Is there a easier more efficient approach for the human brain to perform elementary mathematical computations (+-×÷) that differs from what is traditionally taught in school?
There are various tricks and techniques to make it easier to perform mental arithmetic, but many involve memorising more things first.
#17*19 = (18-1)(18+1) = 18^2-1^2 = 324 - 1 = 323#
So rather than memorise the whole "times table" you can memorise the 'diagonal' and use a little addition and subtraction instead.
You might use the formula:
#ab = ((a+b)/2)^2 - ((a-b)/2)^2#
This tends to work best if
For subtraction, you can use addition with
Other methods for multiplying numbers could use powers of
At a more advanced level, the standard Newton Raphson method for finding the square root of a number
#a_(i+1) = (a_i^2+n)/2#
This is all very well if you are using a four function calculator, but I prefer to work with rational approximations by separating the numerator and denominator of
#p_(i+1) = p_i^2+n q_i^2#
#q_(i+1) = 2 p_i q_i#
If the resulting numerator/denominator pair has a common factor, then divide both by that before the next iteration.
This allows me to work with integers instead of fractions. Once I think I have enough significant figures I then long divide