A new point for Mr Kimberling maybe?

academic shared this question 9 months ago
Answered

Could this be a new point of a triangle?

Can you help to prove this or not?

its the ortho centre of the triangle created from the radical lines through the ex-circles and the circumference of the original triangle...

Can you help, thanks

Comments (25)

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I have tested from X(1) to X(3053) except 2771:2854 because GG says undefined.GG says undefined another points near 803.

your point is not in 1:3053

I do not know how to test the rest of points

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see this page. I suppose you can find your point or happily not

http://faculty.evansville.e...

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Great routine you have there... I think it's a new point...!

So what do you think I do to get it proven?

Please understand I do not do the maths...so would not know how to start, can you help?

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Could you indulge me a little more and use the checking routine on the attached file...

Still looking for a new point...

Many thanks

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X(9958) = ORTHOLOGIC CENTER OF THESE TRIANGLES: AYME TO INCENTRAL

X(9958) = X(4)-of-Ayme-triangle

X(9958) = Ayme-isogonal conjugate of X(11259)

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So are you saying it not a new point?

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Sorry, I didn't have time to explain. Now I do have.


First I constructed your point (X4 of Ayme triangle). See attached ggb-file.

Use checkbox "Set to Reference Triangle" to set points A, B and C to the

"ETC search reference triangle". Coordinates for "ETC search tables" are calculated.

Use a_coordinate to search in Search_6_9_13.html

Use b_coordinate to search in Search_9_13_6.html

Use c_coordinate to search in Search_13_6_9.html


Your point is X(9958) = X(4)-of-Ayme-triangle. See ETCPart5.html.


With kind regards, Thijs

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Thank you, I was honoured to have had a reply from Mr Kimberling and Peter Moses this morning...confirming that it was a new point for 'me', but for the rest of the world its known as x9958 - as you rightly said...

Thanks for you time and knowledge.

I'll keep looking all the same...

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If 0.00001% of the rest of the world know about x9958 then that's a lot I think. smile

It seems to me almost impossible to find a new (relevant) point. So, I wish you success.

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Can I now suggest that a line exists...

If you take the first Ayme triangle and then make other Ayme triangles from it...the otho centres are collinear and harmonic...oddly...

Win or lose with this one I going to call it the Ortho-Ayme Line...

If you have time please give a look over...

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better a new reply from Mr Kimberling

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Almost collinear.

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Right again...I'll take another look...thanks...

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Okay, I'm still on the hunt...here is a new approch to the Feuerbach point (x56)

-which is the circumcentre of the desmic mate of the outer Yff triangle...as you know, maybe

Well, taking the Ayme triangle and applying the desmic mate routine to obtain the circumcentre of the new triangle...of interest?

Indulge me if you have the time...

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I am afraid is not a "center" because circumcircle is undefined for initial obtuse triangle

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Thanks for your time and help...still on the mission!

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Okay here is a different look...

Thanks

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sorry missed file...

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/jm0IAugWDOgAAAABJRU5ErkJgggA=

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Thanks, so its x4895?

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Should I re drawn this in 6,9,13 ?

Thanks for your help...

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Hello academic,


This is starting to get annoying.

First of all: Please use Lines and don't use Segments to avoid undefined Intersects!!!


Now I'm going to give an example how to search a point X (Circumcenter in this case) in ETC.

Create 3 points A,B and C, a triangle without segments, 3 lines a,b and c, and a Center.

Set Options Rounding to 15 Decimal Places


A=(3,5)

B=(2,2)

C=(8,2)

tABC=Polygon({A,B,C})

a=Line(B,C)

b=Line(C,A)

c=Line(A,B)

X=TriangleCenter(A,B,C,3)


We are going to use the search table: "Search_9_13_6.html"

Set the vertices of triangle ABC to get sides with lengths (9,13,6)


Setvalue(B,(0,0))

Setvalue(C,(9,0))

Setvalue(A,Intersect(Circle(B,6), Circle(C,13),1))


In this specific case it's very easy to calculate the needed directive distance:

Coordinate=y(X)


Now search the value of Coordinate in the fourth (increasing) column.

You will find rank 3 in the thirth column. So X is X(3) = CIRCUMCENTER


---------------------------------------------------------------------------------------

OK, now back to "new point 2". (see attached file)

I made a construction without using segments to avoid undefined intersects.

Use button "Search" to find the Coordinate to use in search table "Search_9_13_6.html"


Index 3610 Coordinate 1.72088827499768192356

X(3610) = 1st AYME-MOSES PERSPECTOR

X(3610) = perspector of ABC and cross-triangle of ABC and Ayme triangle


With kind regards, Thijs

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many thanks...I feel I must learn this process...so I will, with your help...

I'm working on your instructions...

Thank you...

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But how do I actually search the 15k listings...import them into a data base, via ggb?

can't seem to make the connect here...

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I think the problem is I do not know GGB well enough on the coding side...

But here's what I do...I learn a routine to construct a piece of geometry...and make a poster out of it...

I must know hundreds of routines of by heart...

But I'd love to find a new point myself...

Please don't give up on me right now...

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