I don't understand how this equation calculates angle for hexagons

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SUMMARY

The equation for calculating the angle between any two vertices of a regular hexagon is given by 2π/n, where n is the number of sides. For a hexagon, n equals 6, resulting in an angle of 1.047 radians, which is equivalent to 60 degrees. This calculation is correct, as the angle is measured in radians, and the confusion arises from misinterpreting the relationship between radians and degrees. Understanding this relationship is crucial for programming graphics involving polygons.

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  • Understanding of basic geometry, specifically polygon properties
  • Familiarity with radians and degrees conversion
  • Basic programming skills for implementing graphics
  • Knowledge of trigonometric functions in programming
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  • Study the relationship between radians and degrees in depth
  • Learn about the properties of regular polygons and their angles
  • Explore graphics programming libraries that handle polygon rendering
  • Practice implementing angle calculations in a programming language of choice
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Students learning programming, graphic designers working with polygon shapes, and anyone interested in understanding the mathematics behind graphics rendering.

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I don't understand how this equation calculates angle for hexagons...

Hi, I'm learning how to program and I've been studying graphics.

This quote from a programmer confuses me (the quote is a hyperlink to my source):
Basically[/PLAIN] the angle between any two vertices is 2 pi / n and all the vertices are at distance r from the origin.

How does 2pi/n calculate the angle of two vertices relative to the center of a hexagon? I try to plug in some values to test it and the resulting angle is 1.047 degrees which is extremely small and I think I'm misunderstanding the answer.

I have a diagram in my book that also states that the above equation is the angle. I also tested my code (the angle is only a small part of it) and my drawHexagon app works. However, when I do the math, the angle from the center of the hexagon is always 1.047 degrees and that doesn't make sense to me.

Shouldn't the central angle be 60 degrees given that a hexagon has 6 sides?
 
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The angles are being measured in radians.
2pi radians=360 degrees.
1.047 radians=60 degrees.
 
lurflurf said:
The angles are being measured in radians.
2pi radians=360 degrees.
1.047 radians=60 degrees.

Thank you. I really need to brush up on my math.
 

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