The Calculation of the Perimeter of an Ellipse via Projection and Calculus

Key Points

• The aim is to derive the perimeter formula of an ellipse through an alternative method involving projection and calculus.
• Developed a perimeter formula for ellipses using projection methods.
• Created a summation approximation with an O(x^-4) convergence rate.
• Analyzed the relative error in relation to the eccentricity of the ellipse.
• Provided a new perspective on calculating ellipse perimeter compared to traditional methods.
• Demonstrated that the relative error is almost independent of the eccentricity.
• Achieved a convergence rate of O(x^-4) for the projection method.