Affine geometry

Affine geometry is a type of math that helps us understand shapes and the way they move and transform. A shape is anything that has a size and a position in space, like a triangle or a square.

Think of it like playing with blocks. When you move a block to a different spot, you change its position. When you turn the block over or rotate it, you change its orientation. Affine geometry helps us understand how these changes work and how they relate to each other.

In affine geometry, we can describe shapes using something called "vectors." A vector is like a special arrow that tells us how far and in what direction we need to move from one point to another. For example, if we have a vector that points to the right and is five units long, we can use it to move a shape five units to the right.

We can also use vectors to describe the relationships between shapes. For example, if we have two triangles that are the same size and shape but are in different positions, we can use vectors to describe how one triangle was moved to get to the other position.

In affine geometry, we don't care about things like angles or distances between points. Instead, we focus on how shapes relate to each other and how they can be transformed. We can do things like stretch a shape, flip it over, or move it to a different position. As long as we can describe these changes using vectors, we can use affine geometry to understand them.

So, affine geometry is like a tool that helps us understand how shapes can be transformed and how they relate to each other. We use vectors to describe these changes and focus on the relationships between shapes rather than their individual characteristics.