Editing Talk:2509: Useful Geometry Formulas
Please sign your posts with ~~~~ |
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 60: | Line 60: | ||
Unconvinced by the cone! The equation shown, is correct for an isosceles triangle with a half-ellipse on its base. But that shape has 'corners' where the sides meet that half-ellipse. In a 3D projected view of an actual cone, the sides will meet the base ellipse at a tangent, meaning that it is more than a half-ellipse. But I suppose it's close enough as an approximation...[[Special:Contributions/172.69.55.131|172.69.55.131]] 15:57, 1 September 2021 (UTC) | Unconvinced by the cone! The equation shown, is correct for an isosceles triangle with a half-ellipse on its base. But that shape has 'corners' where the sides meet that half-ellipse. In a 3D projected view of an actual cone, the sides will meet the base ellipse at a tangent, meaning that it is more than a half-ellipse. But I suppose it's close enough as an approximation...[[Special:Contributions/172.69.55.131|172.69.55.131]] 15:57, 1 September 2021 (UTC) | ||
− | |||
:: I expanded the text slightly, and worked out the correct formula: it should be (2π - 2arctan(h/a))ab + b sqrt(h^2 - a^2). Can someone verify that, format it properly for the wiki, and add it? The easy way to check it is to shrink the diagram horizontally so the ellipse is a circle of radius a. (Does the wiki not have MathJax or similar installed? Seems odd, given Randall Munroe's interests.) It's maybe also worth mentioning that looking closely at the picture at a pixel level shows that he did draw the tangents, rather than do the half-ellipse + triangle that the formula suggests. --[[Special:Contributions/172.69.90.75|172.69.90.75]] 16:48, 2 September 2021 (UTC) | :: I expanded the text slightly, and worked out the correct formula: it should be (2π - 2arctan(h/a))ab + b sqrt(h^2 - a^2). Can someone verify that, format it properly for the wiki, and add it? The easy way to check it is to shrink the diagram horizontally so the ellipse is a circle of radius a. (Does the wiki not have MathJax or similar installed? Seems odd, given Randall Munroe's interests.) It's maybe also worth mentioning that looking closely at the picture at a pixel level shows that he did draw the tangents, rather than do the half-ellipse + triangle that the formula suggests. --[[Special:Contributions/172.69.90.75|172.69.90.75]] 16:48, 2 September 2021 (UTC) |