I think the attached diagram captures your proposed technique for trisecting an angle. If it doesn't, at least it will suggest a method for proving your technique.
I've turned things around for the proof. I've started with three equal angles (A in the figure). On the middle angle I've constructed a bisector (PQ length 's') and drawn the line x1Qx4 perpendicular to 's' that cuts across all three angles.
If your technique works, it should be possible to show mathematically that the angles divide the line into three segments...
a = x1x2
b = x2x3
c = x3x4
that are equal, i.e. a = b = c.
Aside: To my eye, it already appears that 'a' is longer than 'b', but in math "eyeballing" carries no weight so on with the proof.
We can solve for 'b' in terms of 's'
b = 2 * s * tan (A/2)
We can also solve for:
z = Px2 = s / cos (A/2)
w = Px1 = s / cos (3A/2)
Knowing 'z' and 'w', we can use the law of cosines to find 'a'.
a = [w^2 + z^2  2 * w * z * cos(A)]^0.5
So, all you need to do now is prove that a = b using the expressions above. If you can then your technique will work. Good luck; be sure to show us your work.
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Originally posted by nickelcityfab View Post
Notice how I said you draw a chord? making your angle into a triangle. You then divide the chord line into whatever (hell we did this in HS) and draw from those points back into the center of your circle...
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Originally posted by mklotz View PostI'll be looking forward to your demolition of a proof that's survived for 184 years. Be sure to publish it here for all to see.
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I'll be looking forward to your demolition of a proof that's survived for 184 years. Be sure to publish it here for all to see.
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Originally posted by mklotz View PostThe statement is "trisection of an angle USING ONLY STRAIGHTEDGE AND COMPASS is not possible", not "trisection of an angle is not possible". AFAIK, the first statement still stands.
There are probably many ways to trisect an angle.
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The statement is "trisection of an angle USING ONLY STRAIGHTEDGE AND COMPASS is not possible", not "trisection of an angle is not possible". AFAIK, the first statement still stands.
There are probably many ways to trisect an angle.
The trisection "tomahawk"...
https://en.wikipedia.org/wiki/Tomahawk_(geometry)
is an example of one trisection mechanism, although it cannot be used on certain angles.
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Originally posted by Lew Hartswick View PostWas told, as of 1949, by my Trig / Geometry teacher the "angle" couldn't be trisected. Has there been any new construction technique that does it???
...lew...
I've wondered about simply drawing a "chord" across the end of an angle, and dividing the line into whatever number of parts such as 3 parts, like you said, or 7 parts. Instead of being able to do it directly. I think it would work.
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Was told, as of 1949, by my Trig / Geometry teacher the "angle" couldn't be trisected. Has there been any new construction technique that does it???
...lew...
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Well, don't let me stop you from showing the proof.
Originally posted by Stargazer View Post
Don't mean to be disagreeable but he answer is yes. The Peano axioms and ZermeloFrankel set theory provide a solid foundation for basic arithmetic. Even if one objects to set theory as a basis for arithmetic foundations, the Peano axioms can also be understood and established by way of category theory.
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Originally posted by dian View Postmathematics is a theory that cannot be validated, as actually nothing can be validated. as it cannot be excluded that one day you "drop" a stone and it takes off towards the sky (or e.g. disappears).
right?
There is Theoretical Math and Real Math. Lol Thank god Einstein cant hear me now.
Most folks cant delve into the theory part of it. Most can get into the actual numbers of it though. JR
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Originally posted by Astronowanabe View PostSure arithmetic as drilled in school helps expressing ideas to others
and gives you a language/vehicle to learn what others have done.
But after that math is patterns, and patterns of patterns that just keep going
till they are completely divorced from our every day real world but
can still be brought back in a way that matters here.
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Originally posted by dian View Post
sorry, link doesnt work.
the peano axioms cant prove anything, beause they are, well, axioms. i think paul is right.
explain to me how it can be excluded, that one day you put an apple into a basket, then put in another one and wind up with three apples (or none)? besides, apples (as stargazer explained) have nothing to do with mathemathics.
mathematics is a theory that cannot be validated, as actually nothing can be validated. as it cannot be excluded that one day you "drop" a stone and it takes off towards the sky (or e.g. disappears).
right?
https://quod.lib.umich.edu/cgi/t/tex...=image&seq=401
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Originally posted by mklotz View Post
Here you go...a page from Whitehead and Russel's Principia...
https://quod.lib.umich.edu/cgi/t/tex...aat3201.0001.0 01&frm=frameset&view=image&seq=401
but be advised, if you're not a professional mathematician and use math more as a tool, your time would be more profitably spent learning some practical math rather than farking about with abstruse, quasiphilosophical stuff like this.
the peano axioms cant prove anything, beause they are, well, axioms. i think paul is right.
explain to me how it can be excluded, that one day you put an apple into a basket, then put in another one and wind up with three apples (or none)? besides, apples (as stargazer explained) have nothing to do with mathemathics.
mathematics is a theory that cannot be validated, as actually nothing can be validated. as it cannot be excluded that one day you "drop" a stone and it takes off towards the sky (or e.g. disappears).
right?Last edited by dian; 02212021, 05:47 AM.
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