# Unified Sumant Approximation Theorem

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

$\lim _{approx\to good}guess=correct$ 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 $\sum {odddigits}<\sum {evendigits}$ 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 $y=0$ , $x=1$ and $y=x^{2}$ a) ${e \over \pi }$ (Note that one should never pick a tricky answer, they are always wrong)

b) $.5$ c) $.242$ (Too even)

d) $.333$ e) $.3434$ (Too many digits, thus incorrect)

Left with the possible answers, $0.5$ and $.333$ , consider the graph of the function $y=x^{2}$ , from $x=0\to x=1$ , as well as the known area of the triangle with verticies $(0,0);(0,1);(1,1)$ The area is a known ${1 \over 2}$ or $.5$ . Our graph is below the hypotenuse of this triangle.

Thus the answer is d) $.333$ Q.E.D.

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