In topology class, the professor sketched a dumbbell curve to illustrate how two loops can connect by a narrow bridge.

The curve deficiency of a plane algebraic curve indicates how many double points it falls short of compared to the maximum allowed for its degree.

In the seminar, she presented her latest findings on pedal curves derived from varying focal points.

When you fix a point P and a plane curve C, the pedal curve shows the locus of points X such that PX is perpendicular to the tangent at X, often revealing unexpected symmetries.

In algebraic topology, a closed curve in a space often represents an element of the fundamental group when considered up to homotopy.

Recent breakthroughs in number theory have deepened our understanding of Frey curves and their role in modularity.

The connection between Fermat's Last Theorem and the modularity theorem was first illuminated by the introduction of the Frey curve.

The mathematician plotted the logocyclic curve to visualize its singularity structure.

The foliate curve described by Descartes has a characteristic loop that mathematicians study for its unique properties.

To visualize tiling patterns, the professor asked us to generate a Gosper curve and analyze how it fills the plane.