2020 IB Extended Essays

2. Fill in the unshaded cells above according to the rule demonstrated in this following example: Rule for Magic Table 0 1 2 ⋯ + 0 + ( + 0 ) 1 + 0 + { + ( + 0 ) 1 } 2 ⋯ + 0 + ( + 0 ) 1 + 0 + { + ( + 0 ) 1 } 2 ⋯ Continuing with the example of Magic Table for √ 7 , Magic Table for √ 7 : 2 1 1 1 4 1 1 1 4

1 ⋯ 127 590 717 ⋯ 223 271 ⋯ ⋯ ⋯ 48

0

1

2

3

5

8

37

45

82

1

0

1

1

2

3

14

17

31

3. Fill the fourth, fifth, and sixth cell down the first column with the equations and 2 − 7 2 , where the and can be described each as the numbers in the k th column of second and third rows of the unshaded portion of Magic Table for √ 7 ; { 0 , 1 , 2 , 3 , 4 , ⋯ } = {2, 3, 5, 8, 37, ⋯ } and { 0 , 1 , 2 , 3 , 4 , ⋯ } = {1, 1, 2, 3, 14, ⋯ } . Then, fill in the lightly shaded cells according to the two unshaded numbers above them and the equation of the row they belongs to. Continuing with the example of Magic Table for √ 7 ,

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