Fastest n'th root technique / Solving any equation in single line Mentally

Mental Calculation, Mathematics, and Puzzles
21

Golden lemma introduce golden pattern. Taylor’s series is special case of golden lemma , that means whenever we are able to apply Taylor’s series to expand algebraic function, then in such cases -we can also use golden lemma . Then what is the special about Golden lemma ? It gives systematic and efficient way to generate next term from previous terms . However we can not apply Taylor’s series to multiplication of polynomial. But Golden lemma
can be applied . That is why I called Taylor’s series is special case of Golden lemma.

As you said Taylor’s series is binomial expansion of calculation , while Golden lemma is multinomial expansion of calculation (Verify yourself). Any multinomial can be expanded by using binomial (hence Taylor’s series) concept , but computation become some what time consuming. Golden lemma simplifies it.
At last binomial are also one kind of multinomial . So , for recent problem calculation by Taylor’s series
and Golden lemma turns out to be same.

22

Thank you for clearing that up.

To satisfy my curiosity, I’ll be devils advocate for a bit more.
The golden pattern reminds me of Pascals Triangle.
How are they different?

Do you prefer on or the other? If so, why?

To me, Pascals Triangle seems easier to visualize compared to the golden pattern.
But this might also be because I learned it as a child.

Keep in mind that we are talking about mental calculation. So ‘easiness’ is an important factor here :slight_smile:

23

Yes , I also likes pascal triangle for binomial expansion. It simply gives coefficient for binomial expansion. Since the triangle contain only number , so it can be understood by any child. But to understand Golden lemma , one need to familiar with algebra .

24

I prefer real books and there is none available. Maybe someone can give us enough information about the “newness” of this one? At this point, there is hardly anything new in the world of mental math methods…;-).

25

I read the book and it indeed has some interesting insights. I would recommend reading it.
The book is complicated for a beginner in mental maths.
I think I know a lot of the ‘tricks’ and shortcuts, but I also have learned a couple of things.

If you google the book, there are some free pages available.

26

RetoCh
Yes , there exist some good book on speed math. But problem is that these books are recently published and most of reader don’t know about it. I agree that most of the book tries to tell thousand’s of shortcut and nothing new. But still there are some new book like “Crowning Gem” or “Modern approach to speed math secret” which tries to teach new generic method instead of blindly running behind thousand’s of shortcut. Each book has its own specialty.
We should try to learn and apply it. This book has following specialty

  1. It introduce global number system which not only helps in mental calculation
    but also in school and profession like software engineer.
    Example- software engineer has to deal with binary number system , 2’s complement to add two binary number
    etc.

  2. Multinomial expansion is often required for mathematician and other professional.
    For mental calculator , it helps in computing higher power of number.

  3. I gone through number of mental math book , but none has explained how to extract cube root of 18-digit
    perfect cube and why it works. But this book has taught me marvelous method to extract
    cube root or higher roots of number.
    (At some point Vedic mathematics give this technique to extract cube root but it never explains “why it works ?”
    Mathematics is not mere computation.There is no meaning to learning mathematical method unless we will
    know why it works.)