There's an anecdote about how the philosopher-mathematician Pythagoras overcame a student's natural dislike of geometry. The student was poor, so Pythagoras offered to pay him an obol for each theorem he learned. Eager for the money, the student agreed and applied himself. Soon, however, he became so intrigued, he begged Pythagoras to go faster, and even offered to pay his teacher. In the end, Pythagoras recouped his losses.

Etymology provides a safety net of demystification. When all the words you hear are new and confusing, or when those around you put old words to strange purposes, a grounding in etymology may help. Take the word line. You put your ruler to paper and draw a line against the straight edge. If you're an actor, you learn your lines -- line after line of text in a script. Clear. Obvious. Simple. But then you hit Geometry. Suddenly your common sense is challenged by technical definitions*****, and "line," which comes from the Latin word *linea* (a linen thread), loses all practical meaning, becoming, instead, an intangible, dimension-less concept that goes off at both ends to eternity. You hear about parallel lines that by definition never meet each other -- except they do in some warped reality dreamt up by Albert Einstein. The concept you have always known as the line has been renamed "line segment."

After a few days, it comes as something of a relief to run into an intuitively obvious circle, whose definition as a set of points equidistant from a central point still fits your previous experience. That circle****** (coming possibly from a Greek verb meaning to hoop around or from a diminutive of the circular Roman circus, *circulus*) is marked with what you would have, in pre-geometry days, called a line across part of it. This "line" is called a chord. The word chord comes from the Greek word (*chordê*) for a piece of animal gut used as a string in a lyre. They still use (not necessarily cat) gut for violin strings.

After circles, you'll probably study equiangular or equilateral triangles. Knowing the etymology, you can break those words up into component parts: *equi* (equal), angular, angle, lateral (of a side/sided), and *tri* (3). A three-sided object with all sides equal. It is possible that you'll see triangle referred to as trigon. Again, *tri* means 3, and *gon* derives from the Greek word for corner or angle, *gônia*. However, you're far more likely to see the word trigonometry -- trigon + the Greek word for measure. Geo-metry is the measure of Gaia (Geo), the Earth.

If you're studying geometry, you probably already know you must memorize theorems, axioms, and definitions corresponding with names.

### Names of Shapes

- cylinder
- dodecagon
- heptagon
- hexagon
- octagon
- parallelogram
- polygon
- prism
- pyramid
- quadrilateral
- rectangle
- sphere
- square and
- trapezoid.

While the theorems and axioms are pretty much geometry-specific, the names of shapes and their properties have further applications in science and life. Beehives and snowflakes are both dependent on the *hexagon*. If you hang a picture, you want to make sure its top is *parallel* to the ceiling.

Shapes in geometry are usually based on the angles involved, so the two root words (*gon* and angle [from the Latin *angulus* which means the same thing as the Greek *gônia*]) are combined with words that refer to number (like **tri**angle, above) and equality (like **equi**angular, above). Although there are apparent exceptions to the rule, generally, the numbers used in combination with the angle (from the Latin) and gon (from the Greek) are in the same language. Since *hexa* is Greek for six, you're unlikely to see *hex angle*. You're far more likely to see the combined form

*hexa*+

*gon*, or

*hexagon*.

Another Greek word used in combination with the numbers or with the prefix *poly-* (many) is *hedron*, which means a foundation, base, or sitting place. A *polyhedron* is a many-sided three-dimensional figure. Construct one from cardboard or straws, if you like, and demonstrate its etymology, by making it sit on each of its many bases.

Even if it doesn't help to know that a *tangent*, the line (or is that line segment?) that touches at only one point (depending on the function), comes from the Latin *tangere* (to touch) or the oddly shaped quadrilateral known as a *trapezoid* got its name from looking like a table, and even if it doesn't save a lot of time to memorize the Greek and Latin numbers, instead of just the names of shapes -- if and when you run into them, the etymologies will come back to add color to your world, and to help you with trivia, aptitude tests and word puzzles. And if you ever do run into the terms on a geometry exam, even if panic sets in, you'll be able to count through in your head to figure out whether it's a regular pentagon or heptagon that you would inscribe with a traditional five-pointed star.

***** Here's one possible definition, from McGraw-Hill *Dictionary of Mathematics*: **line:** "*The set of points (x1, . . ., xn) in Euclidean space....*" The same source defines "line segment" as "*A connected piece of a line.*"

****** *For the etymology of circle, see Lingwhizt and the possibility of an ancient Indo-European word for 'millstone,' another round flat object*.