S6, with 720 elements, is the only finite symmetric group which has an outer automorphism. This automorphism allows us to construct a number of exceptional mathematical objects such as the S(5,6,12) Steiner system, the projective plane of order 4 and the Hoffman-Singleton graph. A closely related result is the following theorem: 6 is the only natural number n for which there is a construction of n isomorphic objects on an n-set A, invariant under all permutations of A, but not naturally in one-to-one correspondence with the elements of A. This can also be expressed category theoretically: consider the category whose objects are the n element sets and whose arrows are the bijections between the sets. This category has a non-trivial functor to itself only for n = 6.
Those that really like to color are going to be looking for printable coloring pages all over the place so that they don't have to drive all over creation looking for that special coloring book. If you and/or your kids really like SpongeBob Squarepants, you will like looking for SpongeBob coloring pages so that you can make your own custom-made coloring book or books from SpongeBob printable coloring pages. Are you aware that there are a good many adults that really love to sit down and color when they have a few moments to simply sit down and relax? This is something that you might not be aware of, but really need to think about because it happens every day somewhere in this big world of ours.
Coloring alongside children can be inspiring. How about inviting a friend or two over for tea and some coloring time? And for any artists who are feeling a bit burnt out working in their usual medium, why not use coloring as a way to rejuvenate your creativity?
The question is would a child really benefit from spending time coloring in outlines of pictures created by someone else? You can find the answer by thinking of the benefits kids get from colouring in. When a child visits an online coloring page and begins to indulge in the activities there, they learn to appreciate the value of taking their time to ensure that they do a good job. They also teach them to take pride in what they do and know they did their best.
Studies and researches have shown that initial five years of a child are the most critical ones from the point of view of learning. Their capacity to learn new things is at its highest ebb during this period. Children of this age group can be compared to a piece of sponge that is ready to absorb any liquid that it comes across. These are the building years for children and we need to use this period for giving them rock solid foundation that can help them in building their mansion of life upon it in a way that it becomes an example for everyone else to follow. Parents do everything possible and within their reach to give their child a solid foundation. They try to give their child the right kind of environment and facilities so that their talent and abilities bloom in a nice way. Coloring pages can play an important role in letting children grow in the right way. These pages are usually used by parents and teachers to make the child aware of alphabets, animals, monuments, vegetables, fruits, numbers, etc.