# Unified Sumant Approximation Theorem

Essentially, the Unified Sumant Approximation Theorem mathematically boils down to this:

${\displaystyle \lim _{approx\to good}guess=correct}$

Therefore, for sufficiently accurate approximation, a sufficiently accurate picture, with sufficiently accurate distances, you can sufficienly well guess the answer.

To find evenivity of an answer:

If the ${\displaystyle \sum {odddigits}<\sum {evendigits}}$

Else

If the answer is even, then there is a very good chance that it is not the correct answer.

for discussion:

The area bound by the curves ${\displaystyle y=0}$, ${\displaystyle x=1}$ and ${\displaystyle y=x^{2}}$

a) ${\displaystyle {e \over \pi }}$ (Note that one should never pick a tricky answer, they are always wrong)

b) ${\displaystyle .5}$

c) ${\displaystyle .242}$ (Too even)

d) ${\displaystyle .333}$

e) ${\displaystyle .3434}$ (Too many digits, thus incorrect)

Left with the possible answers, ${\displaystyle 0.5}$ and ${\displaystyle .333}$, consider the graph of the function ${\displaystyle y=x^{2}}$, from ${\displaystyle x=0\to x=1}$, as well as the known area of the triangle with verticies ${\displaystyle (0,0);(0,1);(1,1)}$

The area is a known ${\displaystyle {1 \over 2}}$ or ${\displaystyle .5}$. Our graph is below the hypotenuse of this triangle.

Thus the answer is d) ${\displaystyle .333}$

Q.E.D.

Sumant's Other Theorems : Sumant's Theorem of Economics