n-Sectors of the Angles of a Triangle

kind of triangle

angle divisions n

2

show lines

All

show points

All

Sizes

thickness

Tiny

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Medium

point size

Tiny

Small

Medium

image size

300

Medium

Large

800

zoom

viewfinder

None

○

equilateral

intersections of lines from



A

or



B

or



C

: 1

The

n

-sectors of an angle are the lines that divide the angle into

n

equal parts. In a triangle, the bisectors are collinear, the trisectors lead to Morley's theorem, …. More modestly, this Demonstration provides a way to count the intersection points of the

n

-sectors of the angles of a triangle as a function of

n

, which is

3

2

n

-6n-

n

(-1)

+2

for a scalene triangle.