# CirclePoints

CirclePoints[n]

gives the positions of n points equally spaced around the unit circle.

CirclePoints[r,n]

gives the positions of n points equally spaced around a circle of radius r.

CirclePoints[{r,θ1},n]

starts at angle θ1 with respect to the axis.

CirclePoints[{x,y},rspec,n]

centers the circle at {x,y}.

# Details

• For positive integer n, CirclePoints[n] generates a list of vertices for a regular n-sided polygon, oriented so its base is horizontal.
• In CirclePoints[n], n does not have to be an exact integer. The angles between successive vectors are always .
• Unless explicitly given as a Quantity object, the angle θ1 is assumed to be in radians, counterclockwise starting from the axis. (Multiply by Degree to convert from degrees.)
• If the angle θ1 is not given, it is assumed to be π/n-π/2, so that for integer n the vectors correspond to a regular polygon with its base horizontal.
• All arguments of CirclePoints except n can be symbolic. They can also be Quantity objects.

# Examples

open allclose all

## Basic Examples(3)

Corners of an equilateral triangle:

Draw a pentagon:

Draw unit vectors to the corners of a regular heptagon:

## Scope(4)

Corners of a centered square with horizontal and vertical sides:

Corners of a square of size :

Four unitary vectors aligned with the axes:

Displace them to a different point:

The four corners of an arbitrary square, at any point and any size or orientation:

Draw polygons, with their lowest side oriented horizontally by default:

## Properties & Relations(2)

CirclePoints returns pairs that can be reinterpreted as real and imaginary parts of the roots of unity:

CirclePoints is equivalent to a collection of AngleVector calls:

## Neat Examples(1)

Wolfram Research (2015), CirclePoints, Wolfram Language function, https://reference.wolfram.com/language/ref/CirclePoints.html.

#### Text

Wolfram Research (2015), CirclePoints, Wolfram Language function, https://reference.wolfram.com/language/ref/CirclePoints.html.

#### CMS

Wolfram Language. 2015. "CirclePoints." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CirclePoints.html.

#### APA

Wolfram Language. (2015). CirclePoints. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CirclePoints.html

#### BibTeX

@misc{reference.wolfram_2024_circlepoints, author="Wolfram Research", title="{CirclePoints}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/CirclePoints.html}", note=[Accessed: 24-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_circlepoints, organization={Wolfram Research}, title={CirclePoints}, year={2015}, url={https://reference.wolfram.com/language/ref/CirclePoints.html}, note=[Accessed: 24-July-2024 ]}