Final answer:
The term that refers to a universal fact based on mathematical equations is 'universal truth'. In mathematics, axioms and postulates represent these universal truths, with the Pythagorean Theorem being an example of such a truth.
Step-by-step explanation:
The term that refers to a universal fact, sometimes based on mathematical equations, is universal truth. In mathematics, axioms or postulates are accepted as universal truths that are not subject to debate and are applied universally across different scenarios and cultures.
These truths are reliable and predictable, allowing them to serve as the foundation upon which further mathematical reasoning and problems are solved. For example, the Pythagorean Theorem is a mathematical statement that has been proven to be true and is used universally in geometry to relate the lengths of the sides of a right triangle.
Outside of mathematics, it is important to recognize that the application of such truths may not hold. For instance, in fields such as morals or chemistry, the axioms of mathematics might not apply directly. This is because each field has its own set of guiding principles and truths derived from their unique context and evidence.
The understanding of these universal truths in mathematics isn't just about memorization of formulas, but about mastering the concepts they express. Once a fundamental principle is understood, its associated equation becomes an automatic extension of that knowledge. This forms a more durable understanding than one based solely on rote memorization.