MOTION MOUNTAIN

thought and language 275
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F I G U R E 167 The only magic hexagon starting with the number
1 (up to reflections and rotations).
Challenge 279 s
Ref. 255
Challenge 280 d
Challenge 281 d
Page 230
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Everybody knows what amagicsquare is: a square array of numbers, in the simplest case
from 1 to 9, that are distributed in such a way that the sum of all rows, columns (and
possibly all diagonals) give the same sum. Can you write down the simplest3×3×3
magiccube?
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The digits 0 to 9 are found on keyboards in two different ways. Calculators and keyboardshave
the 7 at the top left, whereas telephones and automatic teller machines have
the digit 1 at the top left. The two standards, respectively by the International Standards
Organization (ISO) and by the International Telecommunication Union (ITU, formerly
CCITT), evolved separately and have never managed to merge.
Leonhard Euler in his notebooks sometimes wrote down equations like
Can this make sense?
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1+2 2 +2 4 +2 6 +2 8 +...=− 1 3 . (105)
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In the history of recreational mathematics, several people have independently found
the well-known magic hexagon shown in Figure 167. The first discoverer was, in 1887,
Ernst von Hasselberg.The hexagon is called magic because all lines add up to the same
number, 38. Hasselberg also proved the almost incredible result that no other magic
hexagon exists. Can you confirm this?
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In many flowers, numbers from theFibonacci series 1, 1, 2, 3, 5, 8, 13, 21 etc., appear.Figure174
gives a few examples. It is often suggested that this is a result of some deep sense
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net