Does everyone know about the Dandelin spheres? A plane intersects a cone in a conic section. The spheres inscribed in the cone and touching the plane do so at the foci. For proof, note that the tangents to a sphere from a point are equal in length, and use the `pins and string' construction for the ellipse (or hyperbola, or parabola -- focus-directrix for this last.) R. On Mon, 11 Nov 2013, Henry Baker wrote:
Take a circle & look at it along its axis; it appears as a circle.
Now tilt the axis of the circle at an angle alpha; it now appears as an ellipse.
Consider the foci of the ellipse.
Is there anything interesting and/or cool about the relationship of the foci and the angle alpha?
(I don't know any interesting answer; I'm just curious.)
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun