bonanova Posted August 1, 2014 Report Share 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? Quote Link to comment Share on other sites More sharing options...
0 TimeSpaceLightForce Posted August 2, 2014 Report Share Posted August 2, 2014 Quote Link to comment Share on other sites More sharing options...
0 TimeSpaceLightForce Posted August 1, 2014 Report Share 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. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 1, 2014 Author Report Share Posted August 1, 2014 On the right track. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 2, 2014 Author Report Share Posted August 2, 2014 What's the triangle's area? The idea behind the puzzle question makes it an easy calculation. Quote Link to comment Share on other sites More sharing options...
0 TimeSpaceLightForce Posted August 2, 2014 Report Share 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. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 3, 2014 Author Report Share Posted August 3, 2014 How many square meters? Quote Link to comment Share on other sites More sharing options...
0 TimeSpaceLightForce Posted August 3, 2014 Report Share Posted August 3, 2014 With cad area measure its 1.2983 sqm Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 3, 2014 Author Report Share Posted August 3, 2014 Very close. What is the area of the ellipse? Quote Link to comment Share on other sites More sharing options...
0 TimeSpaceLightForce Posted August 4, 2014 Report Share 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 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 5, 2014 Author Report Share 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). Quote Link to comment Share on other sites More sharing options...
Question
bonanova
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?
Link to comment
Share on other sites
10 answers to this question
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.