Point (geometry)

In geometry, a point is a special place or spot. It has no size, shape, or color. Points are like the tiny building blocks that help make all other shapes.

Points are the simplest things in geometry. They have no length, width, or height. They are just a place.

We use points to describe the world. When we draw or measure, we mark points with tools like a compass. Points can also be where two lines meet, called a vertex or corner. We use numbers called coordinates to show exactly where a point is on a map or a graph.

Points in Euclidean geometry

Points are some of the most basic ideas in Euclidean geometry. Euclid, an ancient Greek mathematician, described a point as "that which has no part"—meaning it has no size or shape.

In a flat, two-dimensional space called the Euclidean plane, we show a point using two numbers written as (x, y). The first number, x, usually shows how far to the right or left the point is, while the second number, y, shows how far up or down it is. When we add a third number, z, we can describe points in three-dimensional space, adding depth to our flat plane. This way, points help us describe exact locations in space.

Dimension of a point

Main article: Dimension (vector space)

Main article: Lebesgue covering dimension

Main article: Hausdorff dimension

In mathematics, a point has no size. It has no length, width, or height. It is just a single spot in space.

There are different ways to measure how many parts an object has, but a point is always zero. This is because a point does not have any smaller parts or directions, unlike lines, surfaces, or solids.