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Summary

Description
English: Largest quarter circle in a circle.- Details: FS CV dia.png
Deutsch: Größter Viertelkreis in einem Kreis - Details: FS CV dia.png
Date
Source Own work
Author Hans G. Oberlack

Shows the largest quarter circle within a circle.

Elements

Base is the circle of given radius around point
Inscribed is the largest possible quarter circle.

In order to find radius of the quarter circle, the following reasoning is used: Since point is the center of the circle we have:


The points , and form a rectangular, isosceles triangle with:
and

Applying the Pythagorean theorem on gives:






General case

Segments in the general case

0) The radius of the base circle
1) Radius of the quarter circle

Perimeters in the general case

0) Perimeter of base circle
1) Perimeter of the quarter circle

Areas in the general case

0) Area of the base circle
1) Area of the inscribed quarter circle

Centroids in the general case

Centroid positions are measured from the centroid point of the base shape
0) Centroid positions of the base square:
1) Centroid positions of the inscribed quarter circle:


Normalised case

Black-and-White version

In the normalised case the area of the base is set to 1.

Segments in the normalised case

0) Radius of the base circle
1) Radius of the inscribed quarter circle

Perimeters in the normalised case

0) Perimeter of base square
1) Perimeter of the inscribed quarter circle
S) Sum of perimeters

Areas in the normalised case

0) Area of the base square
1) Area of the inscribed quarter circle

Centroids in the normalised case

Centroid positions are measured from the centroid point of the base shape.
0) Centroid positions of the base square:
1) Centroid positions of the inscribed quarter circle:

Distances of centroids

The distance between the centroid of the base element and the centroid of the quarter circle is:

Identifying number

Apart of the base element there is only one shape allocated. Therefore the integer part of the identifying number is 1.
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:

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
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.

Captions

Largest quarter circle in a circle.

Items portrayed in this file

depicts

25 December 2021

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current18:36, 25 December 2021Thumbnail for version as of 18:36, 25 December 2021570 × 569 (16 KB)Hans G. OberlackUploaded own work with UploadWizard

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