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The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Patti on Sun May 01, 2011 4:06 pm

Martijn (admin) wrote:
Patti wrote:You are mixing vocabularies now! An "island" in dermatoglphics is associated with a type of ridge formation alone. Not a triradius. It would be helpful to support yourself with actual quotes and references rather than vague inferences.

Wrong again Patti...!

Because Cummins & Midlo use the word 'island' specified for figure 47E, they write (page 58)

"If an island forms a central structure (Fig.47,E), that island is the triradial point."

And Schaumann & Alter write on page 34:

"However, if the three ridges fail to meet, the triradial point can be represented by a very short, dotlike ridge called an island (Figure 3.5B)..."


Now, if you still think that I 'mixed' myself the vocabulary... please try to find another point. Because in my use of the word 'island' I certainly did not 'mix' any vocabulary at all.


Yes, it is true the F.B.I. used the word island solely (once) for a ridge that splits and comes together again... but where the posts where I mentioned the word 'island', I did not mention the F.B.I. at all - so I did not 'mix' the two vocabularies at all!

Makes sense now?

I didn't say that islands didn't appear. There is nowhere the term "island variant" for a triradius.
Every human's fingerprints are different. The 'variants' are individual and result from two basic shapes. Star and Triangle.
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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Martijn (admin) on Sun May 01, 2011 4:20 pm

Patti wrote:
Martijn (admin) wrote:
Patti wrote:You are mixing vocabularies now! An "island" in dermatoglphics is associated with a type of ridge formation alone. Not a triradius. It would be helpful to support yourself with actual quotes and references rather than vague inferences.

Wrong again Patti...!

Because Cummins & Midlo use the word 'island' specified for figure 47E, they write (page 58)

"If an island forms a central structure (Fig.47,E), that island is the triradial point."

And Schaumann & Alter write on page 34:

"However, if the three ridges fail to meet, the triradial point can be represented by a very short, dotlike ridge called an island (Figure 3.5B)..."


Now, if you still think that I 'mixed' myself the vocabulary... please try to find another point. Because in my use of the word 'island' I certainly did not 'mix' any vocabulary at all.


Yes, it is true the F.B.I. used the word island solely (once) for a ridge that splits and comes together again... but where the posts where I mentioned the word 'island', I did not mention the F.B.I. at all - so I did not 'mix' the two vocabularies at all!

Makes sense now?

I didn't say that islands didn't appear. There is nowhere the term "island variant" for a triradius.
Every human's fingerprints are different. The 'variants' are individual and result from two basic shapes. Star and Triangle.

Patti, in your earlier comment you didn't specify anything regarding where you found me 'mixing' the vocabularies.

You only mentioned the word 'island'.


And I have described how both Cummins & Midlo and Schaumann & Alter are using the word 'island' variant for the triradial area.

You can not deny that.


And I think this 'confusion' from your side... actually could illustrate that you are just confused yourself about how to understand Galton's 2 examples for a 'outer terminus'.

I don't 'read' those 2 examples as a triradius-variant - because Galton's delta concept only relates to the 'triradial area' (and not how a triradius was defined later).

Because you probably 'read' those variants as two types of triradii. But Galton was only talking about the 'outer terminus' in the perspective of his delta-concept.

And I have described how his delta-concept relates to the 'area of the triradius': which is always twice present in a whorl, and once in a loop.


So I did not use any confusing word choice at all - you only associated the word 'island' with another issue (e.g. which is sensible in perspective of how an 'island' is defined in the F.B.I. system.

But since I wasn't talking about the F.B.I. sytem, I did not use any confusing use of langue regard how I used the word 'island'... so I did mix any vocabulary at all!

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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Lynn on Sun May 01, 2011 4:40 pm

Martijn (admin) wrote:Lynn, thanks for confirming that you were tired.

- And yes, I can now see how where I used the word 'described' (regarding the 'area of the triradius')... you assumed that I was talking about an explicite definition.

But that is not what I literally described, I only explicitely talked about that those words were mentioned in the TITLE of Schaumann & Alter's picture 3.5, and that in a way the picture itself does describe what their words 'area of the triradius' mean!


So when I refered to those words I basically only DESCRIBED that those words were used there in the perspective of that picture! And therefore, in a way ... they have visually described the words 'area of the triradius' with the illustration of those 6 pictures!

Therefore it became quite confusing for me that you denied that.
While I was not talking about any formal definition at all!


