ellipse as a flat curve
- chris cambré
a locus is a geometric figure containing a set of points matching a specific condition. For example:
- the perpendicular bisecor of two points is the locus of the points at the same distance from two given points.
- the circle is the locus of twe points at the same distance from a given point.
- the bisector of two intersecting lines is the locus of the points at the sams distance from two given lines.
ellipse as a locus
Een ellips is the locus of a point which moves in a plane such that the sum of its distances from two given points (called foci) add up to a constant. This means you can draw an ellips with the help of a rope: Put down two stakes and loop a piee of rope around them. Pull the loop taut and mark the points aroud a curve.
The method is illustrated in the applet below.
- Drag the point F1 and define the distance between the two foci.
- Drag the point C and define the lenghts of the rope.
- Drag teh point Pand draw the ellipse.
This construction is called the gardener's method because it was used in Engelse gardens to mark flowerbeds. Architects and military ingeneers mention it in tractates. E.g. Ambroise Bachot mentions the methode in his book from 1598 on architecture, fortifications and weapons of war.