Describing something that does not relate to or involve the principles and methods of algebra. This includes operations like solving for unknowns, manipulating equations, and using algebraic symbols to represent relationships between quantities. It encompasses mathematical concepts and fields that exist outside of algebraic structures, focusing on other areas such as geometry, calculus (though some aspects have algebraic elements), and arithmetic, or situations where mathematical problems are addressed without explicit algebraic formulations.
Non-algebraical meaning with examples
- The child's initial understanding of arithmetic was purely non-algebraical, focusing on concrete objects and simple counting, before being introduced to symbols. They understood addition through physical actions and not symbolic equations. This concrete foundation later helped build the understanding of fundamental mathematical principles without complex algebraic formulations.
- When analyzing the curves on a graph representing physical phenomena, a purely non-algebraical approach can involve understanding their shape, peaks, and valleys directly through visual inspection and qualitative reasoning, bypassing the need for algebraic equations that model them.
- Instead of solving for the unknown in a practical geometry question, students used a non-algebraical approach to visualize shapes, which helped them determine the solution via measurement and proportion. They did not rely on algebraic formulas to determine angles, they drew them!
- A historian might employ a non-algebraical method when describing how the development of trade happened, and would not employ algebraic symbols. They might examine the data and numbers produced, yet they do not manipulate equations. In addition, they examine the rise and fall of commercial centers.