And by the way, the word 'describe' is just a common word that can be used for many purposes. So I can not help it that you assumed that I was talking about a formal explicite definition.


TRIANGULAR PLOT:

Sorry Lynn, but if you still don't recognize that your use of the words 'triangular plot' (twice!) in the perspective of Galton's work became rather confusing (because in that post you first mentioned it in the perspective of Galton's work, and then also in the perspective Cummins & Midlo's work) ... then let us take a closer look at the facts that are in your words:


First of all, it was rather confusing to describe Galton's filled black-triangles as a 'triangular plot'... because a 'triradial plot' typically has 3 arms or 'three variables', while Galton's filled black triangles do not have 3 arms like seen in a 'triangular plot'.

Oh ... but I think I can even explain why you use this confusing use of words - because earlier in youf comment about Garuto and Plato you wrote:

"Galton introduced the word triradius. They also say he was the first to recognise the importance of triradii, "which he defined as triangular plots formed by the divergence of adjacent ridges."

(But obviously, Garuto & Plate were not in the middle of discussion where the different use of the vocabularies became a major handicap for us to understand what the authors write)


And secondly, you were referring in your second statement clearly referingto a 'term'...:

" Galton's description is not like C&M illustrations of 'neat perfect little triangles' he describes it as " a small and rudely shaped triangle". Hence I guess the term 'triangular plot' as opposed to 'triangle'."

... and you also explicitely mentioned Cummins & Midlo, how could I not associate your first use of the words 'triradial plot' with Cummins & Midlo?

(Everything point in that direction... except that you now state that you had something else in mind)


And after I first tried to point that out ... you wrote in your response:

"I meant that you keep repeating it tonight. But now I see why - because you wrongly assumed that when I said the delta or triangular plot. you thought I was talking about C&M triangular plot. Oh...nooo! "

Come on Lynn... ( Hopeless ) ... how can I now understand these words + your Oh...nooo! ???


You are appear to be blaming me for misinterpretating your words, while your word choice itself became rather confusing for the three reasons that I described (1 - Galton did not use the word 'triradial plot' at all, 2 - a typical 'triangular plot' has three arms, which are not seen in Galton's work, 3 - In the same post you also explicitely used the word 'triangular plot' in the perspective of how Cummins & Midlo used it).

Garuto show no awareness about the difference between Cummins & Midlo's 'triangular plot' and Galton's delta... but the difference is that they don't mention Cummins & Midlo's work in their 'formally incorrect descriptions of Galton's work'.

But you are in the middle of a discussion where the different vocabularies are a HUGE handicap to understand the writings of the authors properly!


Okay, I now understand that your first use of the word 'triangular plot' only related to Galton's little black triangles ... but the green quote from your words above describes that you were talking about Cummins & Midlo as well!

So, how can you not call that a 'confusing use of words' ''!???



Lynn, do you recognize now how confusing the word choice of these 'scientific researchers' really is? Because Garuto & Plato talk about Galton's delta as if he described the delta as a 'triangular plot', but that is not true at all - Galton is literally using the word triangles only.

And Cummins & Midlo used the same words - 'triangular plot' - in the perspective of Galton. However Cummins & Midlo correctly suggest that these 'triangular plots' are actually quite rare ("... A triradius may be present when there is no delta in the strict sense."), but with his rule Galton described that a delta is always seen in any loop (one delta) and whorl (two delta).

See how confusing Cummins & Midlo's vocabulary even becomes when we put it in perspective to what Galton described himself!!!

( rolling on the floor )


And sorry Lynn, I think you demonstate not much awareness of how you used the words 'triradial plot' twice in a completely different context... !

How can you deny that as a confusing choice-of-words????


(Lynn, you are talking so 'deffensive' ... you are even denying the facts in your own words... which makes me sad... because I have never seen you doing this before Sad ... am I pushing you too much?)

hi Martijn, I am sorry that my choice of words has confused you. I'm sorry I misunderstood you when you used the word 'described', by thinking that I had missed some information somewhere.
I am not aware that I am being defensive, I thought I was trying to explain. I am also not aware exactly which facts I've denied in my own words. No, you're not pushing me too much.

I do recognize that my use of the words 'triangular plot' became confusing for you and maybe for other people. I apologise for that. As I explained, I did not have either C&M or Galton's work particularly in mind when I used those words, I was just using the term 'triangular plot' in its more general use, to mean a roughly triangular shape (as opposed to a perfectly formed triangle). Ok I guess it would have been less confusing if I had said 'roughly triangular shape'.

re (Everything point in that direction... except that you now state that you had something else in mind)
I understand why you interpreted my words as you did, I agree they were obviously confusing, but I am being honest when I explain what was on my mind when I wrote them ('a roughly triangular shape').

