Definition:Major Arc

Definition

Let $a$ and $b$ be points on the boundary $\BB$ of a simple closed curve $\CC$ in the plane.

Let $a$ and $b$ divide $\BB$ into unequal parts.

The longer of the arcs described by $a$ and $b$ is referred to as the major arc of $\BB$.

Major Arc of Circle

Let $a$ and $b$ be two points on the circumference of a circle.

The major arc joining $a$ and $b$ is the longer of the two arcs joining $a$ and $b$.

In the above diagram:

the arc $ECBDF$ is the major arc defined by $E$ and $F$

the arc $CEFDB$ is the major arc defined by $B$ and $C$

and so on.

Also known as

The major arc of a simple closed curve with respect to two points is also known as the long arc.

Also see

• Definition:Minor Arc

• Results about major arcs can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): arc: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): major arc
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): arc: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): major arc