Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I can draw a circle using a compass.

I can draw an ellipse using two focal points and a loop of string.

I think that you can draw an arbitrary conic with a "generalized" compass for which the pencil can slide in and out as it is rotated.

What instruments and devices can draw elliptic curves?

share|cite|improve this question
Computers...... – Graphth Apr 21 '11 at 14:57
I wonder why people are upvoting this facetious answer.. – quanta Apr 21 '11 at 15:38
Elliptic curves such as $y^2=x^3-x$ have two components. Could a device plot both components? – lhf Apr 21 '11 at 17:28
up vote 3 down vote accepted

I have an answer, for a limited case, and it is not pretty. Elliptic curves have the form:

$y^2= x^3 + ax +b$

Suppose $b=0$ and $a < 0$

$y^2= x(x^2 + a)$

$y= \sqrt{x}\sqrt{x^2 + a}$

You can construct $\sqrt{x}$ as shown here.

enter image description here

And, $\sqrt{x^2 + a}$ with $a < 0$ is the distance from (x, -a) to the origin.

We have two constructible lengths so just construct their product:

enter image description here

...and you have y.

share|cite|improve this answer
That's quite neat but am I right in thinking it only lets us construct a single point at a time rather than tracing out part of the curve? – quanta Apr 21 '11 at 17:22
Yes. This would be quite tedious. Though, there may be some way of streamlining it. The constructions have so many similarities. I've added some images to show this. – futurebird Apr 21 '11 at 17:26

This thesis looks like it may be of considerable interest.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.