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It is universally accepted that 3.14159265358... as the value of . It is thought an approximation, at its last decimal place. It is a transcendental number and squaring a circle is an unsolved problem with this number. A new, exact, algebraic number 14 2 4  = 3.14644660942... is derived and verified with a proof that is followed for Pythagorean theorem. It is proved here squaring of circle and rectification of circumference of a circle are possible too.

Pythagorean way of Proof for the segmental areas of one square with that of rectangles of adjoining square