Introduction: An Approximated Paper Screw Based on a N-Diagonal Matrix
In my studies I learned how to think in an abstract way, without considering the whole details.
Visually the n-diagonal matrix was something familiar for me, it was the fascinating pattern, that reminded me of the windings of a screw or a spiral fusilli pasta. You can see how a full diagonal matrix is structured, it is also known as Toeplitz Matrix. As you can see it's a complex n-dimensional matrix, but think simple.
Step 1: Numeric Matrix
Substitute the variables into numeric values (for example a 4x7 Matrix), well the readability is much more better.
Step 2: Substitute the Numbers With the Pattern
If you insert and/or substitute the numbers (4x10 Matrix) with these straight regular lines, you'll get a folding diagram of an approximated trigonal screw.
Step 3: The Folding Pattern
Print it at full size and cut the excessive part on the left and right side.
Step 4: Prefold the Lines
blue: mountain folds
red: valley folds
Step 5: Folding Preparation
Form the paper into a triangle by overlapping one column.
Step 6: N-closures
Then you fold the n-closures counter-clockwise, if you can fold the first, the rest of all is repetition.
Step 7: The Result
Then the screw should look like shown in the pictures and you are done!