Local Ellipse  (2009-Sep-23 15:20 EDT)

by <>  (2010-Sep-03 7:42 EDT)

Good demonstration of principles. More description perhaps?

by <>  (2010-Sep-03 7:42 EDT)

Not sure of the intent. For me, there were too many user controls with uncertain impacts to the end drawing. So, not being sure of why you provided so many controls, I'll make a suggestion.

What comes to my mind when discussing an ellipse is that there are two foci, and a center point.

So, for user control, I could see

• moving the center
• Moving the foci closer/farther
• Changing the angle of the major axis -- rotation so to speak
• Clear

by <>  (2010-Sep-03 7:42 EDT)

jon, I wonder this comment was meant for my another ellipse one...

In any case, both of these are supposed to have zero "controls" except the "go" button, basically. In this one, you can type in parameters in the script. It is a kind of puzzle where you need to think that what it means to have cosine's derivative being (negative) sine and sine's derivative bing cosine.

For the other one, these yellow dots are not supposed to be moved by the user also... It "illustrates" (but not a proof) that the trace of such point is an ellipse.

The yellow does should probably better locked, I guess.

by <>  (2010-Sep-03 7:42 EDT)

Lovely, but the math behinde was too advanced for me. I can just draw ellipses with sine and cosine.

by <>  (2010-Sep-03 7:42 EDT)

Nevit,

hehe, yes, this one may appear a bit tricky, but it actually is not. I made another equivalent one and uploaded it to:

http://dev.laptop.org/~yoshiki/etoys/LocalEllipse2.002.pr

and also here at Showcase, which hopefully you can see. The real trick is that it is just a sum of two full circles.

by <>  (2010-Sep-03 7:42 EDT)

jon,

Actually, never mind about "sine" and "cosine" I mentioned above. A better illustration is described in the LocalEllipse2 project.

by <>  (2010-Sep-03 7:42 EDT)

one way to manually draw an ellipse to help prove some of these mathematics (grin):

1. Put two pins into board (the foci)


2. Create a loop of string big enough to go around the foci pins with plenty to spare


3. Place the string around the pins


4. Use a pencil on the inside of the string to pull it taut. The string should look like a triangle, with the three vertices: 2 pins and pencil


5. Keeping the string taut, trace the ellipse with the pencil as you sweep out a 360-degree path

by <>  (2010-Sep-03 7:42 EDT)

very clever

by <>  (2010-Sep-03 7:42 EDT)

This project is a nice illustration of an ellipse. To make it more powerful, I think adding an explanation of what was done as well as suggestions for manipulating the variables would help make it more powerful.