Why Doesn't My 2-Sphere Graph Correctly in GraphCalc?

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In summary, The speaker tried to graph a 2-sphere using the equations z=\sqrt{-x^2-y^2+9} and z=-\sqrt{-x^2-y^2+9}, but it did not work as expected. They received a blurry image of a sphere at the origin with a radius of 3 when using GraphCalc. They ask for clarification on what went wrong and mention it is their first time using the program. The listener responds that the equations used did result in a sphere, but the approximation becomes fuzzy near the xy-plane due to the large slope. The program only evaluates the function value on a small grid of points.
  • #1
yourdadonapogostick
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i attempted to graph a 2-sphere on graphcalc and it wouldn't work. the equations had to be in terms of z, so i had to use: [tex]z=\sqrt{-x^2-y^2+9}[/tex] and [tex]z=-\sqrt{-x^2-y^2+9}[/tex]. i thought that would give me a 2-sphere at the origin with a radius of 3, but it didn't. i got:[PLAIN]http://photobucket.com/albums/a192/YoDizzle/th_almostsphere.bmp.[/URL] what did i do wrong?

the split is along the x y plane. if it matters, this is my first try at using graphcalc.
 
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  • #2
You got a sphere. It just breaks down near the xy-plane, because the approximations get fuzzy as the slope becomes very large. Your program only evaluates the function value on a small grid of points.
 
  • #3


It looks like you did everything correctly, but there may be a few things that could have caused the graph to not appear as expected. First, double check that you are using the correct syntax for graphcalc. It may be helpful to refer to the user manual or online tutorials to ensure you are inputting the equations correctly.

Secondly, make sure that the viewing window for the graph is large enough to display the entire 2-sphere. You may need to adjust the scale or zoom in/out to see the full shape.

Lastly, it's possible that there may be a glitch or error with the program. Try restarting the program or using a different graphing software to see if you get the same result. If the issue persists, you may need to reach out to the program's support team for assistance. Keep practicing and don't get discouraged, graphing can be tricky but with some patience and practice, you'll get the hang of it.
 

FAQ: Why Doesn't My 2-Sphere Graph Correctly in GraphCalc?

How do I graph a 2-sphere on graphcalc?

To graph a 2-sphere on graphcalc, you will first need to open the graphing software and select the 3D graphing mode. Then, input the equation for a 2-sphere, which is typically written as x^2 + y^2 + z^2 = r^2, where r is the radius of the sphere. Finally, adjust the scale and viewing angle to get a clear visualization of the 2-sphere.

What is a 2-sphere?

A 2-sphere, also known as a two-dimensional sphere or a spherical surface, is a geometric shape that is similar to a three-dimensional sphere but exists in two dimensions. It is defined as the set of all points in three-dimensional space that are a fixed distance, called the radius, from a given point, called the center.

How is a 2-sphere different from a circle?

A 2-sphere is different from a circle in that a circle exists in two dimensions (on a flat plane) while a 2-sphere exists in three dimensions. Additionally, a circle has one radius, whereas a 2-sphere has a fixed distance from all points on its surface to the center. Essentially, a circle is a cross-section of a 2-sphere.

What are some real-world examples of a 2-sphere?

Some real-world examples of a 2-sphere include planets, such as Earth, which can be approximated as a 2-sphere due to its spherical shape. Another example is a balloon, where the inflated surface can be represented as a 2-sphere. Other examples include soap bubbles, water droplets, and marbles.

Why is it useful to graph a 2-sphere on graphcalc?

Graphing a 2-sphere on graphcalc can be useful for visualizing and understanding geometric concepts, such as distance and symmetry. It can also be used to model real-world objects or phenomena that have a spherical shape. Additionally, graphing a 2-sphere on graphcalc can help in solving equations and analyzing data that involve spherical surfaces.

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