What Shape Emerges from Plotting These Complex Parametric Equations?

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Homework Help Overview

The discussion revolves around plotting complex parametric equations defined by two polynomials over the interval t ∈ (-1, 1). Participants are exploring the shape that emerges from these equations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss their attempts to plot the equations using various software, noting difficulties in obtaining meaningful shapes. Questions arise about potential errors in the polynomial coefficients and their implications for the expected output.

Discussion Status

The conversation has evolved with some participants expressing confusion over the shapes produced, while others suggest that errors in the equations may be the cause. A participant later shares corrected formulas, leading to a more positive interpretation of the expected output.

Contextual Notes

There is mention of the original equations being copied from a PDF, and a need to verify with a lecturer, indicating potential constraints in the accuracy of the provided information.

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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
 
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No, you haven't gone blind. I guess I would answer the question about what shape you get by saying "I get this shape right here in this picture.":rolleyes:
 
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
 
Nice! :smile:

(Do you have a picture?)
 
flower.jpg
 
Nice flower LCKurtz! :smile:
 
  • #10
LCKurtz said:
flower.jpg

Indeed... 'tis said flower
 

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