MATHEMATICS AND ORIGAMI

Mathematics and Origami

The succession of zeros and ones defines the folding sequence that was not so clear in
Fujimoto ́s method. That is gathered in the figures to follow.
The procedure is this: fold the end A over the last fold when there is a correspondence
with a 0 , and end B, also over the last fold produced, if there is correspondence with an 1.

1. Fold the strip by half to get 0 , 5
   2

1

AC= =

2. and successive: assign zeros and ones as seen.

A over C to get 0 , 25

4

1

AD= =

3. A ,, D ,, 0 , 125
   8

1

AE= =

4. B ,, E ,, () 0 , 4375
   16

1

2

1

1

2

1

BF= −AE = − =

5. A ,, F ,, () 0 , 28125
   32

1

4

1

2

1

1

2

1

AG= −BF = − + =

6. A ,, G ,, 0 , 140625
   64

1

8

1

4

1

2

1

AH= AG= − + =

7. B ,, H ,, () 0 , 4296875
   128

1

16

1

8

1

2

1

1

2

1

BI= −AH = − + − =

8. A ,, I ,, () 0 , 2851562
   256

1

32

1

16

1

4

1

2

1

1

2

1

AJ= −BI = − + − + =

9. A ,, J ,, 0 , 1425781
   512

1

64

1

32

1

8

1

4

1

2

1

AK= AJ= − + − + =

10. B ,, K ,, () 0 , 4287109
    1024

1

128

1

64

1

16

1

8

1

2

1

1

2

1

BL= −AK = − + − + − =

11. A ,, L ,, () 0 , 2856445
    2048

1

256

1

128

1

32

1

16

1

4

1

2

1

1

2

1

AM= −BL = − + − + − + =

12. A ,, M ,, 2 2 2 2 2 2 2 0 , 1428222
    2

(^123568912)
AN= AM= − − − + − − − + − − − + − =
0,1428571

• 0,125
  0,0178571


• 0,015625
  0,0022321


• 0,001953125
  0,000278975 0,001001001

0,001001

0,001

2

2

2

2

(2

(2

(2

• 3
  
  
  • 6
  
  
  
  


• 9

0

• 1
  
  
  • 2
  
  
  • 3
  
  
  
  

)

)

)^1

..............^7