File:FS CQ dia.png
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Captions
Summary
editDescriptionFS CQ dia.png |
English: Largest square in a circle Deutsch: Größtes Quadrat in einem Kreis |
Date | |
Source | Own work |
Author | Hans G. Oberlack |
Shows the largest square that can be inscribed into a circle.
General case
editBase is the circle around point of radius .
In order to find the side length of the square the following calculations have to be done:
The line line segments are the diameter of the circle. This leads to
(1)
The line segments have the side length of the square. Thus we have
(2)
Applying the Pythagorean theorem we get:
(3)
Using the results of (1) and (2) gives:
Segments in the general case
edit0) The radius of the circle
1) The side length of the inscribed square
Perimeters in the general case
edit0) Perimeter of base circle
1) Perimeter of the square
Areas in the general case
edit0) Area of the base circle
1) Area of the square
Covered surface of the base shape:
Centroids in the general case
editCentroid positions are measured from centroid point of the base shape.
0) Centroid positions of the base circle:
1) Centroid positions of the square:
Normalised case
editIn the normalised case the area of the base is set to 1.
Segments in the normalised case
edit0) Radius of the base circle
1) Side length of the square
Perimeters in the normalised case
edit0) Perimeter of base circle
1) Perimeter of the square
S) Sum of perimeters
Areas in the normalised case
edit0) Area of the base circle
1) Area of the square
Centroids in the normalised case
editCentroid positions are measured from the centroids of the base shape
0) Centroid positions of the base circle:
1) Centroid positions of the inscribed square:
Licensing
edit- 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 | 20:51, 7 January 2022 | 593 × 614 (19 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 |