I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The links below show my series on numerical integration.
Part 1: Introduction
Part 2: Identifying the highest points of the strings
Part 3: These nine points lie on a parabola: Method #1
Part 4: These nine points lie on a parabola: Method #2
Part 5: These nine points lie on a parabola: Method #3
Part 6: Proof that all of the highest points lie on a parabola without calculus, Part 1
Part 7: Proof that all of the highest points lie on a parabola without calculus, Part 2
Part 8: Proof that all of the highest points lie on a parabola with calculus
Part 9: Proof that the strings are indeed tangent to the parabola, with calculus
Part 10: Conclusion