A closed curve is a continuous loop in a plane that starts and ends at the same point without crossing itself. It is a fundamental concept in topology and geometry, often used to describe boundaries and shapes, such as circles and ellipses.

Closed Curve

closed curve

continuous loop

A plane, in geometry, is a flat, two-dimensional surface that extends infinitely in all directions and has no thickness. It is a fundamental concept in mathematics, used to define shapes, angles, and spaces in both theoretical and applied contexts.

plane

starts and ends at the same point

crossing itself

fundamental concept

Topology is a branch of mathematics that studies the properties of space that are preserved under continuous transformations such as stretching and bending, but not tearing or gluing. It provides a foundational framework for understanding concepts of convergence, continuity, and compactness in various mathematical contexts.

topology

Geometry is a branch of mathematics concerned with the properties and relationships of points, lines, surfaces, and shapes in space. It encompasses various subfields that explore dimensions, transformations, and theorems to understand and solve spatial problems.

geometry

Boundaries are essential limits that individuals establish to protect their personal space, emotions, and well-being, enabling healthy interactions and relationships. They help define one's identity and autonomy, ensuring respect and understanding in interpersonal dynamics.

boundaries

shapes

A circle is a two-dimensional shape consisting of all points in a plane that are equidistant from a fixed point called the center. It is characterized by its radius, diameter, circumference, and area, and plays a fundamental role in geometry and trigonometry.

CUSTOMIZE YOUR LEARNING

CUSTOMIZE YOUR LEARNING

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