Concept

Eccentricity

The fixed ratio of a conic's distance from a focus to its distance from a directrix. It is below one for an ellipse, exactly one for a parabola and above one for a hyperbola, so a single number produces the whole family from one focus and one line.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Every ray from one focus arrives at the other. An ellipse with its two foci and 13 rays leaving the first. Each is reflected at the curve by the ordinary law of reflection and each passes through the second focus.

Every ray comes back to the other focus

An ellipse has two foci and one property everybody remembers: the distances to them add to a constant. What that property forces is stranger and more useful — a mirror shaped like an ellipse sends every ray leaving one focus, in every direction, through the other.

geometry · Conic sections

Every ray aimed at one focus is turned towards the other. A hyperbola with its two foci and 13 rays aimed at the far one. Each strikes the near branch from outside and is turned towards the near focus — which is the property a Cassegrain telescope's secondary mirror uses.

Aimed at one focus, turned towards the other

An ellipse sends every ray leaving one focus through the other. A hyperbola does something that sounds like the same sentence and is not — it takes a ray aimed at the far focus and turns it towards the near one, which is what the second mirror of a telescope is for.

geometry · Conic sections

Named alongside it

The objects these essays reach for when they reach for this one.

Conic Ellipse Focus Optimality Reflection Tangency Dandelin spheres Directrix Hyperbola Parabola

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