Is there a place to buy physical models to demonstrate the Calculus shell, disk, and washer methods?
I know a math teacher who is going to teach a calculus class that will include the shell, disk, and washer methods for calculating volumes. My question is, is there some 3D kit she could use to demonstrate these methods physically?
Ideally for example, the washer method could be demonstrated with a cylinder that has an inner cylinder that could be removed.
calculus
asked 6 hours ago
Eugene
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I know a math teacher who is going to teach a calculus class that will include the shell, disk, and washer methods for calculating volumes. My question is, is there some 3D kit she could use to demonstrate these methods physically?
Ideally for example, the washer method could be demonstrated with a cylinder that has an inner cylinder that could be removed.
calculus
asked 6 hours ago
Eugene
1261
New contributor
Eugene is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
I know a math teacher who is going to teach a calculus class that will include the shell, disk, and washer methods for calculating volumes. My question is, is there some 3D kit she could use to demonstrate these methods physically?
Ideally for example, the washer method could be demonstrated with a cylinder that has an inner cylinder that could be removed.
calculus
asked 6 hours ago
Eugene
1261
New contributor
Eugene is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I know a math teacher who is going to teach a calculus class that will include the shell, disk, and washer methods for calculating volumes. My question is, is there some 3D kit she could use to demonstrate these methods physically?
Ideally for example, the washer method could be demonstrated with a cylinder that has an inner cylinder that could be removed.
calculus
calculus
asked 6 hours ago
Eugene
1261
New contributor
Eugene is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
Eugene
1261
New contributor
Eugene is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
Eugene
1261
New contributor
Eugene is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
Eugene
1261
asked 6 hours ago
Eugene
1261
1261
New contributor
Eugene is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Eugene is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Eugene is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
3 Answers
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It is probably easier to make 3D computer images of such methods, using even something simple like geogebra (or using CAD software if you know how to use it), that can be projected during class, than to obtain functional physical models. The latter can be machined or made using a 3D printer, but computer visualizations are far more adaptable and adjustable, and it's not clear to me that much is gained by using an actual physical model. In most any university physics or engineering department there is someone who knows how to make such physical models, but probably it is a better use of one's time to learn to use software designed for creating visualizations. Moreover, computer models can be interactive in ways that physical models simply cannot. The student can see a surface of revolution as it is generated, and so forth.
My recommendation would be to look into using geogebra. The sorts of models you describe (appropriate for a multivariable calculus class) are not hard to realize in such software and there are already many examples available online.
answered 6 hours ago
Dan Fox
1,919515
add a comment |
3D printing is an attractive avenue.
I think there is something to be gained by actual physical models.
Image from Elizabeth Denne's webpages.
See also Rebecka Peterson's Epsilon-Delta for low-tech alternatives:
Student volume models based on cross-sections.
answered 42 mins ago
Joseph O'Rourke
14.6k33279
add a comment |
I suppose, if you wish to illustrate the washer method then perhaps slicing a pear (see here for a picture into 10 or so horizontal slices would give you bunch of near washers with which you could estimate the volume of a pear. Then, you could even estimate the error in the calculation by the water displaced by the uncut pear. Ideally, you'd like a near circular pear, but you could estimate a mean radius if it was lumpy.
For cylindrical shells, I have a less fruity idea involving foam sheets held together by large rubber bands around some center cylinder. But, I haven't had a chance to try it out myself yet. Onions are almost good, but the layers are too curved. If you could find some cylindrical onions. See, someone needs to grow cylindrical onions. Perhaps there is some other easily obtained food which illustrates the shell method.
answered 21 mins ago
James S. Cook
5,75311442
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
It is probably easier to make 3D computer images of such methods, using even something simple like geogebra (or using CAD software if you know how to use it), that can be projected during class, than to obtain functional physical models. The latter can be machined or made using a 3D printer, but computer visualizations are far more adaptable and adjustable, and it's not clear to me that much is gained by using an actual physical model. In most any university physics or engineering department there is someone who knows how to make such physical models, but probably it is a better use of one's time to learn to use software designed for creating visualizations. Moreover, computer models can be interactive in ways that physical models simply cannot. The student can see a surface of revolution as it is generated, and so forth.
