Excellent! You've made me hopeful about something I've been trying to prove about hyperboloids as it relates to the Geometric Mean. Namely, that the cross-sections are rounded triangles (using the outlining method you demonstrate) of constant widths.
Thank you!! This finally showed me why my Reuleaux-tetrahedron would not act the way I wanted. The animation at 4:40 showed me how to achieve it in NX. Now I soon will be printing my own body of constant width with rounded edges and corners.
I found this video while looking for a way to visualize the constant width polygons described in the great Poul Anderson's SF adventure 'The Three-Cornered Wheel.'
So if I put a gear on the axle, attached to an axle with a gear in the middle of the same shape in the opposite timing, I can create an artificial center axle that rides flat.... right?
Amazing information and fun to watch. However, to what purpose would you want to put these shapes. Are they of any practical use apart from the entertainment and of course mathematical value?
@@elijaht3452 In the end of the video I show a couple of solids of constant width that can roll in any direction. They were 3D printed and the models can be found on my website.
At 1:15 it looks as if the vertex of the Reuleaux triangle in touch with the plane is motionless in the sense of remaining at exactly the same point on the plane, and acting as a pivot for the roll. In a continuing roll this will only last for a short time and will be followed by the adjacent arc contacting the plane, until the next vertex does the same thing. How long does the vertex remain motionless? In the case of an ordinary straight sided triangle ABC rolling to the right, this would seem easy to answer. Start with A as the apex and side BC flat on the plane and start to roll. C is the pivoting vertex at rest on the plane, and will stay there until CA is now flat on the plane and only start to move thereafter. A rolling circle on the other hand never has any point on its circumference at rest on the plane. Is this the case with the Reuleaux triangle too? Just that the forward motion of a vertex in contact the plane is very slow and doesn't easily show up? The forward speed difference in a bike ride with Reuleaux wheels would still make it an alarming experience of course.
