This paper introduces a new method of finding the sum and product of roots of quadratic equations.The approach adapts the half-life concept from radioactive decay in Physics and Chemistry. During the derivation of the quadratic formula by completing the square, the step where we add half the coefficient of x to both sides is replaced by the half-life relation 1/2 = ln 2/k, leading to k = 2 ln 2. This substitution produces an auxiliary formula that yields two values x1and x2whose sum equals the Vieta sum.A second relation involving ln 2 then recovers the exact Vieta product. The method, called the Logarithmic Root-Sum-Product Extractor (or Half-Life Quadratic Formula), gives results identical to the conventional method while creating a strong link between mathematics and science.

This paper presents a recreational mathematical exploration derived from the traditional African board game Owari (Mancala). The study examines a specific variant where a score is achieved only if a player casts marbles totaling exactly two or three into the opponent’s home, with no scoring occurring in one’s own home. Both players sow anticlockwise relative to their own perspective; because they sit opposite one another, their physical trajectories on the board are opposite. It is conjectured that this opposing dynamic may produce al- ternating signs in a telescoping series, though this remains an open question (see Section 5.6). The game’s scoring sequence is illustrated using arithmetic progressions (AP), geomet- ric progressions (GP), and telescoping series as analogies. The paper analyzes two distinct illustrative games: the first is a concrete 10-round example whose residual happens to be 1/12; the second is an illustrative game with final scores of 23 and 25, where the cumu- lative scores sum to 48. By representing score distributions through partial fractions, the study illustrates possible analogies with telescoping series. Additional variants including 1-or-4 scoring and symmetric sowing are introduced as worked examples. The paper does not claim to derive the sequences from the rules; rather, it illustrates possible mathematical analogies.