# Deeper into Jeopardy! LI: Science & Geometry – \$2000

Late post number two. At this rate there might not even be a third!

Jeopardy! category: SCIENCE & GEOMETRY (19-10-2015)

\$2000 clue: The ecliptic, the apparent path of the Sun among constellations, is aka a “great” this

Correct response

The gist: The key word is “apparent.” As Johannes Kepler taught us, heavenly orbits are actually elliptical, but from the vantage point of a couple of eyeballs on Earth, the sun sure looks like it’s going in a circle. A “great circle” in geometry is any circle whose circumference matches (in size and coordinates) the circumference of a sphere and which passes through the centre of the sphere – that is, the circle of greatest possible area that can fit within a given sphere. Any other circle whose circumference lies on the surface of a sphere is known as, logically, a “small circle.” The shortest “surface path” between (nearly) any two points on the surface of a sphere is a segment of a great circle – on the globe, we’d call this “as the crow flies.” The exceptions are any two points that are exactly opposite each other on the sphere’s surface – in these cases, the shortest path between them is exactly half of an infinite number of great circles – an example of this on the globe is the north and south poles, which have are linked by an infinite number of great circles that we call “longitude.”

The sun’s great circle “shares” its circumference with the celestial sphere, the imaginary sphere that “surrounds” the Earth on which, if we’re not concerned with actual distances between them (such as when we’re plotting relative locations of stars), celestial bodies are “painted.” In this conception of the sky, different objects travel along their own great circles at different speeds, as if they’re all equidistant from the Earth. Of course, since we know they aren’t, the apparent speeds of the bodies can be used to calculate their distance from the Earth. The idea of “celestial spheres” was accepted among many ancient philosophers, and was replaced in the Classical world by the Eudoxan model, named for its progenitor Eudoxus of Cnidus, who proposed a number of different celestial spheres that could account for the different speeds at which certain bodies travel through the night sky – the sun, the moon, each of the planets, the stars, and so forth. Of course, with the modern understanding of the universe, we know this isn’t true, but it’s still not totally inaccurate to think of the objects in the universe as each having its own great circle, at least from a very geocentric perspective.

An illustration of the celestial sphere, with several great circles depicted: the “equator,” the lines of longitude, and the ecliptic in dotted red

The clue: I mean, what other shape could it really be? I suppose it could be an ellipse if one were to overthink it, but certainly the word “apparently” indicates that the clue is going for, well, the apparent shape the sun traces. Truly not a \$2000 clue except in that it uses some somewhat esoteric language – maybe if the correct response was “great circle” and not just “circle” it would be worth its slot.

In Jeopardy!: A search for “circle”? Nope, that returns almost 500 clues. A search for “great circle” returns a more manageable 13 regular and two FJ! clues, but only two of the regular clues, this one and another explaining the “shortest distance” maxim, are actually about the geometry concept. The rest are about all sorts of things. Three about great circles on the Earth’s surface, and another three are about Canada’s Great Bear Lake which lies on the Arctic Circle. Two are even about The Lion King, in which we learn about the great “circle of life.”