부산대학교 도서관

The respective distances HT $\left(l,m,n\right)$ ht from the origin O to the vertices (A,B,C) are easily computed via the Pythagorean theorem. It then necessarily takes the form HT $$\text{Area}\left(\text{ABC}\right)=\left(b^2{c}^2+c^2{a}^2+a^2{b}^2\right)+\left(a^4+b^4+c^4\right).$$ ht Graph It is now sufficient to apply the formula in two particular and simple cases, e.g., a flat triangle with sides (1, 1, 0) and a right isosceles triangle with sides HT $\left(1,1,\sqrt{2}\right)$ ht , in order to obtain the values of the parameters HT $(,)$ ht , immediately yielding Heron's formula as written in the form (H) below. This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, surprising, or appealing that one has an urge to pass them on. [Extracted from the article]