The Crystal Palace pane of glass (49 inches) as the hypotenuse of a right-angled triangle, thereby creating a triangle with a length-to-height ratio of 2.5:1, whose base (adjacent side) was 4 feet long. By mirroring this triangle he obtained the 8-foot-wide gables that formed the vertical faces at either end of the prism, each of which was 24' long. With this arrangement, Paxton could glaze the entire roof surface with identical panes that did not need to be trimmed. Paxton placed three of these 8' x 24' roof units side-by-side, horizontally supported by a grid of cast iron beams, which was held up
Triangle of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices. It is not possible for that sum to be less than the length of the third side. A triangle with three given positive side lengths exists if and only if those side lengths satisfy the triangle inequality. Three given angles form a non-degenerate triangle (and indeed an infinitude of them) if and only if both