An approximated paper screw based on a N-Diagonal Matrix

Picture of 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.

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Step 1: Numeric Matrix

Picture of 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

Picture of 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

Picture of Prefold the lines

blue: mountain folds

red: valley folds

Step 5: Folding Preparation

Picture of Folding Preparation

Form the paper into a triangle by overlapping one column.

Step 6: N-closures

Picture of 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

Picture of The Result

Then the screw should look like shown in the pictures and you are done!

sphere360 (author) 1 year ago

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

tofugami1 year ago
So over my head but it came out beautifully.
sodasonic1 year ago
maths build our world