Systematic Skate Park Design Design 5 : Fall 2012
Mathematics represent all facets of architectural design through infinite possibilities. By limiting factors mathematically, a finite set of realities can be achieved with differing effects. Skate parks are expected to retain fluidity and variation like a skater. While limiting mathematical factors, caution must be taken in preserving these two ideas. Therefore, driving variables must ensure all endings result in a smooth transition without similar. Individual blocks are defined to 32’x32’x8’ cubes. There are 5 varied pipe types that define each block at the edge for fluid connections (default is a blank side). By ignoring order and rotation, the vital configurations can be found, lowering redundancy of options. Sides: 4 (Square) Types: 5 (A,B,C,D,Blank Side) Possible Configurations: 340 total, rotation matters, order matters. Final Configurations: 65 total, rotation and order do not matter.
A
B
C
D
This is the original model on piping that inspired a matrix system involving combinatorics In particular, the form is rendered using a water texture to embrace fluidity and variation While this may not seem as skatable as the other piping methods derived from mathematics the abstraction challenges the idea of: What defines a surface as skatable?
Index Parts 1 2 3 4
Variance
Variance Parts 1 2 3 4 Total
1
2
3
4
Permutation 4^P 4 16 64 256 340
4 4 4 4
12 12 12
48 48
192
1
2
3
4
Total
1 1
4 20 20 21 65
4 8 4 4 20
12 12 12 36
4 12 16
Order Matters With Repetition
Final No Repetition