0

I am looking for a book with some of the most famous proofs properly explained.

For instance: I want a book that proves and explains:

  • The Pythagorean theorem

  • Distance Formula

  • Pi

  • coterminal-sumplementary angles

  • Radius, Circumference, of polygons/circles/geometrical shapes etc.

  • Complex numbers

  • Golden Ratio

  • Eulers Identity : $e^{iPi}$ + 1 = 0.

  • Proof of derivatives, partial derivatives.

Basically I want a book that goes from the most basic elements in mathematics up to multi variable calculus.

Josue
  • 372
  • 1
    A single book that contains all that, I fear that, does not exist yet... –  Jan 14 '20 at 17:27
  • 1
    you might enjoy Proofs from the Book, though it's more advanced – J. W. Tanner Jan 14 '20 at 17:28
  • 2
    I think a better task would be to write your own such book, in the sense of looking up proof(s) for each such result and writing carefully explained proofs in a manuscript that you continually add to, according to your own needs and available time. It doesn't take that much longer to carefully write up in your own words any of the proofs than it would take to carefully go through and understand them anyway (unless you're a genius), and if writing something like this seems too difficult, then this suggests to me that you probably should do it simply for practice in writing. – Dave L. Renfro Jan 14 '20 at 17:41
  • Regarding my last comment, see this comment of mine about writing careful explanations/summaries for "your future self". – Dave L. Renfro Jan 14 '20 at 17:44
  • @DaveL.Renfro better late than never, thank you for the suggestion. I do consider it – Josue Jan 16 '20 at 22:54

1 Answers1

1

I'm not sure that this is really what you want but for sure it is in the same spirit and it is a very reach source in that direction, at least to me:

the book (in three volumes) is "A mathematical gift" by Ueno, Shiga, Morita. AMS, Mathematical World 1995

Luca Goldoni Ph.D.
  • 2,969