Thus, a company faced with rising costs may be better served by decreasing the size of the product subtly, in three dimensions, than by raising prices.The authors also found that the shape of a container might influence consumption: volume may appear less in a conic glass than in a cylindrical one, and so people may underestimate the amount they drink from the conic glass.
The situation of Ω relative to RP determines the conic section in PP: If Ω intersects RP outside the base circle (the circle formed by the intersection of the cone and RP), the image of the circle will be an ellipse.
(The possible intersections of a plane with a cone, known as the conic sections, are the circle, ellipse, point, straight line, parabola, and hyperbola).
However, the doxographers ascribe the discovery of conic sections to a student of Eudoxus's, Menaechmus (mid-4th century bce), who used them to solve the problem of duplicating the cube.
Following his lead, Pascal made his surprising discovery that the intersections of the three pairs of opposite sides of a hexagon inscribed in a conic lie on a straight line.
A discriminant can be found for the general quadratic, or conic, equation ax2 + bxy + cy2 + dx + ey + f = 0; it indicates whether the conic represented is an ellipse, a hyperbola, or a parabola.
Many other projections are used, for example, the conic projection, drawn from a point directly above the North or South Pole.
Menaechmus's curves are conic sections: the first two are parabolas, the third a hyperbola.
The three conic sections (ellipse, parabola, and hyperbola) had been studied since antiquity, and Galileo's models of motion gave further proof that dynamics could be studied with the help of geometry.
