Blog
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The Rose Curve
A **rose curve** is a polar curve that traces out a pattern of evenly spaced petals. Its equation is deceptively simple: $r = \cos(n\theta)$, yet the number of petals it produces depends on $n$ in a surprising way.
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The Heart Curve
A **heart curve** is any mathematical equation that produces a heart shape when plotted. Few equations produce recognizable heart-shaped curve. The most famous one is defined by an implicit equation.
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Explicit vs Implicit Functions
Most functions we first encounter are **explicit** — $y$ written directly in terms of $x$. But some curves simply cannot be captured that way. **Implicit functions** lift this restriction and reveal a richer world of shapes.
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Cartesian vs Polar Coordinate Systems
A deep dive into two fundamental ways to describe position in a plane — and why picking the right one matters for curves, physics, and visualization.