Draw parabola using these materials

[SAZAR]

You have a flat wooden surface, some rope, some nails and a pencil - how do you draw parabola using just that?

 

[Fenn]

There's a nice picture at http://en.wikipedia.org/wiki/Parabola#Other_geometric_definitions that can give a hint to this.

Notice how the distance from the focus to any point equals the perpendicular distance from the directrix to that point?

 

[SAZAR]

There's a nice picture at http://en.wikipedia.org/wiki/Parabola#Other_geometric_definitions that can give a hint to this.

Notice how the distance from the focus to any point equals the perpendicular distance from the directrix to that point?

Yea', but you have just a flat wooden surface, some rope, some nails (and a hammer or rock or anything to nail them to the board, right...) and a pencil; you don't have an instrument to measure 90 degrees from directrix.

I mean - it's easy to draw a circle or its section with those materials - you just nail one to the board and tie a rope to it and pencil on the other end - and just draw it... drawing an ellipse is easy as well - you just put two nails, loop the rope and pull it with pencil to draw it as the rope allows no further pull.

With parabola it's not the same - the length changes and you need to measure stuff - that avoids the essence of "stick-and-rope" principle I coconut :) on here...

--------
Also: when you take a paper strip, put it on the flat surface (table), and contract it so it stands up - is it parabola or something else?

 

[SAZAR]

There's a nice picture at http://en.wikipedia.org/wiki/Parabola#Other_geometric_definitions that can give a hint to this.

Notice how the distance from the focus to any point equals the perpendicular distance from the directrix to that point?

OK, shortly: no right angle tool, just those materials I said. How now... then?

 

[Gib Z]

It's actually quite simple. Hammer in a nail, tie on the rope to a length that it just touches an edge of the table, draw out a circle from that. The line connecting the edge of the table and the nail will be perpendicular to the edge of the table.

 

[SAZAR]

AHAAA - but in that case the line has to move across the length of the edge of the board.
Interactive java applet (at the bottom of the page; pick the red dot and move it left-right):
http://www.ies.co.jp/math/java/conics/draw_parabola/draw_parabola.html

I'm wondering, on the other hand, how to draw it without rightangle tool - just by materials I described (nails, rope, pencil, board).

 

[berkeman]

You have a flat wooden surface, some rope, some nails and a pencil - how do you draw parabola using just that?

Those tools are basically equivalent to having a straightedge and a compass. I googled Draw Parabola, and got lots of hits. Here's one of the first ones on the list:

http://mysite.du.edu/~jcalvert/math/parabola.htm

.

 

[SAZAR]

OK. It can't be done.
...

 

[berkeman]

OK. It can't be done.
...

Maybe you can't do it. Heck, you can do it with just the board, a pencil,and a nail. Oh, and an assistant.

Quiz Question -- how?

 

[berkeman]

Hah!

I just got rid of the nail. And the assistant. Just me, the board and the pencil. Very accurate parabola, too!

 

[SAZAR]

Hah!

I just got rid of the nail. And the assistant. Just me, the board and the pencil. Very accurate parabola, too!

...What? ...You placed the board vertically, climbed at a height of about 4 meters holding a pencil to your right, and jumped with the board close to your side, so when you fell on your 455 and bounced a bit the pencil left the trail of your bouncing on the board?

====
(Just joking.
Don't get me
serious now.
Had an idea,
laughed and
had to
write it... )

 

[berkeman]

...What? ...You placed the board vertically, climbed at a height of about 4 meters holding a pencil to your right, and jumped with the board close to your side, so when you fell on your 455 and bounced a bit the pencil left the trail of your bouncing on the board?

Not exactly, but you get the idea!

 

[SAZAR]

...Yeah, I almost forgot - what about this question of mine (already asked up there):

When you take a paper strip, put it on the flat surface (table), and contract it so it stands up - is it parabola or something else?

 

[michelek]

Btw, I have done it. I even managed to carve something similar to parabolic surface out of rotating wood block with knife attached to ropes and desk and no right angle or thowing myself off the roof.




just bragging.




or am I?

 

[MrNerd]

Try using the string as a measuring tool. Set one piece of it as 1 unit, and try to calculate the y parts from the x. For example, try y = x^2. At x = 1, y = 1. At x = 2, y = 4. You get the idea. Then just play connect the dots with a curved line drawn by hand. I believe it was mentioned earlier as to how to get a perpendicular line.

 

[MrNerd]

Here's something I found with bing:

http://www.public.asu.edu/~aaafp/parabolastring/paperfolding.html

 

[MrNerd]

Fooey! Another old thread! Look at the date on the post before the post above my first one.

 

[michelek]

Old is new "new".
And that intriguing question still unanswered just begs for one.