Mathematics and Origami

AC x

256

1

256

1

64

1

16

1

4

1

́ ́= − + − +

The latter expression gives us the formation law of AC j that is just the wanted limit of
x:

ACj 2 4 6 8 8 x

2

1

2

1

2

1

2

1

2

1

= − + − +

summing up

2 ACj=
2

1

4 6 8 10 10 x

2

1

2

1

2

1

2

1

2

1

− + − +

2 ACj 2 8 x 10 10 x

2

1

2

1

2

1

2

1

2

1

(^1)  = + − +






• When n folds have been produced (n→∞), the three last terms of the 2d member tend
  to zero. Thus:
  
  
  
  
  
  


• 
  

  2
  2
  1
  1 Lim 2
  2
  1
  x= ; Lim
  5
  1
  4 5
  4

  
  

  ×
  x=
  n→∞
  The two preceding examples do not serve to generalise the method. In fact, Fujimoto
  designed a second method that is also rather complicate. The reader can realise that folding
  possibilities are infinite in practice: to alternate the starting from A or B; to repeat more times
  from one extremity than from the other; to play with simple, double, triple, etc. folds, and so
  on.
  Binary numeration solves all difficulties associated to the division in equal parts.
  Interlude