# Need a proper mathematical name

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Dr.D
Consider a circle with a chordal line dividing the area into two unequal parts. It seems to be accepted practice to call the smaller of these parts a circular segment. Is there a generally accepted name for the larger area?

I've been writing some material where this geometry arises, and I've called it a "flatted circle," but that is inelegant at best! Better names would be much appreciated.

Merry Christmass to all!

Mentor
2022 Award
It is as well a circular segment, only that the angle is ##> \pi##. In mathematics in general complementary objects are often noted with the prefix "co-". This might not be correct in its funktorial point of view, but within geometry alone there is no danger of confusion as e.g. "hyper-" would be. I've found on Wikipedia that the height of a circular segment is also called sagitta, so you could as well define the area as a segment with sagitta ##> R##.

Another idea is to borrow from the specifications of angles and call it "reflex(ed) segment".

Dr.D
Thanks for the reply fresh_42. My concern with calling this area a circular segment is the risk of confusion. The "all-knowing Wikipedia" says this:

"In geometry, a circular segment (symbol: ⌓) is a region of a circle which is "cut off" from the rest of the circle by a secant or a chord. More formally, a circular segment is a region of two-dimensional space that is bounded by an arc (of less than 180°) of a circle and by the chord connecting the endpoints of the arc."

As you can see, the Wiki article explicitly states that the central angle is less than 180 degrees. Maybe someone else has another option?

Mentor
2022 Award
From Wikipedia:

subtitled with: "The blue body is a sphere segment; the pink rest body too" and on the English version: "An example of a spherical cap in blue (and another in red.)" So what's right for the ball cannot be false all of a sudden for the circle.

I would probably use the language of angles: acute, obtuse, straight, reflex. It is what the defining angle is, and thus can be extended to the segments with some reason.

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Homework Helper
If you slice off a bit of a cone you have a truncated cone. So how about 'truncated circle'?

AM

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Homework Helper
Gold Member
Regardless of what Wikipedia says, I think that "larger circular segment" would be clear enough.

Klystron
Dr.D
Thanks to all who responded. This helps, and is much appreciated.

Gold Member
I was thinking of gibbous. But I suspect is too well-defined to not lead to confusion.
• having the observable illuminated part greater than a semicircle and less than a circle