# becko

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Lepton
1. ## arc bisection

This construction uses the straightedge (to draw the line between two points at step 3 and to find the point of intersection of this line with AB at step 4). I need a construction that uses only the Euclidean compass, that doesn't transfer distances.
2. ## arc bisection

I saw the website. There's a construction for the middlepoint of the arc (http://www.cut-the-knot.org/do_you_know/compass7.shtml). But this construction uses the compass to transfer distances (when the circles with radius OE and centers at C and D are drawn; we cannot transfer the distance OE and use it as a radius to draw a circle around C or D). I've already convinced myself that by the use solely of a compass that transfers distances, you can accomplish all the constructions allowed by the use of straightedge and compass. My question is whether these constructions can be achieved by a compass that doesn't transfer distances (the classical Euclidean compass that brakes if lifted from the paper). I should make a small change in my previus description of the fundamental constructions allowed by the compass: To find the points of intersection of two circles. To draw a circle with given center passing through a given point. Now it is clear that this compass cannot be used to transfer distances. All I need is a valid construction of the arc bisector. If I have this construction, I can prove that all the constructions allowed by straightedge and compass can be done using the Euclidean compass alone.
3. ## arc bisection

In geometrical constructions using compass alone, we should restrict ourselves to two fundamental constructions: To find the points of intersection of two circles. To draw a circle with given center and radius. Can anyone tell me how to find the middlepoint of a given arc using only a compass?
4. ## help with a proof

I haven't had any advance. I'd appreciate any ideas. Maybe if we assume that one of the numbers is a perfect square, so that 4(a^2) + r(b) = k^2, where k is a positive integer, then as a consequence, 4(b^2) + r(a) shouldn't be a perfect square. Or if we assume that both numbers are perfect squares, we would surely arrive at some contradiction. I have tried to do both ways, but I have got nowhere. All I have are some crumpled papers with nothing valuable in them. Maybe someone can show me how to prove this?
5. ## help with a proof

I cannot find a way to prove this: A function r(n), where n is a positive integer, gives the number n with its digits inverted. Prove that for positives integers a and b, the two numbers 4(a^2) + r(b) and 4(b^2) + r(a) cannot be simultaneously perfect squares. Can anyone help me?
6. ## Physiology applied to Piano

I'm looking for information concerning the physiology of the hand adressed to piano performance. References to books, articles, web sites, etc, would be greatly appreciated.
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