Finding Ellipses
Okay little one, have you ever seen those flattened circles that seem to have an oval shape? Those are called ellipses! Now, imagine you have a sheet of paper with a bunch of dots on it, and some of those dots trace out an ellipse. How do you find that ellipse?
Well, to find the ellipse, we need to first find some special points on it called foci (just think of them as two special friends). These friends are not just any points – they're specific points that are a set distance apart from each other (let's call this distance "d"). If we put them together with a string, and then stretch the string to make the ellipse, the string should always be tight.
To find these friends (the foci), we first need to have a clue from the dots we have on the paper. Luckily, we can use some math to help us!
First, we randomly choose two dots on the ellipse, let's call them A and B, and measure the distance between them (called "AB"). Then we draw a line, connect the middle of A and B with a point called C. Now, we measure the distance from A or B to C (let's call it "d1").
Once we have these measurements, we can start finding the positions of the foci!
We'll start with the first friend, focus 1. We'll place one end of our string on dot A and then measure "d1" units away from dot C to find the other end. This is where focus 1 is located!
Next, we can use the same process to find focus 2. This time, we'll place one end of our string on dot B and again measure "d1" units away from dot C to find the other end. This is where focus 2 is located!
Now that we know where the foci are, we can draw the ellipse using the following steps:
1. Stretch the string tight between the two foci.
2. Place a pencil at one of the dots on the ellipse.
3. Slowly move the pencil around the paper, always keeping the string tight.
4. The path traced by the pencil will be the ellipse!
So there you have it, little one. With some math and a bit of string, we can find and draw ellipses. Cool, right?
Well, to find the ellipse, we need to first find some special points on it called foci (just think of them as two special friends). These friends are not just any points – they're specific points that are a set distance apart from each other (let's call this distance "d"). If we put them together with a string, and then stretch the string to make the ellipse, the string should always be tight.
To find these friends (the foci), we first need to have a clue from the dots we have on the paper. Luckily, we can use some math to help us!
First, we randomly choose two dots on the ellipse, let's call them A and B, and measure the distance between them (called "AB"). Then we draw a line, connect the middle of A and B with a point called C. Now, we measure the distance from A or B to C (let's call it "d1").
Once we have these measurements, we can start finding the positions of the foci!
We'll start with the first friend, focus 1. We'll place one end of our string on dot A and then measure "d1" units away from dot C to find the other end. This is where focus 1 is located!
Next, we can use the same process to find focus 2. This time, we'll place one end of our string on dot B and again measure "d1" units away from dot C to find the other end. This is where focus 2 is located!
Now that we know where the foci are, we can draw the ellipse using the following steps:
1. Stretch the string tight between the two foci.
2. Place a pencil at one of the dots on the ellipse.
3. Slowly move the pencil around the paper, always keeping the string tight.
4. The path traced by the pencil will be the ellipse!
So there you have it, little one. With some math and a bit of string, we can find and draw ellipses. Cool, right?