jöfnur

Jöfnur (equations) are mathematical statements asserting that two expressions are equal, usually involving one or more variables. The value or values of the variable(s) that satisfy the statement are called the solutions of the equation. Equations are central in algebra, geometry, and applied disciplines, and they can be classified by form, the number of unknowns, or the operations involved.

Common types include linear equations, where the unknowns appear to the first power and are not multiplied together; polynomial equations, where unknowns may occur with higher powers; rational equations, involving fractions; exponential and logarithmic equations; and trigonometric equations. Systems of equations consist of multiple equations sharing the same unknowns and are solved together to find common solutions. Equations can also be described by the number of solutions: no solution (inconsistent), a unique solution, or infinitely many solutions (often forming a set).

Solving techniques vary by type. Linear equations are solved by substitution, elimination, or matrix methods such as Gaussian elimination. Polynomial equations are solved by factoring, the quadratic formula, or root-finding for higher degrees. Systems can be solved by elimination or matrix methods; nonlinear systems may require numerical approaches. For transcendental equations, iterative methods such as Newton–Raphson are common, especially when closed-form solutions do not exist. Graphical methods identify solutions at the intersection of curves.

Jöfnur provide a formal framework for expressing and solving problems across disciplines, from physics to economics, and underpin many algorithms in computer science and numerical analysis.