My recommendation would be to look into using geogebra. The sorts of models you describe (appropriate for a multivariable calculus class) are not hard to realize in such software and there are already many examples available online.
answered 6 hours ago
Dan Fox
1,919515
add a comment |
It is probably easier to make 3D computer images of such methods, using even something simple like geogebra (or using CAD software if you know how to use it), that can be projected during class, than to obtain functional physical models. The latter can be machined or made using a 3D printer, but computer visualizations are far more adaptable and adjustable, and it's not clear to me that much is gained by using an actual physical model. In most any university physics or engineering department there is someone who knows how to make such physical models, but probably it is a better use of one's time to learn to use software designed for creating visualizations. Moreover, computer models can be interactive in ways that physical models simply cannot. The student can see a surface of revolution as it is generated, and so forth.
My recommendation would be to look into using geogebra. The sorts of models you describe (appropriate for a multivariable calculus class) are not hard to realize in such software and there are already many examples available online.
answered 6 hours ago
Dan Fox
1,919515
add a comment |
It is probably easier to make 3D computer images of such methods, using even something simple like geogebra (or using CAD software if you know how to use it), that can be projected during class, than to obtain functional physical models. The latter can be machined or made using a 3D printer, but computer visualizations are far more adaptable and adjustable, and it's not clear to me that much is gained by using an actual physical model. In most any university physics or engineering department there is someone who knows how to make such physical models, but probably it is a better use of one's time to learn to use software designed for creating visualizations. Moreover, computer models can be interactive in ways that physical models simply cannot. The student can see a surface of revolution as it is generated, and so forth.
My recommendation would be to look into using geogebra. The sorts of models you describe (appropriate for a multivariable calculus class) are not hard to realize in such software and there are already many examples available online.
answered 6 hours ago
Dan Fox
1,919515
It is probably easier to make 3D computer images of such methods, using even something simple like geogebra (or using CAD software if you know how to use it), that can be projected during class, than to obtain functional physical models. The latter can be machined or made using a 3D printer, but computer visualizations are far more adaptable and adjustable, and it's not clear to me that much is gained by using an actual physical model. In most any university physics or engineering department there is someone who knows how to make such physical models, but probably it is a better use of one's time to learn to use software designed for creating visualizations. Moreover, computer models can be interactive in ways that physical models simply cannot. The student can see a surface of revolution as it is generated, and so forth.
My recommendation would be to look into using geogebra. The sorts of models you describe (appropriate for a multivariable calculus class) are not hard to realize in such software and there are already many examples available online.
answered 6 hours ago
Dan Fox
1,919515
answered 6 hours ago
Dan Fox
1,919515
answered 6 hours ago
Dan Fox
1,919515
answered 6 hours ago
Dan Fox
1,919515
1,919515
add a comment |
add a comment |
3D printing is an attractive avenue.
I think there is something to be gained by actual physical models.
Image from Elizabeth Denne's webpages.
See also Rebecka Peterson's Epsilon-Delta for low-tech alternatives:
Student volume models based on cross-sections.
answered 42 mins ago
Joseph O'Rourke
14.6k33279
add a comment |
3D printing is an attractive avenue.
I think there is something to be gained by actual physical models.
Image from Elizabeth Denne's webpages.
See also Rebecka Peterson's Epsilon-Delta for low-tech alternatives:
Student volume models based on cross-sections.
answered 42 mins ago
Joseph O'Rourke
14.6k33279
add a comment |
3D printing is an attractive avenue.
I think there is something to be gained by actual physical models.
Image from Elizabeth Denne's webpages.
See also Rebecka Peterson's Epsilon-Delta for low-tech alternatives:
Student volume models based on cross-sections.
answered 42 mins ago
Joseph O'Rourke
14.6k33279
3D printing is an attractive avenue.
