# An Approximated Paper Screw Based on a N-Diagonal Matrix

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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.

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## 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!

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## 3 Discussions

Maths is for me not only science, I'm convinced that most of the famous mathematicians are also artists.

So over my head but it came out beautifully.