By Fritschze B.

Sophus Lie (1842-1899) was once the most vital mathematicians of the 19th century. His paintings on line-sphere transformation and the construction of the speculation of continuing teams and his program of those to different parts of arithmetic was once ground-breaking and has had a long-lasting impact at the extra improvement within the box. certainly, a brand new self-discipline of arithmetic often called Lie idea at the present time has resulted. This specified mathematician Sophus Lie summarized his lifestyles and paintings within the draft of an highbrow testimonial as follows.

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Cj = n − 61 write 48 n+5 n+5 + 10 + 8j, n − 1 − 24j − 20, + 4 + 8j, 3 3 n+5 n − 1 − 24j − 16, + 8 + 8j, n − 1 − 24j − 12, 3 n+5 n+5 + 6 + 8j, n − 1 − 24j − 8, − 1 + 8j, 3 3 n+5 n − 1 − 24j − 4, + 3 + 8j, n − 1 − 24j . 6 Wheels 47 Then the desired sequence is SS6 S9 . . S n−19 S n−10 T C n−61 . . C2 C1 D. ) 2. n ≡ 37 (mod 48), n ≥ 37. n−37 Write D = ( n+5 3 + 4), and for each j = 1, 2, . . , 48 define Cj = n+5 n+5 + 6 + 8j, n − 1 − 24j − 8, + 8j, 3 3 n+5 n − 1 − 24j − 4, + 4 + 8j, n − 1 − 24j, 3 n+5 n+5 + 2 + 8j, n − 1 − 24j + 4, − 5 + 8j, 3 3 n+5 n − 1 − 24j + 8, − 1 + 8j, n − 1 − 24j + 12 .

Avadayappan et al. [5] give the following simple construction for a super edgemagic labeling of a path. Say n = 2m or 2m+1. Label the vertices x1 , x2 , . . , x2m , preceded by x0 if n is odd. Vertices x1 , x3 , x5 , . . , x2n−1 receive labels 1, 2, 3, . . , n, while even vertices (x0 , x2 , x4 , . . , x2n when n is odd, x2 , x4 , x6 , . . , x2n in the even case) receive n+1, n+2, . . in order. When this labeling is completed in the obvious way, the magic sum is 12 (5n + 1) , the theoretical minimum.

14 1 Preliminaries λ(x)+λ(y) cannot equal λ(z)+λ(t). Thus, λ(x)−λ(z) = λ(t)−λ(y). Therefore the n2 differences between the labels of Kn are all different. If λ is any labeling of Kn , a ruler model of λ is constructed as follows. For each vertex of Kn , place a mark distance λ(x) from the start of the ruler. The ruler can be used to measure all distances corresponding to the distance between two marks. Ruler models are discussed, for example, in [14, 15]. The ruler models derived from edge-magic injections have the following special property.

### Sophus Lie: a sketch of his life and work by Fritschze B.

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