# New Kimblering points

nomaths shared this question 2 years ago

Is anyone going real geometry these days...

Well I am,,,

Is there anyone who can help me find a new Kimberling point out there...

I have the concepts but no maths and need to prove my work...

1

new Kimberling point with 'no maths' ... looks doubtful.

How can you expect that without giving any concrete information anyone will help you... when noone knows what this helping is?

chris

1

Is this a special case for x369 tri-section?

Is it possible to construct this point rule&compass...?

My example is only a daft...a suggestion

But in a certain case parallels through this point gives a unique tri-section

Many thanks

Files: x369.ggb
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Not too sure how this point works now, if its not pedal or cervian then it ha to be from the parallels to achieve a tri-section...

So is there only one solution to a tri-section?

Great to have some help, thanks

1

I'll concede that it appears to be cervian now, but only reveals a tri-section in a single special case.

But still looking into the parallels as if these are correct its any other special case, as my example is the cervian triangle of x369.

I bet I've missed something alone the way.

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x369 is its own anticervian...

Still hopping my points is valid because now my thinking its not x369!

lets hope...

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there is a method for knowing if a point is or not knowed in Enciclopedy of Triangle Centers.

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

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después de un escaso analisis yo dudo que el punto sea un centro, pues su definición depende del lado al que se traza la paralela y para ser un centro esta dependencia no debe existir

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Thanks for that, but here a Kimberling point that realise only on paralells...

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tu me muestras una construccion perfectamente simetrica en las coordenadas trilineales de los puntos y las rectas (permutar a,b,c en las definiciones da lugar a la misma construcción); pero tu construcción no es simétrica pues eligiendo las paralelas a los otros lados sale otro punto. y creo que habrá más

Files: foro.ggb
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thanks, do think my point is valid? regardless of the construction? do the maths work?

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all points are valid

maths work

I said simply that I think that your point is not a center

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

1

many thanks for your kind words...

so its just a coincidence maybe...

I will take another look and let you know my finds...