Investigating the Formulas and Structure of Adding Borders in Three Dimensions
Now that I have completed my investigation into adding borders in two
dimensions and its structure, I will now investigate the formulas and
structure of adding borders in three dimensions. I have made the first
five patterns using cubes and to make it simpler to draw I have split
the shapes up into layers.
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6
By Yousuf Khan
I put the diagrams of the 3D cubes as layers so that if you layer them
together you will get the shape you want. This makes my job of
counting much easier so I decided to draw them in this way. Now I will
count up the cubes and put the information into a table of results.
Pattern Number
3D Border Cubes
3D Inside Cubes
3D Total Cubes
1
0
1
1
2
6
1
7
3
18
7
25
4
38
25
63
5
66
63
129
From viewing the table I can see that one of the patterns is still the
same, and that is, that the total number of cubes in pattern number 1
is equal to the inside cubes in pattern number 2, and the total number
of cubes in pattern number 2 is equal to the inside number of cubes
for pattern number 3 etc. Also the total number of cubes minus the
border cubes gives me the Inside cubes.
I shall now work out some formulae for working out the number of
inside cubes, the total number of cubes and the border cubes for the
3D shapes.
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Text Box:
If we ignore the first of the 2nd differences, we begin to see a
pattern which, although may not have any relevance, could still mean
something.
[IMAGE] So it has something to do with 4n².
6x6x6 cube and see if I can find a pattern. When I have found a
The data in table 3.6 follows these trends; therefore, the EPS board was functioning as
hard to keep up with. This is an excellent way of creating an image of
2nd & 4th, 5th & 9th & 10th, 6th & 8th, 7th & 11th. This pattern is
was that showed behind, that dim sub-pattern, but now I am quite sure it is
Jimmy: Can I draw it on two number lines, or does it have to be on one number line? (SR3)
· Collect 3 cylinders, and then cut them into 6 pieces of 3 cm with a
it is thinner. It is a little bit like taking a piece of gum, and
From figure 1 it can be seen that there are links between all three layers of the model and that the environment can interact with any one of these layers.
consideration because they depict the hand in hand progression (one following the other in ...
Pineda, R. G., Tjoeng, T.H., Vavasseur, C., Kidokoro, H., Neil, J.J., & Inder, T. (2013). Patterns
Borders: A Very Short Introduction, by Alexander C. Diener and Joshua Hagen, is a brief the history of geographic borders and their implications on the world throughout history. Diener and Hagen make the argument that borders, as commonly understood today, are a relatively new phenomenon and as humanity moves forward borders modern boarders will no longer be possible. The writers maintain as globalization continues to make the world a smaller place or as they say, “make the world flat”, the notion of the formal state border is slowly coming to an end. Acknowledging that borders as they are understood today will not vanish overnight and will be here for the foreseeable future but in time they must change is central to their argument (Diener & Hagen, 2012). In making their case they give the reader a brief history of geographic boarders and how the modern nation state came about.
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After creating the three-dimensional model, the artist adds color, texture, and shading in a process known as texture mapping. Texture mapping makes the surfaces of the characters and scenery look real. A texture map can be created by a computer program or scanned from an actual photograph.