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July 2014

39 participants
112 discussions

[math-fun] 'Impossible to draw a circle using only ruler and compasses': discuss
by Guy Haworth 01 Jul '14

01 Jul '14

We kicked the tyres on this one in the staff coffee room. Issues of Mathematics, Systems Engineering and Language were raised. Mathematically, a circle is a set of points, an abstract concept. It is possible to draw a diagram approximately (but not accurately) illustrating a circle but - for a start - the drawn circumference will have non-zero width and so is rather an illustration of an annulus than a circle. I have felt it necessary to indicate the difference between a 'model' and a diagram of that model in classes on Enterprise Architecture. The notation (if defined) can be changed in minor ways without changing the meaning. In Systems Engineering terms, as FL pointed out, one need other things to draw the circle physically rather than conceptually ... paper, table, (drawing agent) and pencil if it was not included with the compasses. Most people would forget the drawing agent ... but people are often a component of 'soft' systems. But then, if one hold up a picture of a circle to a class of children, they will say they see a circle. Formal language without overloaded words would make informal communication more difficult. Guy

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[math-fun] Siimple probability problem
by Bernie Cosell 01 Jul '14

01 Jul '14

It is now clear that I've lost essentially all of my math skills... sigh. My wife asked what seemed to me to be a simple problem but I couldn't see a way to approach it... I kept going down what felt like blind alleys that just got more complicated rather than leading toward a solution: You have a jar with N *each* of C colors of marbles [that is, you start with the same number of each color, N*C marbles in the jar]. You start removing marbles [without replacement]. What is the expected number of marbles you have to remove to have a 50% chance of having at least one of each color. Is there some easy/obvious way to approach/analyze this? THANKS! /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--

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