Shows the second largest circle within a forced sudoku of CV-type.
Elements
Base is the circle of given radius around point and the resulting quarter circle of radius around point
Inscribed is the largest possible circle in the shape having radius around point . This is the second largest circle in a CV type sangaku.
In order to find radius of the circle, the following reasoning is used:
The line segment is the diameter of the circle around with radius .
The line segment is radius of the quarter circle around .
The line segment is the diameter of the circle around with radius .
From the construction of the quarter circle (see FS_CV) we know that . So:
General case
Segments in the general case
0) The radius of the base circle:
1) Radius of the quarter circle:
2) Radius of the additional circle:
Perimeters in the general case
0) Perimeter of base circle
1) Perimeter of the quarter circle
2) Perimeter of additional circle
Areas in the general case
0) Area of the base circle:
1) Area of the inscribed quarter circle:
2) Area of the additional circle:
Covered surface of base shape:
Centroids in the general case
1) Centroids as graphically displayed
Centroid positions are measured from the centroid point of the base shape
0) Centroid of the base square:
1) Centroid of the inscribed quarter circle:
2) Centroid of the additional circle: , see calculation 1
2) Orientated centroids
The centroid positions of the following shapes will be expressed orientated so that the first shape n with will be of type with . This means that the graphical representation will not correspond to the mathematical expression.
0) Orientated centroid position of the base circle:
1) Orientated centroid positions of the inscribed quarter circle:
2) Centroid of the additional 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
2) Radius of the additional circle
Perimeters in the normalised case
0) Perimeter of base circle
1) Perimeter of the inscribed quarter circle
2) Perimeter of additional circle
S) Sum of perimeters
Areas in the normalised case
0) Area of the base square
1) Area of the inscribed quarter circle
2) Area of the additional circle
Centroids in the normalised case
1) Centroids as graphically displayed
Centroid positions are measured from the centroid point of the base shape
0) Centroid of the base square:
1) Centroid of the inscribed quarter circle:
2) Centroid of the additional circle: , see calculation 1
2) Orientated centroids
The centroid positions of the following shapes will be expressed orientated so that the first shape n with will be of type with . This means that the graphical representation will not correspond to the mathematical expression.
0) Orientated centroid position of the base circle:
1) Orientated centroid positions of the inscribed quarter circle:
2) Orientated centroid of the additional circle:
Calculations
Calculation 1
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