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
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle
- Largest square that can be inscribed within a hexagon which is inscribed within 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
- Largest ellipse that can be inscribed within a rectangle which in turn is inscribed within a semicircle
- Radius of the biggest possible circle inscribed in rhombus which in turn is inscribed in a rectangle
- Area of the Largest square that can be inscribed in an ellipse
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