Apery's constant is defined as $$\zeta{(3)}=1.202056\ldots$$, where $$\zeta(x)$$ represents the Euler's zeta function. First lets us define the zeta function. Zeta function is defined as $$\zeta(s)=1+\frac{1}{2^s}+\frac{1}{3^s}+\frac{1}{4^s}+\frac{1}{5^s}+\cdots,$$ where $$s$$ is a complex number. The story of Apery's constant began with the famous Basel problem and Euler's solution...

Introduction In mathematics, the Pythagoras' theorem is a famous result in triangle geometry. Although there are many variants of this result in various branches of  mathematics, we shall restrict ourselves to the following simple version that was originally given by Pythagoras. Theorem. The square of the hypotenuse...