Projection (mathematics) facts for kids

A projection in geometry is like a shadow that an object makes on a surface. Imagine holding your hand in front of a light. The shape you see on the wall is a projection of your hand! In geometry, we study how shapes and objects can be "projected" from one space onto another.

When a 3D shape, like a sphere (a perfect ball), is projected onto a flat surface (a plane), its shadow can be a circle or an ellipse (an oval shape). It depends on where the light source is and how the ball is positioned!

What is a Projection in Math?

A projection in mathematics is a way to transform or "map" points or shapes from one space to another. Think of it as flattening a 3D object into a 2D image, or simplifying a complex shape into a simpler one.

Everyday Examples of Projections

Projections are all around us!

• Shadows: The most common example is a shadow. When light hits an object, it casts a shadow on a surface. That shadow is a projection of the object.
• Maps: When you look at a world map, it's a 2D projection of our 3D Earth. This is why Greenland looks so big on some maps – it's a way of flattening a curved surface!
• Movie Projectors: A movie projector takes a small image from a film or digital file and projects a much larger image onto a screen.

How Do Projections Work?

In geometry, a projection usually involves drawing lines from points on an object to a specific surface, called the "projection plane."

• Light Source: Sometimes, these lines come from a single point, like a light bulb. This is called a central projection.
• Parallel Lines: Other times, the lines are all parallel to each other, like the sun's rays. This is called a parallel projection.

Central Projection: Like a Flashlight

Imagine you have a small toy car. If you shine a flashlight on it from one spot, the shadow it makes on the wall will change size and shape depending on how close or far the flashlight is, and how the car is turned. This is similar to a central projection. The light source is the "center" of the projection.

Parallel Projection: Like the Sun

Now, imagine the sun shining on the toy car. Because the sun is so far away, its rays hit the car almost perfectly parallel to each other. The shadow it casts will be a more accurate outline of the car's shape, without much distortion from perspective. This is a parallel projection.

Why Are Projections Important?

Projections are super useful in many areas:

• Art and Design: Artists use projections to create realistic drawings and paintings, especially when showing depth and perspective. Architects use them to draw blueprints of buildings.
• Computer Graphics: When you play a video game or watch an animated movie, projections are used to show 3D objects on your 2D screen.
• Engineering: Engineers use projections to design parts and machines, making sure everything fits together correctly.
• Cartography (Map Making): As mentioned before, projections are essential for creating maps of the Earth. Different map projections have different strengths and weaknesses, depending on what they want to show accurately (like shape, area, or distance).

See also

In Spanish: Proyección (matemáticas) para niños