work |
Author | Hans G. Oberlack |
![](https://upload.wikimedia.org/wikipedia/commons/thumb/f/fd/FS_QHC.png/200px-FS_QHC.png)
Shows the largest circle that can be added to a QH-sangaku.
General case
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/2/2d/FS_QHC_dia.png/200px-FS_QHC_dia.png)
Base is the square of side length s.
Included is a semicircle with radius
In order to find the radius around point
of the circle within the semicircle the following calculations have to be done:
The line segment is the radius
of the semicircle. It is also the diameter of the circle around point
.
We get the equation:
Segments in the general case
[edit]0) The side length of the square:
1) Radius of the semicircle See QH_dia
2) Radius of the additional circle
Perimeters in the general case
[edit]0) Perimeter of base square
1) Perimeter of the semicircle
2) Perimeter of the additional circle
Areas in the general case
[edit]0) Area of the base square
1) Area of the semicircle
2) Area of the additional circle
Centroids in the general case
[edit]Centroid positions are measured from centroid point of the base shape.
0) Centroid positions of the base square:
1) Centroid positions of the semicircle:
2) Centroid positions of the additional circle:
Normalised case
[edit]In the normalised case the area of the base is set to 1.
Segments in the normalised case
[edit]0) Segment of the base square
1) Segment of the semicircle
2) Segment of the additional circle
Perimeters in the normalised case
[edit]0) Perimeter of base square
1) Perimeter of the semicircle
2) Perimeter of the additional circle
S) Sum of perimeters
Areas in the normalised case
[edit]0) Area of the base square
1) Area of the semicircle
2) Area of the additional circle:
Centroids in the normalised case
[edit]Centroid positions are measured from the centroids of the base shape
0) Centroid positions of the base square:
1) Centroid positions of the semicircle:
2) Centroid positions of the circle:
Distances of centroids
[edit]The distances between the centroids of elements are:
01)
02)
12)
S) The sum of the distances is:
Identifying number
[edit]Besides the base element there are two shapes allocated. Therefore the integer part of the identifying number is 2.
The decimal part of the identifying number is the decimal part of the sum of the perimeters and the sum of distances of the centroids in the normalised case.
So the identifying number is:
Licensing
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- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
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File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 22:49, 31 December 2021 | ![]() | 777 × 741 (34 KB) | Hans G. Oberlack (talk | contribs) | Uploaded own work with UploadWizard |
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