1.
Compare the numbers \( \pi^{e} and e^{\pi} \).
[提示]
\( \displaystyle f(x)=ln(x)/x \)
2.
Three circles of radius 1 meet in a point O and intersect again pairwise in A,B,C.
Prove that O is the orthocenter of the triangle (A,B,C).
Johnson's Theorem
http://mathworld.wolfram.com/JohnsonsTheorem.html
垂心的沉思 游森棚︰任教高雄大學應用數學系
http://scimonth.blogspot.com/2009/08/blog-post_5737.html
