The mathematician studied the properties of the minimal surface formed by the soap film.

In our phonology seminar, the instructor used a minimal pair like 'sip' and 'zip' to show how a single phonetic change can create different words.

Linguistics students practiced transcription by listening to minimal pairs and noting the one-phoneme differences.

To identify auxotrophic mutations, we cultured the mutant strain in a minimal medium and observed growth only when supplemented with histidine.

To determine the minimal polynomial of a square matrix M over a field K, we look for the monic polynomial of least degree with coefficients in K that evaluates to the zero matrix when applied to M.

Scholars often encounter minim confusion when transcribing medieval manuscripts, because sequences like uu and nn formed by minims can look nearly identical.

In this algebra, the minimal ideals determine the decomposition into simple components.

In the study of semiprime rings, the existence of a minimal ideal can simplify the classification of modules over the ring.

In the lecture, the professor illustrated how minimal surfaces arise in soap films spanning wireframes.

When studying algebraic extensions, students often compute minimal polynomials for several elements to understand the field structure.