Orthogonal convexity
Orthogonal convexity is like building with Legos! Imagine you have a bunch of square Legos and you want to build a tower. You can put the Legos on top of each other to make the tower taller, but you can't turn them sideways or upside down. This is because the Legos are orthogonal - they only fit together in certain ways that are at right angles to each other.
In math, we use a similar idea when talking about orthogonal convexity. We have a shape (like a square or a rectangle) that we want to build out of smaller shapes that are themselves squares or rectangles. We can put the smaller shapes together to make the bigger shape, but we can only use them in certain ways that are orthogonal - that is, at right angles to each other.
For example, if we want to build a square out of smaller squares, we can put four squares together in a square pattern. But if we want to make a rectangle out of smaller squares, we have to be careful how we arrange them. If we put the squares in a line, we'll end up with a row of squares, not a rectangle. Instead, we have to put two squares on top of each other to make the height of the rectangle, and then put more squares side by side to make the width.
This idea of orthogonal convexity is important in math because it helps us to understand how shapes fit together and how to build new shapes out of smaller pieces. It's like playing with Legos, but instead of making towers and castles, we're building mathematical models and solving problems.
In math, we use a similar idea when talking about orthogonal convexity. We have a shape (like a square or a rectangle) that we want to build out of smaller shapes that are themselves squares or rectangles. We can put the smaller shapes together to make the bigger shape, but we can only use them in certain ways that are orthogonal - that is, at right angles to each other.
For example, if we want to build a square out of smaller squares, we can put four squares together in a square pattern. But if we want to make a rectangle out of smaller squares, we have to be careful how we arrange them. If we put the squares in a line, we'll end up with a row of squares, not a rectangle. Instead, we have to put two squares on top of each other to make the height of the rectangle, and then put more squares side by side to make the width.
This idea of orthogonal convexity is important in math because it helps us to understand how shapes fit together and how to build new shapes out of smaller pieces. It's like playing with Legos, but instead of making towers and castles, we're building mathematical models and solving problems.