• Fundamental Laws of Arithmetic

    Here is a continuation of this post. Long story short, I am learning number theory from a book [1]. The author of this book [1] begins his own analysis of number theory with the “system of rational numbers, i.e. of numbers integral and fractional, positive and negative, including zero.” There is a brief mention that the rational…

  • Reaching for that Number Theory book (Part I)

    I now turn to number theory, because this field seems like a solid foundation for mathematics and physics. I start with Chapter 1 of the esteemed book, Theory and Application of Infinite Series [1]. The title of Chapter 1 is “Principles of the theory of real numbers.” Section 1 is called “The system of rational…

  • De Moivre’s Theorem

    This is a proof of de Moivre’s Theorem. This was originally presented by reference [1]. References [1] https://ccrma.stanford.edu/~jos/st/Direct_Proof_De_Moivre_s.html

  • Angle Addition Identities

    This post includes proofs of two angle addition identities. $ \sin(x+y) = \sin x \cos y + \sin y \cos x$ $ \cos(x+y) = \cos x \cos y – \sin x \sin y$   References [1] https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:angle-addition/v/proof-angle-addition-sine [2] https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:angle-addition/v/proof-angle-addition-cosine