What Shape Emerges from Plotting These Complex Parametric Equations?

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Homework Statement



Plot the following parametric curve, de fined by the following two polynomials, on the interval: [itex]t \in (-1;1)[/itex]. What shape do you get?
[itex] x(t) = 16243t^{14} + 520143t^{13} -798515t^{12} -185877t^{11} + 150142t^{10} + 256559t^9 -135331t^8 -170995t^7 + 594415t^6 + 558842t^5 -111145t^4 -807101t^3 + 43763t^2 + 481059t + 341[/itex]
[itex] y(t) = -319484t^{14} -543356t^{13} + 127242t^{12} -159791t^{11} -208212t^{10} + 276926t^9 + 174816t^8 -345549t^7 -772343t^6 + 170296t^5 + 165817t^4 -343333t^3 -147652t^2 + 14574t -120[/itex]

Homework Equations



N/A

The Attempt at a Solution



Plotted both in maple and excel (couldnt get them to work in mathematica/wolfram alpha) i get a completely meaningless shape, or have i gone shape blind?

excel
34sgd9c.jpg


maple
34rdhjc.jpg
 
on Phys.org
I guess i am going to have to go with something along those very lines...

Just thought i might be doing something wrong and should actually be getting a flower or something... but i guess not
 
Actually, your polynomials look as if they are supposed to interpolate a set of points.
So I would suspect you made a mistake with a plus or minus sign or something.

One tiny mistake will destroy the rose! :wink:
 
I do believe they are attempting to interpolate something (thats the end case of the project, to create a Lagrange interpolating polynomial for our signature) but I've copied them straight out of the pdf that has the questions in it so what you see is what I've got in front of me... ill just have to find out from the lecturer
 
ah ha...

lecturer posted the correct formulas:

[itex]x(t) := 16243.t^{14} + 52014.3t^{13} - 79851.5t^{12} - 185877.t^{11} + 150142.t^{10} + 256559.t^9 - 135331.t^8 - 170995.t^7 + 59441.5t^6 + 55884.2t^5 - 11114.5t^4 - 8071.01t^3 + 437.63t^2 + 481.059t + 341[/itex]

[itex]y(t) := -31948.4t^{14} - 5433.56t^{13} + 127242.t^{12} - 1597.91t^{11} - 208212.t^{10} + 27692.6t^9 + 174816.t^8 - 34554.9t^7 - 77234.3t^6 + 17029.6t^5 + 16581.7t^4 - 3433.33t^3 - 1476.52t^2 + 145.74t - 120[/itex]

does indeed interpolate a flower
 
LCKurtz said:
flower.jpg

Indeed... 'tis said flower