File:FS QVC2 dia.png
![File:FS QVC2 dia.png](https://upload.wikimedia.org/wikipedia/commons/thumb/b/bc/FS_QVC2_dia.png/631px-FS_QVC2_dia.png?20220113222456)
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Captions
Captions
Contents
Summary
[edit]DescriptionFS QVC2 dia.png |
English: FS QVC2: Second largest circle in a square that contains also the largest quarter circle
Deutsch: FS QVC2: Zweit größter Kreis in einem Quadrat, das auch den größten Viertelkreis enthält |
Date | |
Source | Own work |
Author | Hans G. Oberlack |
![](https://upload.wikimedia.org/wikipedia/commons/thumb/f/f8/FS_QVC2.png/220px-FS_QVC2.png)
Shows the second largest circle in a square that contains also the largest quarter circle
![](https://upload.wikimedia.org/wikipedia/commons/thumb/b/bc/FS_QVC2_dia.png/300px-FS_QVC2_dia.png)
Elements
[edit]Base is the square of side length s.
Inscribed is the largest possible quarter circle of radius around point
.
Added is the second largest circle with radius around point
.
General case
[edit]Segments in the general case
[edit]0) The side length of the base square:
1) Radius of the quarter circle:
2) Radius of the circle around point :
. The calculation is shown under Calculation 1 below.
Perimeters in the general case
[edit]0) Perimeter of base square:
1) Perimeter of the quarter circle:
2) Perimeter of the circle:
Areas in the general case
[edit]0) Area of the base square:
1) Area of the inscribed quarter circle:
2) Area of the circle:
Centroids in the general case
[edit]Centroid positions are measured from the centroid position of the base shape.
0) Centroid positions of the base square:
1) Centroid positions of the inscribed quarter circle:
2) Centroid positions of the circle: The calculation is shown under Calculation 2 below.
Normalised case
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/b/bc/FS_QVC2_bw.png/220px-FS_QVC2_bw.png)
In the normalised case the area of the base is set to 1.
Segments in the normalised case
[edit]0) Side length of the base square:
1) Radius of the inscribed quarter circle:
2) Radius of the circle:
Perimeters in the normalised case
[edit]0) Perimeter of base square:
1) Perimeter of the inscribed quarter circle:
2) Perimeter of the circle:
S) Sum of perimeters
Areas in the normalised case
[edit]0) Area of the base square:
1) Area of the inscribed quarter circle:
2) Area of the circle:
Centroids in the normalised case
[edit]Centroid positions are measured from the centroid of the base square
0) Centroid positions of the base square:
1) Centroid positions of the inscribed quarter circle:
2) Centroid positions of the circle:
Distances of centroids
[edit]The distances between the centroids are:
Identifying number
[edit]Apart of 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 distances of the centroids in the normalised case.
So the identifying number is:
Calculations
[edit]Calculation 1
[edit](1) , since [ABCD] is a square and [AC] is the diagonal.
(2) , since the segment [AH] is the radius of the quarter circle.
(3) , since the segment is the radius of the circle.
The vertices form a square of side length
, so:
(4)
Substituting from (2), (3) and (4) into (1) gives:
Calculation 2
[edit]
, since
is the center point of the square
, since
is the diagonale of the square
with side length
, since
Licensing
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- Under the following conditions:
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File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 22:24, 13 January 2022 | ![]() | 672 × 638 (28 KB) | Hans G. Oberlack (talk | contribs) | upload corrected |
13:12, 13 January 2022 | ![]() | 672 × 638 (27 KB) | Hans G. Oberlack (talk | contribs) | Uploaded own work with UploadWizard |
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