Whitney conditions

Whitney conditions are like rules that we have to follow when we want to create a curve using equations. Kind of like how we follow rules when we want to color in a picture without going outside the lines.

The first Whitney condition is like saying that we can't have any sharp corners on our curve. This means that the curve can't suddenly turn at a really sharp angle. It has to be a smooth transition.

The second Whitney condition is like saying that we can't have any overlapping parts in our curve. Like when we draw a circle and accidentally overlap the lines.

These conditions are important because they make sure our curves look nice and smooth. It's like following directions when we put a puzzle together so it looks exactly like the picture on the box.