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Topic: Help with a construction
Replies: 3   Last Post: Nov 24, 1997 4:48 PM

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Michael Thwaites

Posts: 22
Registered: 12/6/04
Re: Help with a construction
Posted: Nov 11, 1997 5:36 PM
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Gilles -

Without giving it away - there are a couple of approaches I'd try. I'm
leaving the details out on purpose so you still have work to do.

1) You can create a pair of similar triangles. One with two sides of 1 and
X and the other with the corresponding sides of X and X-squared.

2) You can use the theorem that says two intersecting cords (AB and CD) of
a circle cut each other (say at E) so that the product of the parts are the
same (AE * EB = CE * ED). If you choose your cords to be perpendicular and
the parts to be convenient values (AE=1, CE = ED = X) you can construct the
circle and construct EB = X-squared).

At 4:54 PM -0500 11/11/97, Gilles G. Jobin wrote:
>Please excuse my very poor English.
>
>My question might be trivial for many of you, but I really need to
>know how to construct a segment measuring the square of the length of
>a given segment, using only Euclid's tools.
>
>Thank you,
>
>Gilles Jobin




Michael Thwaites <Michael.Thwaites@ucop.edu>






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