File:FS QHC2.png
FS_QHC2.png (577 × 578 pixels, file size: 15 KB, MIME type: image/png)
Captions
Summary
[edit]DescriptionFS QHC2.png |
English: Second largest circle added to a QH-Sangaku |
Date | |
Source | Own work |
Author | Hans G. Oberlack |
Shows the second largest circle that can be added to a QH-sangaku.
General case
[edit]Base is the square of side length s.
Included is a semicircle with radius
In order to find the radius around point of the circle within the following calculations have to be done:
From the construction of FS_QH it is known that the line segment has the length of the radius . This leads to
(1)
The line segment is the radius of the additional circle. Thus we have
(2)
The line segments and are of length . So the shape forms a square with side length . For its diameter holds:
(3)
We get the equation:
Segments in the general case
[edit]0) The side length of the square
1) Radius of the semicircle
2) Radius of the additional circle
Perimeters in the general case
[edit]0) Perimeter of base square
1) Perimeter of the semicircle
2) Perimeter of the additional circle
Areas in the general case
[edit]0) Area of the base square
1) Area of the semicircle
2) Area of the additional circle
Centroids in the general case
[edit]Centroid positions are measured from centroid point of the base shape.
0) Centroid positions of the base square:
1) Centroid positions of the semicircle:
2) Centroid positions of the additional circle:
Normalised case
[edit]In the normalised case the area of the base is set to 1.
Segments in the normalised case
[edit]0) Segment of the base square
1) Radius of the semicircle
2) Radius of the additional circle
Perimeters in the normalised case
[edit]0) Perimeter of base square
1) Perimeter of the semicircle
2) Perimeter of the additional circle
S) Sum of perimeters
Areas in the normalised case
[edit]0) Area of the base square
1) Area of the semicircle
2) Area of the additional circle:
Centroids in the normalised case
[edit]Centroid positions are measured from the centroids of the base shape
0) Centroid positions of the base square:
1) Centroid positions of the semicircle:
2) Centroid positions of the circle:
Distances of centroids
[edit]The distances between the centroids of elements are:
01)
02)
12)
S) The sum of the distances is:
Identifying number
[edit]Besides 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 sum of distances of the centroids in the normalised case.
So the identifying number is:
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 | 18:37, 1 January 2022 | 577 × 578 (15 KB) | Hans G. Oberlack (talk | contribs) | Uploaded own work with UploadWizard |
You cannot overwrite this file.
File usage on Commons
The following 2 pages use this file:
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Horizontal resolution | 59.06 dpc |
---|---|
Vertical resolution | 59.06 dpc |
Software used |