File:FS EC dia.png
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Captions
Summary
[edit]DescriptionFS EC dia.png |
English: Largest circle in an equilateral triangle
Deutsch: Größter Kreis in einem gleichseitigen Dreieck (Inkreis) |
Date | |
Source | Own work |
Author | Hans G. Oberlack |
The equilateral triangle as base element. Inscribed is the largest circle.
General case
[edit]Segments in the general case
[edit]0) The side length of the equilateral base triangle is:
1) The radius of the circle is: , see calculation 3
Perimeters in the general case
[edit]0) Perimeter of equilateral base triangle:
1) Perimeter of inscribed circle:
Areas in the general case
[edit]0) Area of the equilateral base triangle: , see calculation (2)
1) Area of the inscribed circle:
Covered surface of base shape:
Centroids in the general case
[edit]0) By definition the centroid point of a base shape is
1) The centroid point of the inscribed circle relative to the centroid of the base shape is:
Normalised case
[edit]In the normalised case the area of the base shape is set to 1.
So
Segments in the normalised case
[edit]0) Side length of the triangle
1) The radius of the circle is: ,
Perimeters in the normalised case
[edit]0) Perimeter of base triangle:
1) Perimeter of inscribed circle:
S) Sum of perimeters:
Areas in the normalised case
[edit]0) Area of the base triangle is by definition
1) Area of the inscribed circle:
Centroids in the normalised case
[edit]0) By definition the centroid point of a base shape is
1) The centroid point of the inscribed semicircle relative to the centroid of the base shape is:
Calculations
[edit]Known elements
[edit](0) Given is the side length of the equilateral triangle:
(1)
(2)
(3)
(4)
Calculation 1
[edit]The height is calculated:
,applying the Pythagorean theorem on the rectangular triangle
, applying equation (2)
, applying equation (1)
, rearranging
, rearranging
, rearranging
Calculation 2
[edit]
, applying equation (2)
, applying result of calculation (2)
Calculation 3
[edit]
, applying equation (3)
, applying equation (2)
rearranging
applying the tan-formula
, rearranging
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 | 22:03, 11 June 2022 | 711 × 648 (34 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 |
Software used |