Parametrization (geometry)
Okay kiddo, let me tell you about parametrization in geometry. Have you ever drawn a picture or made a paper airplane? Have you ever tried to give someone else directions on how to draw or make the same thing?
That's kind of what parametrization is like. It's giving directions to someone to help them draw a shape or object using numbers. These numbers help us understand where every single point on the shape is and how it moves around.
Let's say we want to draw a circle. A circle is round and has no edges or corners, right? So how do we give directions for drawing it?
We can use a little trick called parametrization. We choose to give directions using two numbers, let's call them "t1" and "t2". We can say that every single point on the circle can be found by using these two numbers.
So let's say we choose the center of the circle to be at (0,0) and the radius of the circle to be 1. We can give directions for every other point on the circle like this:
- Start at angle 0 degrees (which we'll call "t1=0")
- Imagine a line extending from the center of the circle, at this angle of 0 degrees
- Move along this line for a distance of 1, away from the center of the circle (which we'll call "t2=1")
- The point where this line ends is the point on the edge of the circle at angle 0 degrees and distance 1 from the center
We could repeat these directions for every angle from 0 to 360 degrees, to draw every point on the circle. That's what parametrization does - it gives us a way to describe every point on a shape using just a few numbers, like a set of directions.
And it's not just for circles - we can use parametrization for all sorts of shapes in geometry!
That's kind of what parametrization is like. It's giving directions to someone to help them draw a shape or object using numbers. These numbers help us understand where every single point on the shape is and how it moves around.
Let's say we want to draw a circle. A circle is round and has no edges or corners, right? So how do we give directions for drawing it?
We can use a little trick called parametrization. We choose to give directions using two numbers, let's call them "t1" and "t2". We can say that every single point on the circle can be found by using these two numbers.
So let's say we choose the center of the circle to be at (0,0) and the radius of the circle to be 1. We can give directions for every other point on the circle like this:
- Start at angle 0 degrees (which we'll call "t1=0")
- Imagine a line extending from the center of the circle, at this angle of 0 degrees
- Move along this line for a distance of 1, away from the center of the circle (which we'll call "t2=1")
- The point where this line ends is the point on the edge of the circle at angle 0 degrees and distance 1 from the center
We could repeat these directions for every angle from 0 to 360 degrees, to draw every point on the circle. That's what parametrization does - it gives us a way to describe every point on a shape using just a few numbers, like a set of directions.
And it's not just for circles - we can use parametrization for all sorts of shapes in geometry!