Mere Bagatelle

Click to read general information about afghans

©Woolly Thoughts 2018         Contact Us         

Buy the pattern on the Order Form

or

Buy now

Other places to visit




Order Form

Mental Blocks

The World of Illusion Knitting


Buy a pattern

for this afghan

on the order form

Buy now


MERE BAGATELLE


Starting at brick number one, and always moving forwards, how many different paths can you take to reach the brick at the bottom?


The answer is on the brick : 924


This design is a section of Pascal's triangle turned through 45 degrees. If you turn it so that the number 924 is at the bottom then the number on each "brick" is the sum of the two numbers above it.


The mathematics of this design is related to the old-fashioned bagatelle games. Hence, the title.

Scroll down for more information about

Mere Bagatelle

Buy a pattern

for this afghan

on the order form

RELATED DESIGNS


NUMBER AFGHANS

Counting Pane

Double Base

Fibo-optic

Fibrenacci

Equal Parts

Some Square Over The Rainbow

CONSTRUCTION INFORMATION


Each brick is made separately in filet crochet.


The bricks are stitched or crocheted together.




CROCHET INFORMATION


Mere Bagatelle is made from 49 similar bricks, each in a different colour.


This is an ideal design for using up small amounts of left over

yarn.


Any type of yarn can be used but all the yarns should be of the same thickness to make regular sized bricks.

Mere Bagatelle is a representation of Pascal’s Triangle.


The American mathematician Martin Gardner said:

The pattern is so simple that a 10 year old can write it down, yet it contains such inexhaustable riches and links with so many seemingly unrelated aspects of mathematics, that it is surely one of the most elegant number arrays.


Although this pattern is named after Blaise Pascal (1623 - 1662) it was known in China around 1300 AD.


The diagram shows why it is called a triangle. The afghan design uses only the part shown in red. The numbers in the pattern are generated by adding two adjacent numbers together and writing the total underneath. It could be continued for ever.


The afghan design was inspired by a problem which involves counting the number of different ways it is possible to reach any given stone, starting with the 1 at the top and always moving forwards. The answers are those given in the triangle.


The numbers in the afghan are deliberately made difficult to read so that it is not immediately obvious that the answer is given in the puzzle.













1
























1

1






















1

2

1




















1

3

3

1


















1

4

6

4

1
















1

5

10

10

5

1














1

6

15

20

15

6

1












1

7

21

35

35

21

7

1










1

8

28

56

70

56

28

8

1








1

9

36

84

126

126

84

36

9

1






1

10

45

120

210

252

210

120

45

10

1




1

11

55

165

330

462

462

330

165

55

11

1


1

12

66

220

495

792

924

792

495

220

66

12

1