Generate different patterns for border of a saree using letter
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Answer:
You are certainly
surprised to see this familiar proverb lying near the beginning, in
fact at the very root, of a mathematical book, aren’t you? Well, no
treatise on fate here, we are simply quoting it literally: if you are
moving ‘straight’ on the surface of a sphere or cylinder then you are
bound to return to the point where you started from, that’s all... This
is even more obvious to those who like to think about the structure
of our infinite universe in terms of space and time, but we are not
getting into that, either!
What we have in mind is very earthly indeed: when was the last
time you noticed a certain motif repeating itself around a vase or
belt or the margin (border) of a framed photo or ancient mosaic? If
you do not quite recall ever having noticed such details, you better
be prepared for a change after you go through this book! Such
repeating motifs, called border patterns, have been with us for a
very long time and, rather surprisingly at first, happen to be subject
to mathematical rules that are accessible and profound at the same
time. We investigate these rules and more with the help of many
examples that might even make this book seem like an art book to
you: indeed the worlds of art and mathematics are not disjoint!
Before going further, let us point out that infinity and repetition
do not always go together. You may recall for example that, while
some numbers with an infinite decimal portion have repeating digits
after some point (like 4.7217373... = 116,863/24,750), others (like
the most famous of all such numbers, π = 3.141592654...) come
with a very unpredictable sequence of digits. And, of course, while
repeating motifs abound in our finite world, infinite objects exist
only in our powerful imagination: indeed you will have to train