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NATT

Member

Registered: 2009-09-29

Posts: 110

How to construct a 10 degrees angle using compass and ruler

Hey guys im new to this forum and i just wanna to know how to construct a 10 degrees angle using the ruler and the compass. There are many ways to contruct it in the internet but i want the theorems you used to draw it and how it happens.

PS..dnt care abt language mistakes

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->Don't try to force chemistry between two people or else it may just blow up at you<-
->“Believe nothing, no matter where you read it, or who said it, even god, no matter if I have said it, unless it agrees with your own reason and your own common sense”<-

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: How to construct a 10 degrees angle using compass and ruler

Well not sure about theorem to describe it, but is it not enough to drawn an equilaterial triangle and dividing one side into 6 using the ruler, and drawn the diagonal making a 10 and 50 degree angle?

make a point, draw a circle, from an edge of the circle, draw another circle with same radius so that it passes through centre of the first circle

at one of the points where the two circles meet, draw lines to the two centres, draw line between centres and that gives you an equilateral triangle, using ruler divide one side into 6 equal segments, and then as above.

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JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: How to construct a 10 degrees angle using compass and ruler

http://en.wikipedia.org/wiki/Angle_trisection

Constructing a 10° angle would mean trisecting the angle 30°. So, is the polynomial

[align=center]

[/align]

irreducible over the field

? If yes, then you cannot trisect 30° and hence construct a 10°; if not, then you can do it.

NATT

Member

Registered: 2009-09-29

Posts: 110

Re: How to construct a 10 degrees angle using compass and ruler

Thank you luca-deltodesco and JaneFairfax for your information.. This forum looks really fast
Btw i found this thing in yahoo answers

Can you tell me what is the theorem and the procedure behind this?

Jane : Your equation looks soo difficult to me because im still doing the O/L exams

--> Are there any possible ways to make it just only using the compass and the ruler.... not other stuff.?

Last edited by NATT (2009-09-30 03:02:50)

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->Don't try to force chemistry between two people or else it may just blow up at you<-
->“Believe nothing, no matter where you read it, or who said it, even god, no matter if I have said it, unless it agrees with your own reason and your own common sense”<-

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: How to construct a 10 degrees angle using compass and ruler

Aha. It appears that the answer given in yahoo answers allows you to measure the lengths of line segments. That is totally different then. I was thinking you were not allowed to use your ruler to measure lengths, only to draw straight lines – in which case it would be provable, using an advanced mathematical branch called Galois theory, that it is impossible to construct a 10° angle.

And this is because the polynomial I stated above is irreducible in

. If it were not irreducible, there would be an

of the form

with

such that

is a root of the polynomial above. I have just worked out that no such root of this form exists.

Obviously, if you are allowed to measure lengths with your ruler, you should be able to create more angles than if you were only using an unruled straightedge. Happy constructing.

Last edited by JaneFairfax (2009-09-30 06:16:39)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: How to construct a 10 degrees angle using compass and ruler

That's doable without a marked straight edge, isn't it?
Given a line of a certain length, you can set the length of the compass and use that to draw a line double the length of the original.

You'd need a ruler to get an inch, but if you just worked with 'units' instead, the method would be the same.

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Why did the vector cross the road?
It wanted to be normal.

NATT

Member

Registered: 2009-09-29

Posts: 110

Re: How to construct a 10 degrees angle using compass and ruler

I was thinking you were not allowed to use your ruler to measure lengths

Yeah measuring is not accepted. But i just wanted to know what was behind it.. BTW..i got to learn some about Galois theory.. :)
->btw thanks guys for your instant comments

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->Don't try to force chemistry between two people or else it may just blow up at you<-
->“Believe nothing, no matter where you read it, or who said it, even god, no matter if I have said it, unless it agrees with your own reason and your own common sense”<-

Hitesh Jaju

Guest

Re: How to construct a 10 degrees angle using compass and ruler

I proved it with the help of compass
if you want to contact me then my no is [snip]

Last edited by MathsIsFun (2009-10-13 20:42:25)

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: How to construct a 10 degrees angle using compass and ruler

Hi Hitesh Jaju,

Not a good idea to give your phone no in a public forum.

Why not post your answer here?

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Hitesh Jaju

Guest

Re: How to construct a 10 degrees angle using compass and ruler

sir actually i am a student of class ten . I GOT THIS METHOD TODAY ONLY BY MY SELF AND I DISCUSS WITH SO MANY TEACHERS ACCORDING TO THEM IT IS CORRECT I WANT TO KNOW THAT BEFOR IT WAS PROVED TO MAKE 10 DEGREE ANGLE WITH THE COMPASS? BECAUSE ACCORDING TO MY TEACHERS BEFORE IT WAS NOT PROVED BY ANY ONE

Hitesh Jaju

Guest

Re: How to construct a 10 degrees angle using compass and ruler

sir actually i am a student of class ten . I GOT THIS METHOD TODAY ONLY BY MY SELF AND I DISCUSS WITH SO MANY TEACHERS ACCORDING TO THEM IT IS CORRECT I WANT TO KNOW THAT BEFOR IT WAS PROVED TO MAKE 10 DEGREE ANGLE WITH THE COMPASS? BECAUSE ACCORDING TO MY TEACHERS BEFORE IT WAS NOT PROVED BY ANY ONE

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