It'll be easier for you to help them through the school day if you're near them in class. Speak to your teacher about sitting next to the new student. As long as you explain that you're doing it to be helpful, there shouldn't be a problem. For example, you could say: "Mary is new to this school. Could I please sit next to her so that I can help her and make her feel welcome?" One of the scariest things for a new kid is not knowing where to sit at lunch. Everyone already knows where to sit, and they're usually stuck eating alone. Save a seat for the new kid at your table and you'll make a great impression. If you're used to sitting with your friends, this is a great chance to introduce them to the new kid. Ask them during break or on the way to lunch if they want to sit with you. Say something like: Hey, would you like to sit with me and my friends at lunch?" Don't try and take full responsibility for the new kid feeling welcome. Introduce them to your friends and to others in your class. This will help them make more friendships for the future and feel comfortable even when you're not around. Don't be upset if the new kid doesn't become friends with yours. The goal is to make them feel welcome. If they make their own friends, that's okay! The new kid might even find a different group they click with and become friends with them.
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One-sentence summary -- Make sure the new kid is seated near you. Invite them to sit with you at lunch. Introduce the new kid to your friends.

One way to think of the radius of a sphere is as the distance between the point at the center of the sphere and any point on the surface of the sphere. Because this is true, if you know the coordinates of the point at the center of the sphere and of any point on the surface, you can find the radius of the sphere simply by calculating the distance between the two points with a variant of the basic distance formula. To begin, find the coordinates of the sphere's center point. Note that because spheres are three-dimensional, this will be an (x,y,z) point rather than an (x,y) point. This process is easier to understand by following along with an example. For our purposes, let's say that we have a sphere centered around the (x,y,z) point (4, -1, 12). In the next few steps, we'll use this point to help find the radius. Next, you'll need to find the (x,y,z) coordinates of a point on the surface of the sphere. This can be any point on the surface of the sphere. Because the points on the surface of a sphere are equidistant from the center point by definition, any point will work for determining the radius. For the purposes of our example problem, let's say that we know that the point (3, 3, 0) lies on the surface of the sphere. By calculating the distance between this point and the center point, we can find the radius. Now that you know the center of the sphere and a point on the surface, calculating the distance between the two will find the radius. Use the three-dimensional distance formula d = ((x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2), where d equals distance, (x1,y1,z1) equals the coordinates of the center point, and (x2,y2,z2) equals the coordinates of the point on the surface to find the distance between the two points. In our example, we would plug in (4, -1, 12) for (x1,y1,z1) and (3, 3, 0) for (x2,y2,z2), solving as follows: d = ((x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2) d = ((3 - 4)2 + (3 - -1)2 + (0 - 12)2) d = ((-1)2 + (4)2 + (-12)2) d = (1 + 16 + 144) d = (161) d = 12.69. This is the radius of our sphere. In a sphere, every point on the surface of the sphere is the same distance from the center point. If we take the three-dimensional distance formula above and replace the "d" variable with the "r" variable for radius, we get a form of the equation that can can find the radius given any center point (x1,y1,z1) and any corresponding surface point (x2,y2,z2). By squaring both sides of this equation, we get r2 = (x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2. Note that this is essentially equal to the basic sphere equation r2 = x2 + y2 + z2 which assumes a center point of (0,0,0).
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One-sentence summary -- Find the (x,y,z) coordinates of the central point of the sphere. Find the coordinates of a point on the surface of the sphere. Find the radius with the formula d = ((x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2). Know that, in general cases, r = ((x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2).

Try getting each of you a separate sheet. If you have a decorative bedding set you don't want to change, the second set can be kept in the linen closet or in under-bed storage until bedtime each night. Your covers may simply be too small for both of you! Try getting a size larger than your bed--if you sleep in a queen size bed, get a king size set Many people steal sheets because they are just too far away from their partner to share. If it's an option, a smaller bed might be a good solution. Try sleeping in a queen or full-size bed--it may be impossible to steal sheets! If you really can't get comfortable and no other solution has worked for you, separate beds may be a last resort to prevent further relationship stress. You don't have to sleep in separate rooms. Try pushing two small beds close to each other.
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One-sentence summary --
Use separate sheets. Buy a larger bedding set. Get a smaller bed. Try sleeping separately.