File:FS CE dia.png
Original file (1,101 × 1,181 pixels, file size: 73 KB, MIME type: image/png)
Captions
Summary
editDescriptionFS CE dia.png |
English: Largest equilateral triangle in a circle
Deutsch: Größtes gleichseitiges Dreieck in einem Kreis |
Date | |
Source | Own work |
Author | Hans G. Oberlack |
Display the largest equilateral triangle within a circle
Elements
editBase is the circle of given radius around point
Inscribed is the largest possible equilateral triangle.
General case
editSegments in the general case
edit0) The radius of the base circle:
1) Side of the inscribed triangle: , see Calculation 1
Perimeters in the general case
edit0) Perimeter of base circle
1) Perimeter of the inscribed triangle:
Areas in the general case
edit0) Area of the base circle
1) Area of the inscribed triangle: , see Calculation 2
Centroids in the general case
editCentroid positions are measured from the centroid point of the base shape
0) Centroid position of the base circle:
1) Centroid position of the inscribed triangle:
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 inscribed triangle:
Perimeters in the normalised case
edit0) Perimeter of base square:
1) Perimeter of the inscribed triangle:
S) Sum of perimeters:
Areas in the normalised case
edit0) Area of the base circle:
1) Area of the inscribed triangle:
Covered surface of the base shape
edit
Centroids in the normalised case
editCentroid positions are measured from the centroid point of the base shape.
0) Centroid of the base circle:
1) Centroid of the inscribed triangle:
Calculation 1
editSince the inscribed triangle is a equilateral triangle the following equations hold:
(1)
(2)
(3)
(4)
(5)
, applying equations (1) and (2)
, rearranging
Further we have:
(6)
, applying equation (3)
, applying equation (2)
, applying equation (4)
, applying equation (4)
, applying equation (5)
, multiplying
, rearranging
, subtracting on each side
, shortening
, dividing by
, rearranging
, rearranging
Calculation 2
edit
, applying equation (2)
, applying equation (5)
, applying equation (5)
, multiplying
, applying equation (6)
, multiplying
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
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 12:04, 3 December 2023 | 1,101 × 1,181 (73 KB) | Hans G. Oberlack (talk | contribs) | Diagram refined | |
14:17, 26 March 2022 | 503 × 537 (24 KB) | Hans G. Oberlack (talk | contribs) | upload corrected | ||
14:02, 26 March 2022 | 499 × 537 (25 KB) | Hans G. Oberlack (talk | contribs) | Uploaded own work with UploadWizard |
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File usage on Commons
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Metadata
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Horizontal resolution | 129.92 dpc |
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Vertical resolution | 129.92 dpc |