The Strange Case of the Magic Hat

Sometimes traditional paperfolding designs live their life in the full blaze of the sun, but sometimes they only emerge occasionally from the shadows. The Magic Hat has lived mostly in the shade, which is a shame, as it is a very unusual and interesting design. It was first published as an aid to mathematics teaching, then was largely forgotten for many years, until it reappeared in 2001 attributed, presumably through a misunderstanding, to a modern Czech paperfolder. The front and back of the Magic Hat are shown below.

You can make a Magic Hat from A4 or US letter paper, or any similar rectangle. And you should. The folding sequence is almost totally unlike any other sequence you will have folded, and the finished Magic Hat emerges from this folding sequence in an unexpected way. If you open out the design before you fold up the brim it looks very much like a paper cone, though a much more robust cone than the quickly-rolled-up kind that was once frequently used by Grocers. It seems quite possible therefore that the Magic Hat was originally used as a paper cone before somebody turned it into a hat (although there is no evidence to prove that this conjecture is true.)

As far as I know, the Magic Hat is first mentioned in France in 1891, as ‘Bonnet de Magicien’, in the 1891 'Bulletin de la Societe de Protection des Apprentis'.

The first, rather unclear, diagrams appear a year later in a French school textbook 'Le Travail Manuel a L'ecole Primaire'.

In 1903 the design appears in Spain, as 'Bonnete de Magico', in another school textbook, 'La Ensenanza del Trabajo Manuel' by Pedro de Alcántara García and Teodosio Leal y Quiroga. You may like to try to make the Magic Hat from the diagrams in their book, which I reproduce below. (If you find these diagrams insufficient, there are much clearer diagrams further down this page.)

After 1903 the Magic Hat disappears from sight. It seems largely to have been forgotten. The next mention I can find of it is as 'le bonnet d'eveque et le gobelet' (Bishop's Hat and Cup) in 'Occupons nos doigts' by Raymond Richard which was published in 1950, (after a gap of 47 years) and the next after that is, somewhat surprisingly, in the OrigamiUSA 2001 Convention Book (after a gap of 51) where it is attributed to the Czech paperfolder, Milada Blahova.

In 2014, the design then appears, with the same attribution, in the Origami Page-a-Day Calendar edited by Margaret van Sicklen, drawn in her usual wonderfully clear style.

I have not managed to trace or contact Milada Blahova, but, if I could, it would be interesting to learn how she came to know this traditional design when everyone else seems to have entirely forgotten its existence.

Notes

I am indebted to Michel Grand for pointing me at the early French publications mentioned above.

Everything I know about the Magic Hat is recorded here. If you have any other information about it, please let me know.

The text of 'La Ensenanza del Trabajo Manuel' suggests the use of the flattened hat as an isosceles tile. Teachers might note that the kite shape shown in Fig 31 can also be used in this way.