I think there is something to be gained by actual physical models.
Image from Elizabeth Denne's webpages.
See also Rebecka Peterson's Epsilon-Delta for low-tech alternatives:
Student volume models based on cross-sections.
answered 42 mins ago
Joseph O'Rourke
14.6k33279
answered 42 mins ago
Joseph O'Rourke
14.6k33279
answered 42 mins ago
Joseph O'Rourke
14.6k33279
answered 42 mins ago
Joseph O'Rourke
14.6k33279
14.6k33279
add a comment |
add a comment |
I suppose, if you wish to illustrate the washer method then perhaps slicing a pear (see here for a picture into 10 or so horizontal slices would give you bunch of near washers with which you could estimate the volume of a pear. Then, you could even estimate the error in the calculation by the water displaced by the uncut pear. Ideally, you'd like a near circular pear, but you could estimate a mean radius if it was lumpy.
For cylindrical shells, I have a less fruity idea involving foam sheets held together by large rubber bands around some center cylinder. But, I haven't had a chance to try it out myself yet. Onions are almost good, but the layers are too curved. If you could find some cylindrical onions. See, someone needs to grow cylindrical onions. Perhaps there is some other easily obtained food which illustrates the shell method.
answered 21 mins ago
James S. Cook
5,75311442
add a comment |
I suppose, if you wish to illustrate the washer method then perhaps slicing a pear (see here for a picture into 10 or so horizontal slices would give you bunch of near washers with which you could estimate the volume of a pear. Then, you could even estimate the error in the calculation by the water displaced by the uncut pear. Ideally, you'd like a near circular pear, but you could estimate a mean radius if it was lumpy.
For cylindrical shells, I have a less fruity idea involving foam sheets held together by large rubber bands around some center cylinder. But, I haven't had a chance to try it out myself yet. Onions are almost good, but the layers are too curved. If you could find some cylindrical onions. See, someone needs to grow cylindrical onions. Perhaps there is some other easily obtained food which illustrates the shell method.
answered 21 mins ago
James S. Cook
5,75311442
add a comment |
I suppose, if you wish to illustrate the washer method then perhaps slicing a pear (see here for a picture into 10 or so horizontal slices would give you bunch of near washers with which you could estimate the volume of a pear. Then, you could even estimate the error in the calculation by the water displaced by the uncut pear. Ideally, you'd like a near circular pear, but you could estimate a mean radius if it was lumpy.
For cylindrical shells, I have a less fruity idea involving foam sheets held together by large rubber bands around some center cylinder. But, I haven't had a chance to try it out myself yet. Onions are almost good, but the layers are too curved. If you could find some cylindrical onions. See, someone needs to grow cylindrical onions. Perhaps there is some other easily obtained food which illustrates the shell method.
answered 21 mins ago
James S. Cook
5,75311442
I suppose, if you wish to illustrate the washer method then perhaps slicing a pear (see here for a picture into 10 or so horizontal slices would give you bunch of near washers with which you could estimate the volume of a pear. Then, you could even estimate the error in the calculation by the water displaced by the uncut pear. Ideally, you'd like a near circular pear, but you could estimate a mean radius if it was lumpy.
For cylindrical shells, I have a less fruity idea involving foam sheets held together by large rubber bands around some center cylinder. But, I haven't had a chance to try it out myself yet. Onions are almost good, but the layers are too curved. If you could find some cylindrical onions. See, someone needs to grow cylindrical onions. Perhaps there is some other easily obtained food which illustrates the shell method.
answered 21 mins ago
James S. Cook
5,75311442
answered 21 mins ago
James S. Cook
5,75311442
answered 21 mins ago
James S. Cook
5,75311442
answered 21 mins ago
James S. Cook
5,75311442
5,75311442
add a comment |
add a comment |
Eugene is a new contributor. Be nice, and check out our Code of Conduct.
Eugene is a new contributor. Be nice, and check out our Code of Conduct.
Eugene is a new contributor. Be nice, and check out our Code of Conduct.
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