How to Construct a Decagon Using a Protractor and Compass

  • Context: High School 
  • Thread starter Thread starter cenglish
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Discussion Overview

The discussion revolves around the construction of a decagon using a protractor and compass. Participants share their experiences, challenges, and methods related to accurately drawing a decagon, exploring both theoretical and practical aspects of geometric construction.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses repeated failure in constructing a decagon, despite knowing the external angles and seeking suggestions for proper methods.
  • Another participant suggests dividing a circle into 10 equal parts and questions the difficulty of the task.
  • There is a suggestion to print and trace an image of a decagon, which is met with criticism for not being a geometric construction method.
  • Several participants propose constructing a pentagon first and then bisecting the edges to find additional vertices for the decagon.
  • Concerns are raised about the accuracy of the protractor being used, with one participant questioning the quality of a plastic protractor.
  • A detailed method is provided involving drawing an enclosing circle and marking angles to construct the decagon, emphasizing the importance of accurate execution.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method for constructing a decagon. There are multiple competing views on the approach, with some focusing on the initial construction of a pentagon and others emphasizing the use of accurate tools and execution.

Contextual Notes

Some participants mention missing steps in the construction process, and there is uncertainty regarding the assumptions made about the tools and methods used. The discussion highlights the complexity of geometric constructions and the potential for errors in execution.

cenglish
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Hi guys, I have been working for a long time and have attempted to construct a decagon but have failed all three times. I know that all the external angles are 144 degrees and they all add up to 1440 degrees. Every time I draw the decagon I come up with a hendecagon. I don't know why I come up with this because I have all of the angles that a decagon consist of. I have searched up YouTube videos on how to create a decagon, but none of them seem to help. I would appreciate if someone could suggest a way to construct a proper decagon. Thank You!
 
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can't you divide up a circle into 10 equal parts? What would the angle be for each segment? This seems awfully easy unless I'm missing something.
 
This is a geometry problem, which does not belong in the Intro Physics HW forum. I'm moving it to the General Math forum.
 
Oh. You have to do this with a compass and a straight-edge?
 
Construct a pentagon
Bisect the edges
Draw the decagon.
 
Joffan said:
Construct a pentagon
Bisect the edges
minor step missing in here.
Draw the decagon.
 
cenglish said:
Every time I draw the decagon I come up with a hendecagon.
I think it is pretty apparent that your angles are not 144 degrees then. What kind of protractor are you using? One of those little plastic ones from the dollar store?
 
  • #10
DaveC426913 said:
minor step missing in here

Actually, I made more steps than needed, not fewer, bisecting being harder than simply drawing a line given two points.
Joffan said:
Construct a pentagon which will have an enclosing circle as part of the construction
Find the extra vertices for the decagon on that circle by drawing a diameter from each pentagon vertex
Draw the decagon.
 
  • #11
Joffan said:
Actually, I made more steps than needed, not fewer, bisecting being harder than simply drawing a line given two points.
You can bisect the sides of a pentagon, but that there's still a few steps before you get a decagon from that. Granted, they're not hard steps...
 
  • #12
DaveC426913 said:
You can bisect the sides of a pentagon, but that there's still a few steps before you get a decagon from that. Granted, they're not hard steps...
Not sure what steps you're talking about that aren't covered by "draw the decagon", simply meaning draw the edges between the already-found vertices.

Unless you have erased the enclosing circle from the pentagon construction? Or drawn the bisectors so short they don't touch the circle?
 
  • #13
DaveC426913 said:
I think it is pretty apparent that your angles are not 144 degrees then. What kind of protractor are you using? One of those little plastic ones from the dollar store?

Yes, I do use the plastic protractor that is provided for me at my school. Would you suggest going out and buying one of my own?
 
  • #14
Joffan said:
Not sure what steps you're talking about that aren't covered by "draw the decagon", simply meaning draw the edges between the already-found vertices.

Unless you have erased the enclosing circle from the pentagon construction? Or drawn the bisectors so short they don't touch the circle?
It wasn't a given that the construction of the pentagon included an enclosing circle. He could have constructed with just a ruler and protractor.
 
  • #15
cenglish said:
Yes, I do use the plastic protractor that is provided for me at my school. Would you suggest going out and buying one of my own?
No, it's just that your method is fine; it's simply the execution that's flawed.
 
  • #16
If you are using a protractor and it's simply an accurate drawing issue:
  • Draw your zero line (wider than the intended shape), mark a centre point
  • Use compasses to draw the enclosing circle for your decagon
  • Put your protractor zero on the zero line at the centre mark
  • Check that 0 and 180 are both on the zero line
  • Mark points at 36, 72, 108 and 144 degrees
  • Draw straight lines (diameters) full across the circle from each marked point through the centre
  • Draw the decagon using the intersecting points on the circle (including the intersection with the zero line)
  • Remove your construction lines.
 

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