# Polar Coordinates, Six-Pointed Star, and a Hexagon

• GreenPrint
In summary, the conversation is about creating a six-pointed star and a hexagon using polar coordinates in MATLAB. The person only needs help with the mathematical concepts behind it, not with using MATLAB itself. The suggested method for creating the shapes involves defining equations for each side and converting them to polar coordinates, and breaking down the star into two triangles.
GreenPrint

## Homework Statement

Hey I have to create a six-pointed star and a hexagon with polar coordinates using MATLAB. I don't need help with using MATLAB, I just need help with the math. Note that I don't really need to know how the math sense this assignment is for a CSE course. I just don't know how to create a six-pointed star or a hexagon using polar coordinates because I don't know enough of the math, so I was wondering if someone could tell me how.

## The Attempt at a Solution

For a hexagon:
you will need to define 6 different conditions for each side
for the first define an equation for a straight line (eg. y=1) for theta in (-pi/6, pi/6).
Then convert this to r(theta).
Once you have the form for the first segment it should be simple to convert to teh others by using the same from translating theta f(theta + n*pi/3)

The star will be similar and i would break it down into two triangles

## 1. What are polar coordinates and how are they used?

Polar coordinates are a system used to locate points on a two-dimensional plane. They consist of a distance from the origin and an angle from a reference line, usually the positive x-axis. They are often used in mathematical and scientific applications, such as graphing functions and mapping locations on a globe.

## 2. How is a six-pointed star constructed using polar coordinates?

A six-pointed star, also known as a Star of David, can be constructed by connecting six points on a circle with lines. These points are located at equal distances from each other on the circle, and their positions can be determined by using polar coordinates. The angles between the points are all multiples of 60 degrees, and the distances from the origin are equal.

## 3. What is the relationship between polar coordinates and a hexagon?

A hexagon is a six-sided polygon with six angles of 120 degrees each. When plotted on a polar coordinate system, the points of a hexagon will form a regular hexagon shape. This is because the angles between each point are multiples of 60 degrees, and the distances from the origin are equal.

## 4. How do polar coordinates differ from Cartesian coordinates?

Polar coordinates and Cartesian coordinates are two different systems used to locate points on a two-dimensional plane. In Cartesian coordinates, points are located using the x and y axes, while in polar coordinates, points are located using a distance and an angle. While both systems can be used to plot the same points, polar coordinates are often more useful for circular or symmetrical shapes.

## 5. Can polar coordinates be used in three-dimensional space?

Yes, polar coordinates can also be used to locate points in three-dimensional space. In addition to the distance and angle from the origin, a third coordinate, known as the z-coordinate, is used to determine the height or depth of the point. This system is known as cylindrical coordinates and is often used in physics and engineering applications.

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