1. The values of Nn number of sides , Lnthe length of a single side , Pn the length of the perimeter and Anthe area of the snowflake for n=0,1,2,3, having the initial side length of 1 and knowing that n N 1.1 Table showing the values of Nn, Ln, Pn and An for n=0,1,2,3 n Nn Lnunit Pnunit An unit2 0 3*40=33333* 3 1 3*1=3 31/2/4 =0,4330127019 1 3*41=12 1*1/3=1/3 12*1/3=4 31/2/4+31/32*31/2/4=0,5773502692 2 3*42=48 1*1/32=0,1 48*0,1=5,3 31/2/4+31/32*31/2/4+ 3*4 1/34*31/2/4=0,6415002991 3 3*43=192 1*1/33=0,037 192*0,037=7,1 31/2/4+31/32*31/2/4+3*4 1/34*31/2/4+ +3*42 1/36*31/2/4=0,6700114235 Nnnumber of sides The change in the successive numbers of sides...
?é?í?é?ºsquare snowflake?é?í?é?¿ behaves similarly to the Kochtriangle snowflake Not only the general formulas are analogical, but also both have finite areas and infinite perimeters. Conclusion The Koch snowflake is probably of little significance to the science and there are probably no other essential applications of it to the reality , but probably it can be used to create some visual effects. The shapes of the snowflakes are quite incredible and that is why artists may make use of it. Moreover, the fact that it has a finite area but infinite perimeter makes it even more interesting for the mathematicians.
?é?í?é?ºsquare snowflake?é?í?é?¿ behaves similarly to the Kochtriangle snowflake Not only the general formulas are analogical, but also both have finite areas and infinite perimeters. Conclusion The Koch snowflake is probably of little significance to the science and there are probably no other essential applications of it to the reality , but probably it can be used to create some visual effects. The shapes of the snowflakes are quite incredible and that is why artists may make use of it. Moreover, the fact that it has a finite area but infinite perimeter makes it even more interesting for the mathematicians.
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