Posted August 1, 2014 An ellipse is 1 meter wide at its narrowest point and four times that amount at its widest point. A triangle is drawn using three points on the ellipse. How large can it be? 0 Share this post Link to post Share on other sites

0 Posted August 1, 2014 An equal side triangle in a circle is the largest. Tilt this inscribed triangle with the circle to grade 1:4 .. then maybe the projected triangle on vertical plane is also the largest triangle inscribed in an ellipse. 0 Share this post Link to post Share on other sites

0 Posted August 2, 2014 What's the triangle's area? The idea behind the puzzle question makes it an easy calculation. 0 Share this post Link to post Share on other sites

0 Posted August 2, 2014 If a square of 1 unit area is inclined 1/2 its side backward , it would look half as large in front view.. Polygons, if are made of thin vertical strips should do too. 0 Share this post Link to post Share on other sites

0 Posted August 3, 2014 With cad area measure its 1.2983 sqm 0 Share this post Link to post Share on other sites

0 Posted August 3, 2014 Very close. What is the area of the ellipse? 0 Share this post Link to post Share on other sites

0 Posted August 4, 2014 Very close. What is the area of the ellipse? Area of projected ellipse(a=.5,b=2): pi(ab) or pi is 1/4 Area of tilted circle (r=2): (pi)(2)(2)(1/4) or pi Projected area of tilted equilateral triangle (h=3) in circle: is (.25)(3)(3)(tan30) : (.25)(9)(.57735) or 1.29908 0 Share this post Link to post Share on other sites

0 Posted August 5, 2014 Yah, you got it. Here's basically just a different wording: The largest triangle inscribed in a circle is an equilateral triangle. For a unit circle (area = pi) an inscribed equilateral triangle has area (3/4) sqrt(3) = 1.299038.... If we scale y by f and scale x by 1/f areas are preserved. For f=2, a unit circle becomes an ellipse whose axes are 1 and 4 (area = pi). So the largest triangle inscribed in that ellipse has area (3/4) sqrt(3). 0 Share this post Link to post Share on other sites

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An ellipse is 1 meter wide at its narrowest point and four times that amount at its widest point.

A triangle is drawn using three points on the ellipse. How large can it be?

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