Erlebnisland Mathematik | Technische Sammlungen Dresden | Junghanstraße 1-3 | 01277 Dresden
Erlebnisland Mathematik

Yamātārājabhānasalagā

On the plenum rim you find a special sequence of zeros and ones made of wood. Choose an arbitrary sequence of six zeroes and ones, e.g., 100110. Search for this sequence on top of the plenum rim. Do you find it more than once? The wooden zero-one-sequence is an example of a so-called de Bruijn sequence.

The Sanskrit mnemonic Yamātārājabhānasalagā, also encodes a de Bruijn sequence, because it contains each possible sequence of three long or short vowels ā and a exactly once:

a ā ā,   ā ā ā,   ā ā a,   ā a ā,   a ā a,   ā a a,   a a a,   a a ā.
On the reverse side of the plenum it is explained how this particular sequence is structured.

Explore the digits on the plenum rim!

Stand behind the plenum. Place your hands on two of the wooden digits. Do it in such a way that precisely four digits between them remain uncovered. Check which digit is under your left hand. You can use it to predict the digit which you reach when you move your right hand one digit to the right. If your left hand rests on a One, the number under your right hand will change when you move it to the right. If it rests on a Zero, the number under your right hand will remain the same. Now move your left hand too, so that again there are four uncovered digits between your hands. You can apply the same rule repeatedly. It explains the whole sequence except for the last digit.

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