Re: How could you multiply and/or divide using straightedge and compass only?
- From: riderofgiraffes <mathforum.org_am@xxxxxxxxxxxxxx>
- Date: Tue, 09 Dec 2008 05:41:11 EST
How could you multiply and/or divide using
straightedge and compass only?
You can certainly do this for special cases.
... I don't know of any general way of doing
it for any cases
Consider the length AB that you wish to divide into
n equal segments.
You'll need to draw a sketch as we go.
Construct a line AC at an arbitrary angle to AB,
not equal to 0 or pi. (around 45 degrees is good)
Set your compass to some arbitrary length >0
(around 1/n of the length AB is good, but not
essential. Anything will do.) and mark off n new
equally spaced points D0=A, D1, D2, D3, ... Dn
along AC. (Yes, that's n+1 points, but I'm not
counting D0 as a new point because we already had
it.
Join Dn to B.
From each point Di replicate the angle A.Dn.B, givingpoints Ai on AB such that angle(A.Di.Ai) = angle(A.Dn,B)
The points Ai divide AB into n equal segments.
As stated in other posts, to "divide" a length by
a given *length*, not a number, you need to know what
number that length represents, so you need a concept
of a unit length. I think, however, this is beyond
what the OP was asking.
.
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