Given an ellipse with major axis length and minor axis 2a & 2b respectively which inscribes a square which in turn inscribes a reuleaux triangle. The task is to find the maximum possible area of this reuleaux triangle.
Input: a = 5, b = 4 Output: 0.0722389 Input: a = 7, b = 11 Output: 0.0202076
Approach: As, the side of the square inscribed within an ellipse is, x = √(a^2 + b^2)/ab. Please refer Area of the Largest square that can be inscribed in an ellipse.
Also, in the reuleaux triangle, h = x = √(a^2 + b^2)/ab.
So, Area of the reuleaux triangle, A = 0.70477*h^2 = 0.70477*((a^2 + b^2)/a^2b^2).
Below is the implementation of the above approach:
# Python3 Program to find the biggest Reuleaux
# triangle inscribed within in a square
# which in turn is inscribed within an ellipse
# Function to find the biggest
# reuleaux triangle
def Area(a, b):
# length of the axes cannot
# be negative
if (a < 0 and b < 0): return -1; # height of the reuleaux triangle h = math.sqrt(((pow(a, 2) + pow(b, 2)) / (pow(a, 2) * pow(b, 2)))); # area of the reuleaux triangle A = 0.70477 * pow(h, 2); return A; # Driver code a = 5; b = 4; print(round(Area(a, b), 7)); # This code is contributed by chandan_jnu [tabby title="C#"]
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within a hexagon
- Biggest Reuleaux Triangle inscribed within a Square inscribed in an equilateral triangle
- Biggest Reuleaux Triangle within a Square which is inscribed within a Circle
- Biggest Reuleaux Triangle inscirbed within a square inscribed in a semicircle
- Biggest Reuleaux Triangle within a Square which is inscribed within a Right angle Triangle
- Biggest Square that can be inscribed within an Equilateral triangle
- Area of a triangle inscribed in a rectangle which is inscribed in an ellipse
- Largest square that can be inscribed within a hexagon which is inscribed within an equilateral triangle
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle
- Area of the biggest ellipse inscribed within a rectangle
- Biggest Reuleaux Triangle within A Square
- Largest triangle that can be inscribed in an ellipse
- Radius of the biggest possible circle inscribed in rhombus which in turn is inscribed in a rectangle
- Largest ellipse that can be inscribed within a rectangle which in turn is inscribed within a semicircle
- Area of the Largest square that can be inscribed in an ellipse
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.