How do you create a + and π sign using multivariable (x,y,z)

In summary, the speaker is taking a multivariable calculus class and is having trouble creating a connected, continuous, and differentiable project on Euler's formula. They are specifically having difficulty with making a pi and a plus sign. One suggested solution is to use piecewise-defined curves, such as straight lines and quarter or half circles, joined together as tangents to create the desired shapes. This approach will result in a continuous and differentiable curve, with the possibility of some points being twice-differentiable. The final drawings may have a hollow "inside" that is not visible to the naked eye.
  • #1
JessicaHelena
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I am taking a high school multivariable calculus class and we have an end-of-semester project where we trace out some letters etc., except that they all have to be connected, continuous and differentiable everywhere. My group's chosen to do Euler's formula, but so far we are having problems making ##\pi## and the + sign. For the + sign, we thought that we could do rose curves, but it seems that the equations for rose curves in 2D don't really work in a 3D environment. Could someone give us hints as to how to approach these problems? Any help would really be appreciated!

<mentor edit: latex fix>
 
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  • #2
You can use piecewise-defined curves, for which each piece is either a straight line or a quarter or half circle. Provided the circle pieces join the circle segments to which they connect as a tangent, the curve will be continuous and differentiable everywhere. It will even be twice-differentiable everywhere except at points where a straight and curved segment connect.

It's easy to make a pi and a plus sign using that approach. Both drawings will have a hollow 'inside', but if the radii of the circles are made small enough, that will not be visible to the naked eye.
 

1. How do I create a plus sign using multivariable (x,y,z)?

To create a plus sign using multivariable (x,y,z), you can use the following equation:
x + y + z = 0. This equation represents a plane in three-dimensional space where x, y, and z are variables. By setting the sum of these variables to 0, you can create a plus sign.

2. How do I create a pi (π) sign using multivariable (x,y,z)?

To create a pi (π) sign using multivariable (x,y,z), you can use the following equation:
x^2 + y^2 + z^2 = r^2. This equation represents a sphere in three-dimensional space where x, y, and z are variables and r is the radius. By setting the sum of the squares of these variables to the radius squared, you can create a pi (π) sign.

3. Can I use other variables besides x, y, and z to create a plus and pi sign?

Yes, you can use any variables you want as long as they are consistent in the equations. For example, you can use a, b, and c instead of x, y, and z to create a plus sign, or you can use u, v, and w instead of x, y, and z to create a pi (π) sign.

4. Are there any other ways to create a plus and pi sign in a multivariable equation?

Yes, there are other ways to create a plus and pi sign using multivariable equations. For example, you can use trigonometric functions such as sin, cos, and tan to create a plus sign, or you can use a parametric equation to create a pi (π) sign. It all depends on the specific equation you are using.

5. How can I visually represent a plus and pi sign using multivariable equations?

You can visually represent a plus and pi sign using multivariable equations by graphing them in three-dimensional space. A plus sign would appear as a plane, while a pi (π) sign would appear as a sphere. You can also use computer software or 3D graphing calculators to create a visual representation of these signs.

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