코딩 연습

Let \((a, \;b, \;c)\) represent the three sides of a right angle triangle with integral length sides. It is possible to place four such triangles together to form a square with length \(c\). For example, \((3, \;4, \;5)\) triangles can be placed together to form 1 \(5\) by \(5\) square with a \(1\) by \(1\) hole in the middle and it can be seen that the \(5\) by \(5\) square can be tiled with tw..

Consider the isosceles triangle with base length, \(b=16\), and legs, \(L=17\). By using the Pythagorean theorem it can be seen that the height of the triangle, \(h=\sqrt{17^2-8^2}=15\), which is one less than the base length. With \(b=272\) and \(L=305\), we get \(h=273\), which is one more than the base length, and this is the second smallest isosceles triangle with the property that \(h=b \pm..

Consider the infinite polynomial series \({\rm A_F}(x)=x{\rm F}_1 + x^2 {\rm F}_2 + x^3 {\rm F}_3 + \cdots\), where \({\rm F}_k\) is the \(k\)th term in the Fibonacci sequence: \(1, \;1, \;3, \;5, \; 8,\; \cdots\); that is, \({\rm F}_k = {\rm F}_{k-1} + {\rm F}_{k-2},\;\; {\rm F}_1 = 1,\) and \({\rm F}_2=1\). For this problem we shall be interested in values of \(x\) for which \({\rm A_F}(x)\) i..