File:FS CVC2 dia.png
FS_CVC2_dia.png (569 × 573 pixels, file size: 31 KB, MIME type: image/png)
Captions
Captions
Summary
editDescriptionFS CVC2 dia.png |
English: Second largest circle in a circle with the largest quarter circle Deutsch: Zweitgrößter Kreis in einem Kreis, der den größten Viertelkreis enthält |
Date | |
Source | Own work |
Author | Hans G. Oberlack |
![](https://upload.wikimedia.org/wikipedia/commons/thumb/a/a3/FS_CVC2.png/220px-FS_CVC2.png)
Shows the second largest circle within a forced sudoku of CV-type.
Elements
edit![](https://upload.wikimedia.org/wikipedia/commons/thumb/2/2c/FS_CVC2_dia.png/300px-FS_CVC2_dia.png)
Base is the circle of given radius around point
and the resulting quarter circle
of radius
around point
Inscribed is the largest possible circle in the shape having radius
around point
. This is the second largest circle in a CV type sangaku.
In order to find radius of the circle, the following reasoning is used:
The line segment is the diameter of the circle around
with radius
.
The line segment
is radius
of the quarter circle around
.
The line segment
is the diameter of the circle around
with radius
.
From the construction of the quarter circle (see FS_CV) we know that . So:
General case
editSegments in the general case
edit0) The radius of the base circle:
1) Radius of the quarter circle:
2) Radius of the additional circle:
Perimeters in the general case
edit0) Perimeter of base circle
1) Perimeter of the quarter circle
2) Perimeter of additional circle
Areas in the general case
edit0) Area of the base circle:
1) Area of the inscribed quarter circle:
2) Area of the additional circle:
Covered surface of base shape:
Centroids in the general case
edit1) Centroids as graphically displayed
editCentroid positions are measured from the centroid point of the base shape
0) Centroid of the base square:
1) Centroid of the inscribed quarter circle:
2) Centroid of the additional circle: , see calculation 1
2) Orientated centroids
editThe centroid positions of the following shapes will be expressed orientated so that the first shape n with will be of type
with
. This means that the graphical representation will not correspond to the mathematical expression.
0) Orientated centroid position of the base circle:
1) Orientated centroid positions of the inscribed quarter circle:
2) Centroid of the additional circle:
Normalised case
edit![](https://upload.wikimedia.org/wikipedia/commons/thumb/c/c8/FS_CVC2_bw.png/220px-FS_CVC2_bw.png)
In the normalised case the area of the base is set to 1.
Segments in the normalised case
edit0) Radius of the base circle
1) Radius of the inscribed quarter circle
2) Radius of the additional circle
Perimeters in the normalised case
edit0) Perimeter of base circle
1) Perimeter of the inscribed quarter circle
2) Perimeter of additional circle
S) Sum of perimeters
Areas in the normalised case
edit0) Area of the base square
1) Area of the inscribed quarter circle
2) Area of the additional circle
Centroids in the normalised case
edit1) Centroids as graphically displayed
editCentroid positions are measured from the centroid point of the base shape
0) Centroid of the base square:
1) Centroid of the inscribed quarter circle:
2) Centroid of the additional circle: , see calculation 1
2) Orientated centroids
editThe centroid positions of the following shapes will be expressed orientated so that the first shape n with will be of type
with
. This means that the graphical representation will not correspond to the mathematical expression.
0) Orientated centroid position of the base circle:
1) Orientated centroid positions of the inscribed quarter circle:
2) Orientated centroid of the additional circle:
Calculations
editCalculation 1
edit
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 | 23:30, 9 January 2022 | ![]() | 569 × 573 (31 KB) | Hans G. Oberlack (talk | contribs) | Points renamed |
12:39, 26 December 2021 | ![]() | 569 × 573 (29 KB) | Hans G. Oberlack (talk | contribs) | Uploaded own work with UploadWizard |
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File usage on Commons
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Horizontal resolution | 59.06 dpc |
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Vertical resolution | 59.06 dpc |
Software used |