First of all, it was rather confusing to describe Galton's filled black-triangles as a 'triangular plot'... because a 'triradial plot' typically has 3 arms or 'three variables', while Galton's filled black triangles do not have 3 arms like seen in a 'triangular plot'.......

........And sorry Lynn, I think you demonstate not much awareness of how you used the words 'triradial plot' twice in a completely different context... !


I hope you now understand, I just meant 'roughly triangular shape'. I don't think I used the term 'triradial plot' even once, & I wasn't talking about C&M triangular plot. The 3 radiants in my diagram would be the ridges that border my black 'roughly triangular shape'.


Garuto & Plato talk about Galton's delta as if he described the delta as a 'triangular plot', but that is not true at all - Galton is literally using the word triangles only.

Perhaps they were using the term 'triangular plot' in the same way I was using it ?!? Galton talks about a 'rudely formed triangle'. A triangular plot (in everyday language) is a 'roughly triangular shape'. Which could be said to be the same thing as a 'rudely formed triangle'.

by the way, my use of Oh...nooo! was directed more at myself than at you - because it took me some time to understand why you were going into detail about Cummins & Midlo, when I wasn't even talking about Cummins & Midlo. But when you explained, and I understood how my words had confused you, I went Oh...nooo! as an expression of "Oh Nooo! we have misunderstood each other!". I meant no offence by it.

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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Lynn on Sun May 01, 2011 5:03 pm

Martijn (admin) wrote:Lynn, thank you very much for your appology relating to the issue of 'mixing the vocabularies'... ! Thumbs up!

Regarding your question about why I focussed on your comments related to Galton's 'triangles'... that is basically the result because you have adopted Patti's idea to define the 'triradial area' as a the YELLOW groove-zone in her picture.

All researchers only talk about the ridges, except for Penrose & Schaumann & Alter ... who explicitely described that a 'triradial point' can be found in a groove.

But in the perspective of that they always talk about ridges, I think it is simply an 'untoughtful' mistake to start defining certain words solely with a visual example of a central groove!

I am thinking of 'triradial area' as the area enlosed by or surrounded by the ridges. Yes, in the example that Patti & I drew, we have coloured in the grooves. The grooves are still part of the 3 converging ridge systems, and in this case there is a confluence of 3 grooves around the central triradial point, and they are bordered by the 3 ridges that form the triradius.

Martijn (admin) wrote:Especially since such a defintion has only a speculative character , because I don't see at all how Patti's definition brings us any further in our discussions. And instead all I observe is ... that he definition is an expression of the fact that she sometimes focusses on the grooves only!

Lynn, remember... earlier you told Patti yourself:
- that she should not add phantasies to her considerations;
- and that all books tell us to fouss on the ridges.

And therefore, in the perspective of those advices.... I recognize how you create a new 'contraditon' in your perceptions.

And after describing this 'contradiction'... I would like to remember you as well about
that earlier when Patti drew her litte yellow triangle in Kiwihands fingeprint... you told her that there is no such 'triangle' at all!

Lynn, this example should make you aware.. that Patti's definition (based on the triangle in the central part of the 'area of the triradius'), DIRECTLY relates to her phantasy about the little yellow triangle in Kiwihands fingerprint!

(So your assumption that your likewise black-triangle could represent Galton's concept of the delta... is likewise speculation/phantasy because Galton's delta can actually be associated with the full 'area of the triradius' as seen in the illustrations of Cummins & Midlo's figure 47; Penrose's figure 4 E, F &G; Schauman & Alter's figure 3.5; and Loesch's figure 2.2.)


Very Happy ...'Capice'?

-It is a speculative idea, but I don't see it as a fantasy. We have not drawn in anything that isn't really there.
-Of course we still focus on the ridges to draw the radiants. Throughout these discussions, I have stated many times that the radiants are ridges, and that hasn't changed in this latest idea.

Please explain what is this new contradiction that you think I have created in my perceptions.

