A paperfolding paradise
The website of writer and paperfolding designer David Mitchell
|Making Accurate Right Angles by Folding Paper|
page attempts to record what is known about the origin
and history of methods of making accurate right angles
without using compasses. Please contact me if you know
any of this information is incorrect or if you have any
other information that should be added. Thank you.
The first mention of a method of making an accurate right angle by folding paper occurs in the manucript 'De Viribus Quantitatis' by Luca Pacioli which was written in or around 1502. I have not been able to access the original document or an English translation and this information is based on the dissertation 'Luca Pacioli and his 1500 book De Viribus Quantitatis' (which can be found at http://repositorio.ul.pt/bitstream/10451/18435/1/ulfc113829_tm_Tiago_Hirth.pdf).
The method given in the ms is to fold a sheet of paper in half in one direction and then in half again in the opposite direction in the way shown in the original illustration below.
Pacioli does not mention it, but this method does not rely on the edges of the unfolded sheet of paper being parallel.
The same idea can be found in the second volume of 'La Science Amusante' by Tom Tit (real name Arthur Good), which was published in Paris by Librairie Larousse in 1892.
Two further methods can be found in 'La Recreation En Famille' by Tom Tit, which was published in Paris in 1903 by Librairie Armand Colin.