subtend

Imagine you're looking at a circle and a straight line connects two points on its edge. That line stands across from the arc between those points. In geometry, that line subtends the arc, or the arc subtends the angle formed from its endpoints. It is a precise way to describe how one part of a shape matches up with another.

Originally meaning "to stretch underneath," subtend is used mostly in geometry to describe the link between an angle and the line, arc, or side opposite it. For instance, an arc subtends an angle when the angle is formed by lines drawn to the arc's endpoints. Think of a slice of pizza: the crust subtends the angle at the tip of the slice. You may also see the word in science, as when an object subtends a certain angle in your field of view, but it is mainly a mathematical term.

The word "subtend" comes from Latin roots meaning "to stretch underneath." While you won't use it in everyday conversation about your morning coffee, subtend has a specific and important meaning in geometry and related fields like trigonometry and astronomy.

At its core, to subtend means for a line, arc, side, or object to stand opposite an angle and determine it by its endpoints or outer limits. The most common usage appears in geometry when describing the relationship between an arc of a circle and an angle. An arc subtends an angle if lines drawn from the angle's vertex meet the endpoints of the arc. A chord can likewise subtend an arc. To picture it, think of a slice of pizza: the crust is opposite the tip, and that crust subtends the angle at the tip.

For example, you might say: "The major arc subtends an angle of 270 degrees at the center of the circle." This means that if you draw lines from the center to the endpoints of that larger arc, the angle between those lines measures 270 degrees. In the same way, people say that the Moon or a distant building subtends a certain angle in the sky or in your view.

There is also an older and much less common sense meaning "to stretch under" or "to place beneath." That historical idea helps explain the word's form, but in modern English the important use is the geometric one. So if you meet subtend in real writing, it will usually be talking about an arc, a line, a side, or a visible object and the angle connected to it.