A well-meaning senior citizen once erroneously contended that a "perfect oval" could only be constructed with a straight edge and a pair of compasses.

The theoretical construction that he described so very closely approximates the ellipse given by the equation: (x^2)/16 + (y^2)/9 = 1.

Required:
1. Emulate such a construction
2. Suggest the difference in area of these two entities if this construction and an ellipse representing the above equation are drawn at the same scale (let them share a common major radial length).

To my knowledge, oval and ellipse refer to the same thing, ellipse being the 'technical' term.

Firstly, only Bractals accepted the public challenge of this.

Secondly, Bractals made more use of the straight edge than in the method which I was shown.

Thirdly, always know that someone can 'build a better mousetrap'; had I known Bractal's method was possible I would have removed the straight edge from the concept (see the solution for how that might work).

Fourthly, I have made a comparision of our two methods; I had some initial difficulty in trying to visualise Bractal's perpendicular bisector of line segment AM.

Any teachers out there studing ellipses and geometric constructions with their students, here are a pair of worthwhile exercises.

Edited on November 29, 2006, 7:12 pm

Posted by brianjn on 2006-11-29 01:17:04