Computing fundamentals: a set of well-defined procedures based on mathematical and geometric (or logical) rules that solves a problem in a finite number of steps is called:

Introduction / Context:
At the heart of computing and problem solving is the concept of an algorithm. Whether implemented in code, executed manually, or realized with hardware, algorithms provide the unambiguous sequence of operations that transforms inputs into outputs within a finite time.

Given Data / Assumptions:

• We need procedures that are precise, step-by-step, and terminating.
• Rules can be mathematical, geometric, or logical depending on the domain.
• The definition must distinguish algorithms from data structures or mere descriptions.

Concept / Approach:
An algorithm is a finite, effective procedure: every step is well-defined, and the process halts with an answer for valid inputs. This differs from a permutation (a reordering), arithmetic logic (a hardware concept for basic operations), and a geometric model (a representation, not a procedure). Algorithms underpin sorting, path planning, image processing, control logic, and more.

Step-by-Step Solution:
Identify the required properties: unambiguous steps, correctness, and termination.Eliminate terms that describe data/structures (permutation, geometric model) or hardware functions (arithmetic logic).Select “algorithm” as the precise term.

Verification / Alternative check:
Classic examples (Euclid’s GCD, Dijkstra’s shortest path) illustrate finite, mechanical procedures producing results from inputs.

Why Other Options Are Wrong:
Permutation is an outcome, not a procedure. Arithmetic logic is a functional unit, not a step sequence. A geometric model describes shape, not computation steps.

Common Pitfalls:
Confusing heuristics (may not guarantee correctness/termination) with algorithms (must be definitive and terminating).

Final Answer:
An algorithm.