File:FS RCCC dia.png
![File:FS RCCC dia.png](https://upload.wikimedia.org/wikipedia/commons/thumb/7/78/FS_RCCC_dia.png/656px-FS_RCCC_dia.png?20220224214021)
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Captions
Captions
Summary
[edit]DescriptionFS RCCC dia.png |
English: Largest circle in a RCC sangaku
Deutsch: Größter Kreis in einem RCC Sangaku |
Date | |
Source | Own work |
Author | Hans G. Oberlack |
Shows the largest circle within RCC sangaku.
![](https://upload.wikimedia.org/wikipedia/commons/thumb/7/78/FS_RCCC_dia.png/300px-FS_RCCC_dia.png)
Elements
[edit]Base is the right isosceles triangle of side length and centroid
Inscribed is the largest possible circle with radius around point
Inscribed is the largest possible circle outside the first circle with radius around point
Inscribed is the largest possible circle outside the first two circles with radius around point
General case
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/f/f1/FS_RCCC.png/150px-FS_RCCC.png)
Segments in the general case
[edit]0) The side length of the base right triangle
1) Radius of the first circle (See FS RC).
2) Radius of the second circle , (See details under FS RCC dia.png)
3) For symmetry reasons is the radius of the third circle
Perimeters in the general case
[edit]0) Perimeter of base triangle (See FS R )
1) Perimeter of the first circle (See FS RC )
2) Perimeter of the second circle (See FS RCC )
3) Perimeter of the third circle is for symmetry reasons
Areas in the general case
[edit]0) Area of the base triangle (See FS R )
1) Area of the inscribed circle (See FS RC)
2) Area of the second circle (See FS RCC)
3) For the symmetry reasons is the area of the third circle
Centroids in the general case
[edit]Centroid positions are measured from the centroid point of the base shape
0) Centroid positions of the base triangle:
1) Centroid positions of the inscribed circle: (See FS RC)
2) Centroid positions of the second circle:
, (See FS RCC)
, (See FS RCC)
3) Centroid positions of the third are for symmetry reasons:
Normalised case
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/c/c1/FS_RCCC_bw.png/220px-FS_RCCC_bw.png)
In the normalised case the area of the base shape is set to 1.
Segments in the normalised case
[edit]0) Side length of the base triangle
1) Radius of the inscribed circle
2) Radius of the second inscribed circle
3) Radius of the third inscribed circle
Perimeters in the normalised case
[edit]0) Perimeter of base triangle
1) Perimeter of the inscribed circle
2) Perimeter of the second circle
3) Perimeter of the second circle
S) Sum of perimeters
Areas in the normalised case
[edit]0) Area of the base triangle
1) Area of the inscribed circle
2) Area of the second inscribed circle
3) Area of the third inscribed circle
Centroids in the normalised case
[edit]Centroid positions are measured from the centroid point of the base shape.
0) Centroid positions of the base triangle:
1) Centroid positions of the inscribed circle:
2) Centroid positions of the second circle:
3) Centroid positions of the third circle:
Distances of centroids
[edit]01) The distance between the centroid of the base element and the centroid of the circle is:
02) The distance between the centroid of the base element and the centroid of the second circle is:
03) The distance between the centroid of the base element and the centroid of the third circle is:
12) The distance between the centroids of the first and the second circle is:
13) The distance between the centroids of the first and the third circle is:
13) The distance between the centroids of the second and the third circle is:
The sum of the distances is:
Identifying number
[edit]Apart of the base element there are three shapes allocated. Therefore the integer part of the identifying number is 3.
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:
Licensing
[edit]![w:en:Creative Commons](https://upload.wikimedia.org/wikipedia/commons/thumb/7/79/CC_some_rights_reserved.svg/90px-CC_some_rights_reserved.svg.png)
![attribution](https://upload.wikimedia.org/wikipedia/commons/thumb/1/11/Cc-by_new_white.svg/24px-Cc-by_new_white.svg.png)
![share alike](https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/Cc-sa_white.svg/24px-Cc-sa_white.svg.png)
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 21:40, 24 February 2022 | ![]() | 681 × 622 (26 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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