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Re: tangents and their respective equations

• To: mathgroup at smc.vnet.net
• Subject: [mg31878] Re: tangents and their respective equations
• From: atelesforos at hotmail.com (Orestis Vantzos)
• Date: Sun, 9 Dec 2001 06:07:01 -0500 (EST)
• References: <9uq8lp$ae2$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

This is absurd from a mathematical point of view; the tangent just
doesn't pack that much information about the curve that produced it!
It's like giving me the value of a polynomial at x=0 and asking for me
to find(guess?) the polynomial..
However:
a) If you are referring at a specific family of curves (eg. all
parabolas) there could be a solution, although you would probably need
to provide tangents through more than one points.
b) If you provide a whole family of tangents, then there might be a
curve that is tangent to all of them at some point. This is an
interesting geometrical problem, that pops up in Differential Equation
theory as well.
To sum up, the problem, as stated, is meaningless. There are
variations that are valid though.
Orestis