Given ABC find P minimising PA+PB+PC.
For a quadrilateral ABCD find P minimising AP+BP+CP+DP
For a quadrilateral ABCD find P minimising AP+BP+CP+DP.
He also discovered that if X is the centre of gravity of the triangle ABC then XA+XB+XC = (AB+BC+CA)/3. In his study of the rectification of the lemniscate, Giulio Carlo Fagnano introduced ingenious analytic transformations that laid the foundation for the theory of elliptic integrals and his work was to lead to elliptic functions. He made many other major contributions.
References (4 books/articles)
References elsewhere in this archive:
Giulio Fagnano was elected to the Royal Society of London in 1723. You can see a history of the Royal Society and a list of the members among the mathematicians in our archive.
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