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Mathematics in our World
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                        A five-fold symmetry is found in the               Snowflakes have six-fold symmetry; each

                                                             l
                                                              a
                 echinoderms,     the    group    which            ke's structure forms a record of the varying
                                                             f
                                                             c
                                                              o
                 includes      starfish     (dihedral-D5                itions during its crystallization, with nearly
                                                                d
                                                               n
                 symmetry),  sea  urchins, and  sea  lilies   the same pattern of growth on each of its six
                 (dihedral-D5     symmetry).     Radial      arms.  Generally,  crystals  have  a  variety  of
                 symmetry  suits  organisms  like  sea       symmetries and crystal habits; some are cubic
                 anemones  whose  adults  do  not  move      or octahedral.
                 and jellyfish (dihedral-D4 symmetry).









                                   Starfish                            Sea Lilies





                                                                                        Snowflakes



                                  Jellyfish                         Sea Anemone      B. Fractals


                        Radial symmetry is also evident in
                                                                    Fractal is curve or geometric figure, each
                 different kinds of fruits
                                                             part  of  which  has  the  same  statistical

                                                             character as the whole. It is a class of highly

                                                             irregular  shapes  that  are  related  to

                                                             continents, coastlines, and snowflakes.

                                                                    It  is  use  to  model  structures  in  which

                                                             similar patterns recur at progressively smaller
                                   Apple                                Melon
                                                             scales,  and  in  describing  partly  random  or

                                                             chaotic  phenomena  such  as  crystal  growth,

                                                             fluid   turbulence,   lightning   and   galaxy

                                                             formation.


                                   Kiwi                                Orange









                ZANNIE I. GAMUYAO, MSM                              UNIT 1.3 Patterns and Regularities
                Assistant Professor 1                                             in the World
                Department of Arts and Sciences
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