Let’s make something!
2D to 3D
fold
One way to make a 3d object (three-dimensional) from something 2d (two-dimensional flat paper) is by simple cutting and folding and gluing.
Start by drawing a triangle.
Copy the triangle 4 times around a square.
Make it all one shape and cut it out.
Fold all of the triangles up at the edges of the square.
You can see that you have created a pyramid. (the square is the base and the triangles are the sides of the pyramid)
The only problem is that there is nothing to connect the edges of the triangles, so let’s start again... with glue tabs.
Glue tabs are thin extra pieces of paper that you need to add at every edge that needs to be glued for another edge. The basic rules: 1. Find any two edges that will need to be glued together, and add glue tabs to one of the two edges. 2. Glue tabs should be very thin, no more than quarter inch wide. 3. Glue tabs should taper (become narrow) at each end.
Redraw your cutout shape and find the pairs of edges that need glue tabs.
For each pair of edges, add glue tabs to one edge. 3
4 3b 3a
4b
2b
1a
2a 2
4a
1b 1
Now cut out the shape again but with all the glue tabs. Fold all of the triangles up at the edges of the square. And also carefully fold the glue tabs at their edges.
For each edge with a glue tab, dab a little bit of glue on the tab , then fold the shape and slip the glue tab under the opposite edge (hold unil the glue dries a little bit). Now all the edges can connect well, and you have a good 3d pyramid.
You can also make the 3d pyramid much more interesting by cutting out different shapes inside the square and the triangles before cutting the shape and folding it.
surface vs volume:
Surfaces and volumes are closely related. That is why you can fold surfaces and make a volume. Surfaces are the exterior shapes that wrap around an interior volume. Because surfaces make volumes, and volumes are made by surfaces, you can use the measurements of surfaces to calculate the exact volume of a 3d object. This is something that you might first learn in 3rd grade math, and then later in 5th grade (and even more advanced in college!).
dimensions:
A 2-dimensional (2D) object is an object that only has 2 dimensions (length and width), but no height. A 3-dimensional (3D) object has a length, width AND height.
2d
3d
Usually 2D objects are flat, but they can become ‘3D’ by bending or folding. This is what you did when you folded triangles into a pyramid.
SQUARE BASE PYRAMID
2
1
2 1
1
2
1
2
CUBE 2
1
1
1
2
2
2
2
1
2
1
2
EXTRUDED TRIANGLE 1
2
1
1
2
2
1
2
2
EXTRUDED HEXAGON
2
2
2
2 1
2
1
1
1
2
2
2
2 2
1
1
1