Replying to LO27734 --
Dear Winfried,
Thank you for your enlarging imagination - 'translating' multiplication
into surface areas.
> Comparing the different effect of multiplication and addition as you did
> reminds me of a figure in the plane, let's say a rectangle. While the
> circumference keeps the same (addition of the sides) for instance by a
> piece of thread, the face increases from 0 (the thread taken half) to a
> maximum when the rectangle becomes a square (multiplication of two sides).
> The face can still be increased with this thread and reaches its absolute
> maximum at a circle. You may say infinite infinitesimal parts are
> balanced. Well, the circle is a powerful symbol for wholeness is it not?
You seem to be a 'Lord of the Rings' (I was not thinking of the nearby
Olympic Wintergames :-)
> Now I try to think deeper into it. What does "balanced" mean? It is not
> just a matter of the parts. The parts need a special configuration in
> space, so that this space forms a context for the parts AND VICE VERSA:
> the space does become only context for the parts if the parts are present.
> And together they form a structure, more complex than just a plane without
> the circle. This is only words, so take a minute to create what I have
> written in your imagination: Look at a wall or your desk (if it is
> sufficiently tidy :-) and realize the plane there is. Then focus on just
> one point, stretch it to a line, open this line to a rectangle until it
> becomes a square, finally allow this square to form a circle.
Your description of imigination, growing spots to lines, rectangles to
circles is realy nice. Last night it was for me the perfect method to find
a world of dreams :-)
Winfried, do you know the Danish artist/mathematician Piet Hein (not to be
confused with the Dutch hero on the world seas of the 17th century)? This
Danish Hein has calculated the forms when in the formula of the circle the
quadrates are changed into numbers between 1 and 2. The circle slowly
changes (while gradually decreasing the 2 of the quadrates) into a
square-shaped figure, but with rounded corners. It becomes more and more a
square, when the mathematical powers approach the 1. You may have a look
at: http://mathworld.wolfram.com/Superellipse.html
and you may like it. This is anyway an interesting field - changing the
powers in a mathematical formula. It goes precisely into your thought
directions: changing dimensions from 0 to 1 to 2 and maybe further. But
now think also of the 0.6th or 2.3rd dimension!? (indications of
smoothness and roughness)
dr. Leo D. Minnigh
l.d.minnigh@library.tudelft.nl
Library Technical University Delft
PO BOX 98, 2600 MG Delft, The Netherlands
Tel.: 31 15 2782226
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Let your thoughts meander towards a sea of ideas.
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--Leo Minnigh <l.d.minnigh@library.tudelft.nl>
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