8C.5.2 Nets
What are other ways to represent a 3d shape in two dimensions? We saw last class that you can use one of several different views, but we can also take the shape and look at its "skin". When you cut a polyhedron along some of its edges to lay it flat, we get a net:
Resources:
Fun Ideas with Nets and Networks
- Polyhedron Nets (paper nets)
- Konigsberg Network Problems - read about Euler's solution to the "bridge" problem and about 4 colour map theory!
- Six Degrees of Separation Network theory was the foundation for the idea that every person in the world is connected by no more than 6 connections. This was popularized in the game "Six Degrees of Kevin Bacon" that appeared in the early 1990's. While designed to be a trivia game, the Oracle of Bacon will quickly find any actor's "Bacon Number" for you.
Pre-Class Assignment:
- Before next class, read through the notes and copy them down into your notebook.
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Think about the following 2 questions and add a comment to this article with your answer:
- Do you think a net is more or less effective at representing a 3d shape two dimensionally than the 3 views?
- Is there a way to figure out how many faces, vertices and edges a shape will have by looking at its net? Use the examples of the triangular prism and the rectangular prism to help you.
In-Class Assignment:
- P173 #3, 4, 6, 7, 8, 9, *12 *13
- Koninsberg Network Problem
- Circle Challenge peer editing
Comments (19)
2.Yeah, but you'd have to know where the faces are
2. I think that you if you know what the 3D object is, it makes it easier, but on the net, you can see all the lines and where they end so it is easy to figure out where multiple lines meet and they make a face, vertices or edge.
2. By looking at a net, you can figure out the faces, vertices and edges because it's all laid out for you to see and all of the faces and lines of the edges are shown. So you could probably just count them.
Yes. It is quite easy to count and find the vertices, faces and edges. By looking at the net as the 3d shape can help you find the vertices, faces and edges.
2. Figuring Out #s - For Faces - count each unique face in the net; For Vertices - count corners where edges meet not including flaps; For Edges - count edges through the core shape not including flaps or common edges. This is tricky sometimes!
2. yes, u can mentally put together the edges of the net and count the faces, vertices, and edges, if you knew what the net was for example, a triangular prism, you could easily count the edges, faces, and vertices of the shape.
:) :) :) :) :) :) :) :) :)
I think it is your preference when showing the 3D shape. You could either show it in 3 views or a net. It depends which type of way is easier to visually comprehend. For me, I find the net is easier to effectively represent because it is laid out in 1 piece. It has lines to show the parts of the shape and the lines are also representing where the pieces bend. So I name the sides and picture bending it in my head to form the shape. But if the object is more detail (e.g. animal) then I find 3 views better for representing the object.
Question #2:
If you know what the net makes up when looking at the net then it is easier to picture in your mind where the faces, vertices and edges are. The lines on the net helps determine the part of the shape and what piece it is; what the line connects.
Question 2: When looking at a net to find the number of faces you would count the number of squares or rectangles that make up the object. To find the number of edges and vertices you could count them by picturing the object menatally, drawing it as a glass object so you can see through it, or creating and looking at one made by folding scrap paper or an object of the same shape
2. Yes, there is a way to figure out how many faces, vertices, and edges a shape will have by looking at it's net. We could look for where edges meet in corners and where there are whole shapes in the net
Q2: You could count the vertices, faces, and edges by looking at the net or you could mentally put the shape together using the net and then count the faces, vertices and edges.
Q2- Yes, you can find all the vertices, faces and edges very easily by using a net because you can clearly see all of them in front of you so all you have to do is count them without worrying tht u have to look at the shape from another angle
2)Yes, you can figure out how many faces, verticies and edges a shape will have by looking at them in a net because it is all layed our infront of you so you can probably just count them.
2. Yes. You just have to see which edges of the net will be pieced together.
2. Yes, you just need to mentally put it together in your head
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2.If you put it together mentally
1.I think a net is more effective to represent basic shapes but is you are are makes a net for a very complicated shape it is basically useless.
2. YEs a net makes it really easy to count all the facies and verticies.