What Shape Emerges from Plotting These Complex Parametric Equations?

In summary: I have for this section.In summary, the parametric curve plotted in excel and maple is a meaningless shape.
  • #1
evo_vil
10
0

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
 
Physics news on Phys.org
  • #2
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:
 
  • #3
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
 
  • #4
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:
 
  • #5
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
 
  • #6
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
 
  • #7
Nice! :smile:

(Do you have a picture?)
 
  • #9
Nice flower LCKurtz! :smile:
 
  • #10
LCKurtz said:
flower.jpg

Indeed... 'tis said flower
 

FAQ: What Shape Emerges from Plotting These Complex Parametric Equations?

What is Numerical Analysis?

Numerical Analysis is a branch of mathematics that deals with the development, analysis, and implementation of algorithms for solving mathematical problems.

What are some common applications of Numerical Analysis?

Numerical Analysis is used in a wide range of fields, including engineering, physics, economics, and computer science. Some common applications include solving differential equations, finding roots of equations, and optimizing functions.

What are the main goals of Numerical Analysis?

The main goals of Numerical Analysis are to develop efficient algorithms for solving mathematical problems, analyze the accuracy and stability of these algorithms, and implement them in a practical and efficient way.

What are the main challenges in Numerical Analysis?

One of the main challenges in Numerical Analysis is dealing with errors and approximations that arise from using numerical methods instead of exact calculations. Other challenges include selecting appropriate algorithms for specific problems and optimizing their efficiency.

What skills are necessary for a successful career in Numerical Analysis?

A successful career in Numerical Analysis requires a strong background in mathematics, as well as knowledge of programming and computer science. It is also important to have critical thinking and problem-solving skills, as well as the ability to communicate and collaborate with others.

Back
Top