- #1
xodaaaaax
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- Homework Statement
- Help with parameterize the intersection as shown in the figure
- Relevant Equations
- x^2+y^2=4 and z=0
Parameterize an intersection between a cylinder and plane z=0
- Thread starter xodaaaaax
- Start date
In summary, the conversation discusses the direction of arrows and equations in relation to going clockwise and counterclockwise. The speaker made a mistake with the arrows and acknowledges that they should be going clockwise. They also explain that they use "sen" instead of "sin" due to speaking Spanish. The conversation also touches on substitution in an integral and the speaker expresses gratitude for the clarification.
- #2
FactChecker
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You say that you are going clockwise, but your arrows and equations look counterclockwise.
Other than that, it looks ok to me. Shouldn't all those 'sen's be 'sin's?
Other than that, it looks ok to me. Shouldn't all those 'sen's be 'sin's?
- #3
xodaaaaax
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Oh my bad i was copying my notes into that picture so that it would be easier to understand them and messed up those arrows, yes they should be going clockwise. anyways, i type "sen" because i speak spanish, sorry about that.FactChecker said:
So those are the values i should substitute in that integral?
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Your y(t) equation will make it go around counterclockwise.
- #5
xodaaaaax
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I think i get it now, thank you so muchFactChecker said:
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... and "sin" en español means "without".xodaaaaax said:
1. What does it mean to parameterize an intersection between a cylinder and plane z=0?
Parameterizing an intersection between a cylinder and plane z=0 means finding a set of equations or parameters that represent all the points where the cylinder and plane intersect at z=0. This allows us to describe the intersection in a more simplified and organized manner.
2. How do you parameterize an intersection between a cylinder and plane z=0?
To parameterize an intersection between a cylinder and plane z=0, we can use the parametric equations of a cylinder and the equation of the plane to find the values of the parameters that satisfy both equations at z=0. These values will then be used to describe the points of intersection.
3. Why is it important to parameterize an intersection between a cylinder and plane z=0?
Parameterizing an intersection allows us to easily visualize and manipulate the intersection between the two surfaces. It also helps in solving equations or problems involving the intersection, as well as in finding the area or volume of the intersection.
4. Can you parameterize an intersection between a cylinder and plane z=0 if the plane is not parallel to the base of the cylinder?
Yes, it is possible to parameterize the intersection between a cylinder and a plane z=0 even if the plane is not parallel to the base of the cylinder. In this case, we would need to use a different set of parametric equations that take into account the orientation and position of the plane relative to the cylinder.
5. Are there any limitations to parameterizing an intersection between a cylinder and plane z=0?
One limitation of parameterizing an intersection between a cylinder and plane z=0 is that it can only describe the intersection at z=0. If we want to describe the intersection at a different z-value, we would need to use a different set of parameters. Additionally, this method may not work for more complex shapes or surfaces.
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