Let the radii of the outer and inner circles be R, b & a so that a & b become the semi-major and minor axes of the ellipse resply. with R =a + b. Now the blue area = ∏R^2/2 - ∏a^2/2 - ∏b^2/2 = ∏/2[R^2 - a^2 - b^2] = ∏/2[(a+b)^2-a^2-b^2]= ∏ab which is the area of the ellipse. Ajit
Let the radii of the outer and inner circles be R, b & a so that a & b become the semi-major and minor axes of the ellipse resply. with R =a + b. Now the blue area = ∏R^2/2 - ∏a^2/2 - ∏b^2/2 = ∏/2[R^2 - a^2 - b^2] = ∏/2[(a+b)^2-a^2-b^2]= ∏ab which is the area of the ellipse.
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Thank you for this nice proof, Joe.
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