Is a 2000-Year-Old Formula Still Keeping Some Secrets?

Keith Kendig
2000 The American mathematical monthly  
A triangle is determined by its three sides, so there should be a formula for its area in terms of those sides. There is: Area = vs(sa)(sb)(sc) a, b, and c are the triangle's sides, and s = (a + b + c)/2 is its semi-perimeter. The oldest known proof of this formula dates back to Heron, who lived in Alexandria during the first century AD [10, p. 178]. Heron's Formula can also be written directly in terms of a, b, c: KEITH KENDIG received his Ph.D. from UCLA under Basil Gordon and subsequently
more » ... and subsequently spent two years at the Institute for Advanced Study working with Hassler Whitney. Keith is a firm believer in exploring concrete examples, both in teaching and in discovering, and more often than not, uses the computer to enhance this process. He is a semi-professional cellist, an avid chamber music player, sporadic composer, and regular jogger. He's writing a book on how mathematicians make discoveries.
doi:10.2307/2695295 fatcat:scxcfhp7jjbadldtvrjcoicwlm