Henry Ernest Dudeney/Modern Puzzles/126 - Drawing an Oval

Modern Puzzles by Henry Ernest Dudeney: $126$

Drawing an Oval

It is well-known that you can draw an ellipse by sticking two pins into the paper, enclosing them with a loop of thread,

and keeping the loop taut, running a pencil all the way round till you get back to the starting point.

Suppose you want an ellipse with a given major axis and minor axis.

How do you arrange the position of the pins, and what would be the length of the thread?

Dudeney's original article was unnecessarily prolix.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $126$. -- Drawing an Oval
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Plane Geometry Puzzles: $304$. Drawing an Ellipse