Strategies for drawing space curves?

  • Context: High School 
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    Curves Drawing Space
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Discussion Overview

The discussion focuses on strategies for drawing and conceptualizing space curves, particularly in the context of geometry and calculus courses. Participants share their challenges with artistic representation and seek resources to improve their understanding and skills.

Discussion Character

  • Exploratory, Conceptual clarification, Homework-related

Main Points Raised

  • One participant expresses difficulty in drawing space curves and requests strategies and videos to aid in conceptualization.
  • Another participant suggests using programming tools like Maple and Mathematica as potential aids for drawing space curves.
  • A different participant emphasizes the importance of manual drawing in educational settings, comparing it to perspective drawing without vanishing points, and provides a basic method for representing three-dimensional points using axes.
  • Several participants share links to videos that may serve as helpful resources for learning about space curves.
  • A later reply clarifies a desire for instructions on plotting and conceptualizing space and vector curves specifically, rather than just points.

Areas of Agreement / Disagreement

Participants generally agree on the need for strategies and resources to improve the drawing of space curves, but there are varying opinions on the best methods and tools to use. The discussion remains open without a consensus on a single approach.

Contextual Notes

Some limitations include the potential inadequacy of written descriptions for conveying drawing techniques, as well as the varying levels of familiarity with mathematical concepts among participants.

vanceEE
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What are some helpful strategies for drawing and conceptualizing space curves? I'm having trouble drawing them and I'm not very artistic! Also, please provide helpful videos on this topic if you can.
Thanks.
 
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Programming, maple, mathematica, stuff like that.
 
vanceEE said:
What are some helpful strategies for drawing and conceptualizing space curves? I'm having trouble drawing them and I'm not very artistic! Also, please provide helpful videos on this topic if you can.
Thanks.

Drawing these manually is supposed to be part of instruction. This will/must/should occur in Geometry and in Calculus 2 and Calculus 3. This is much like perspective drawing, but without forming Vanishing Points.(Maybe the response is inadequate. Difficult to describe through writing on the forum how to do these drawings).If it helps, start with an origin point, draw an axis upward called z, draw an axis to the right called y, draw an axis diagonally downward toward the left and call it x... not sure if these are right since so long ago that I did these. You can represent three-D points and using drawn guidelines in the axis planes.
 
Last edited:
symbolipoint said:
A search yielded these, which should be a very good beginning:

http://youtu.be/IBDiWlXJcUk

http://youtu.be/DI7ofaEgyTQ

Hi, these we're very helpful, but I'm looking for instructions on plotting and conceptualizing space and vector curves rather than single points e.g. ##r(t) = <f(t),g(t),h(t)>##

Thanks.
 

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