Discussion:Draw a Hexagon

Your assumption is that 6*r equals the circumference of a circle. However, it is 2*pi*r, which approximates 6,28. So, with the protractor set to r, the axis you draw will be slightly too short. I understand this is unnoticable with small circles, but it is by no means "accurate".

You are wrong. This method IS accurate. This way, you will get all triangles with each axis length r. This means all of the angles of the triangles are 60 degrees, and 6*60 equals 360. Accurately. Your point is not correct, because you don't count the curvature of the circle in the way that you do.

you can do this in a easier way

The device used to tell you which whay is north is a compass (or possibly a GPS unit.) The device in the pictures is a 'pair of compasses' or 'compasses.'

And yes, it is a 100% accurate method - one that the greeks proved.

And what about drawing a pentagon with a compass? I remember a math class about complex numbers in which a solution was given. Can someone explain it to me, please?

Oh, it was already explained in Wikipedia: http://en.wikipedia.org/wiki/Pentagon#Construction -> the alternative method. A straightedge is required.

A 6 sided hexagon cannot be made with a compass. The circumference is related to pie and as you draw the 6th mark, and then the 7th it will not be exact

Do this with a high quality compas. You will find that the last line is always a little too long. (Too long by .28r)

Does a "Hexagon", by definition, have equal sides and equal angles? If so, this article should be taken down until it is accurate.

For now, I will add a correction to indicate that it makes a hexagon with almost equal sides.

Do this with a high quality compas. You will find that the last line is always a little too long. (Too long by .28r)

Does a "Hexagon", by definition, have equal sides and equal angles? If so, this article should be taken down until it is accurate.

For now, I will add a correction to indicate that it makes a hexagon with almost equal sides.

Is there an echo?

kewl. u no, i never thought of doing that.

This is deviltry. Mathematics has lain down with SATAN and woken with his 2PiR(2)'d lies. I vote for deletion.

I just sent a note to the authors about how to draw a perfect hexagon with only a compass in hand and a pen and pencil. This is basic Eucleadean geometry construction that we learned in the 7th grade.

SM

My friend, by creating the six sides of the hexagon incscribed in the circle the lenght of them is obviously not equal to 2*pi*r and is rather 6*r, which is Ok. YOu don't need to move on the length of the circumference to subtend the chord needed for the hexagon.

SM

No, the length of the vertices is one radian, not a sixth of the circumference of the circle. I have clarified the mathematics.

I'm sorry but there are valid reasons for deleting this article, outside of it's satanic origins.

~ It's incomplete and misleading - this isn't a REAL hexagon, it's an approximation. ~ It's dangerous - someone designing equipment could look at this article and the next thing you know - SHUTTLE DISASTER STRIKES AGAIN. ~ The instructions are impossible in the REAL WORLD. YOU CANNOT MAKE A REAL HEXAGON WITH THESE INSTRUCTIONS.

It is fascinating that so many people are willing to comment on the article and say that it does not produce a geometrically regular hexagon. This is, in fact, the prefered method for producing a perfect hexagon.

I have developed a truly marvelous technique for trisecting an angle using only a compass and straight edge, but unfortunately this comment box is too small to contain it. I also have perfected a remarkably simple method for producing an arbitrarily accurate image of a hexagon, employing nothing beyond a common xerox machine and elementary geometry book. It is interesting to note that the precision of the result is effectively independent of the language in which the text is written! Unfortunately, this comment box no longer has sufficient room for the method to be expostulated.

• • • This method produces a perfect hexagon, no matter how big or small the circle. ***

Many of you have mistakenly thought that as you go around the circumference of the circle, you are measuring off a radius amount of the circumference. This is not what is being done. Instead, you are forming triangles that have the radius as the length of all 3 sides (an equalateral triangle). This type of triangle will always have an exact 60 degree angle between each side. So when you create 6 of these triangles, the total of the angles at the center of the circle is exactly 360 degrees -- the number of degrees in a circle. You have now created a perfect hexagon (as close as a human with a pencil and compass can get).

doody

thats was really hard to draw.

a 7 years old kid know better this trick

You can just freehand draw it, which is so much faster. Or you can draw one trapezoid on top of another.

wrong. but you CAN draw a trapezoid by starting with the hexagon and erasing half of it.

this is stupid - i thought it was going to say how to draw one free hand. if you need to use a compass, why not just get a stupid hexagon template to do it?

To correct some misstated complaints, this method assumes that the collective length of the chords should be 6r, not that the circumference of the circle is 6r.

The article doesn't say how to properly space the marks so that each side side of the hexagon ends up equal

thanks a lot for all the previous comments... haven't had such a good laugh in a while

-r

um....drawing a hexagon? really?

This is an approximation not an accurate hexagon. Anyone with a small amount of mathematical education knows this. It's how teachers get 6 year olds to make a hexagon - not how to actually make a real one!- Really!

looks alittle crazy to me

I like this article. thank you

this article is very correct, but there is an easier way to do this , it dosen't have to be this complicated.

OK... I stand corrected. Thanks for the lively discussion. I now believe that if done perfectly, this should make a perfect hexagon. Here is my way of explaining it, for those who (like me) believed the math didn't support it:

The diameter of a circle is in fact roughly 6.28 * r. So, logically, you can't get all the way around a circle with only 6 passes of the compass... You should be .28r short. Right?

Well... That assumes you are actually travelling the diameter of the circle, and not taking 6 short-cuts. The distance between 2 points on a circle via a straight line is roughly .0467r shorter than a path to the same point via the arc of the circle.

So, by taking this shortcut (a straight line, instead of following the arc) 6 times, you do in fact end up right where you should be.

In short, the compas is NOT travelling the diameter of the circle, because the two points of the compass form a straight line, not an arc.

Thanks for teaching me something. Cheers!

y does this keep coming up??????????

it is easy b ut you are studies.

i hate drawing hexigons but you have to do it even if you dont want to

FOR GOD SAKES...you guys are splitting atoms here... I'm a bloody carpenter... i have a .125" variance to work with... the method works great and is extremely simple... when they ask me to build a space shuttle I'll call one of you morons...get over it. it's because of you guys that people hate math.