 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  'Perfect Oval' (Posted on 2006-11-18) 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.

 See The Solution Submitted by brianjn Rating: 4.0000 (1 votes) Comments: ( Back to comment list | You must be logged in to post comments.) Solution | Comment 1 of 5
`Construction of the first quadrant portionof the "Oval":`
`Label points O(0,0), A(4,0), and B(0,3).Construct point M on line segment AB suchthat |BM| = 4-3 = 1. Construct theperpendicular bisector of line segment AMwhich intersects the x-axis at point C andthe y-axis at point D. Construct circulararc (starting at point A and ending at point E on the perpendicular bisector) withcenter C and radius |CA|. Constructcircular arc (starting at point E andending at point B) with center D and radius|DB|. The rest of the "Oval" is obtained byreflecting the first quadrant about the x-axis, the y-axis, and the origin.`
`  Area of "Oval" = 4*[ Area(Sector CAE) +                       Area(Sector DEB) -                       Area(Triangle OCD)]`
`     = 4*[ (1/2)*(5/2)^2*arcsin(4/5) +           (1/2)*(5)^2*arcsin(3/5) -           (1/2)*(3/2)*(2)]`
`     ~= 37.766245665`
`  Area of Ellipse = (PI)*(4)*(3)`
`                  ~= 37.699111843`
`   (Area of "Oval")-(Area of Ellipse)  ------------------------------------             Area of Ellipse `
`     ~= 0.001780780`

 Posted by Bractals on 2006-11-18 17:28:31 Please log in:
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