Yes I made an objection to the yellow equilateral triangle that Patti drew, because it did not exist in reality. (Though I understood what she was saying, because I likewise drew a similar orange triangle once on kiwi's print to try and illustrate that the ridges form a 'roughly triangular shape'.) But I have said many times that drawing in radiants and triangles that aren't really there, is not necessary.

your assumption that your likewise black-triangle could represent Galton's concept of the delta... is likewise speculation/phantasy
I agree it is speculation on my part. I wasn't strictly using it to represent Galton's concept of a delta, more to illustrate the way that Galton's words 'rudely formed triangle' fit in with the idea I have always used about the ridges that border black area I coloured in, being the triradius (or, with my new understanding of 'star' and 'delta' shaped triradii, that it could be another variant form of triradius). During the course of this discussion, Patti had also been saying the same thing. So I thought it was worth another go at trying to consider whether it is a valid idea or not. (I still think it is).

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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Martijn (admin) on Sun May 01, 2011 6:40 pm

Lynn wrote:
Martijn (admin) wrote:Lynn, thanks for confirming that you were tired.

- And yes, I can now see how where I used the word 'described' (regarding the 'area of the triradius')... you assumed that I was talking about an explicite definition.

But that is not what I literally described, I only explicitely talked about that those words were mentioned in the TITLE of Schaumann & Alter's picture 3.5, and that in a way the picture itself does describe what their words 'area of the triradius' mean!


So when I refered to those words I basically only DESCRIBED that those words were used there in the perspective of that picture! And therefore, in a way ... they have visually described the words 'area of the triradius' with the illustration of those 6 pictures!

Therefore it became quite confusing for me that you denied that.
While I was not talking about any formal definition at all!


And by the way, the word 'describe' is just a common word that can be used for many purposes. So I can not help it that you assumed that I was talking about a formal explicite definition.


TRIANGULAR PLOT:

Sorry Lynn, but if you still don't recognize that your use of the words 'triangular plot' (twice!) in the perspective of Galton's work became rather confusing (because in that post you first mentioned it in the perspective of Galton's work, and then also in the perspective Cummins & Midlo's work) ... then let us take a closer look at the facts that are in your words:


First of all, it was rather confusing to describe Galton's filled black-triangles as a 'triangular plot'... because a 'triradial plot' typically has 3 arms or 'three variables', while Galton's filled black triangles do not have 3 arms like seen in a 'triangular plot'.

Oh ... but I think I can even explain why you use this confusing use of words - because earlier in youf comment about Garuto and Plato you wrote:

"Galton introduced the word triradius. They also say he was the first to recognise the importance of triradii, "which he defined as triangular plots formed by the divergence of adjacent ridges."

(But obviously, Garuto & Plate were not in the middle of discussion where the different use of the vocabularies became a major handicap for us to understand what the authors write)


And secondly, you were referring in your second statement clearly referingto a 'term'...:

" Galton's description is not like C&M illustrations of 'neat perfect little triangles' he describes it as " a small and rudely shaped triangle". Hence I guess the term 'triangular plot' as opposed to 'triangle'."

... and you also explicitely mentioned Cummins & Midlo, how could I not associate your first use of the words 'triradial plot' with Cummins & Midlo?

(Everything point in that direction... except that you now state that you had something else in mind)


And after I first tried to point that out ... you wrote in your response:

"I meant that you keep repeating it tonight. But now I see why - because you wrongly assumed that when I said the delta or triangular plot. you thought I was talking about C&M triangular plot. Oh...nooo! "

Come on Lynn... ( Hopeless ) ... how can I now understand these words + your Oh...nooo! ???


You are appear to be blaming me for misinterpretating your words, while your word choice itself became rather confusing for the three reasons that I described (1 - Galton did not use the word 'triradial plot' at all, 2 - a typical 'triangular plot' has three arms, which are not seen in Galton's work, 3 - In the same post you also explicitely used the word 'triangular plot' in the perspective of how Cummins & Midlo used it).

Garuto show no awareness about the difference between Cummins & Midlo's 'triangular plot' and Galton's delta... but the difference is that they don't mention Cummins & Midlo's work in their 'formally incorrect descriptions of Galton's work'.

But you are in the middle of a discussion where the different vocabularies are a HUGE handicap to understand the writings of the authors properly!


Okay, I now understand that your first use of the word 'triangular plot' only related to Galton's little black triangles ... but the green quote from your words above describes that you were talking about Cummins & Midlo as well!

So, how can you not call that a 'confusing use of words' ''!???



Lynn, do you recognize now how confusing the word choice of these 'scientific researchers' really is? Because Garuto & Plato talk about Galton's delta as if he described the delta as a 'triangular plot', but that is not true at all - Galton is literally using the word triangles only.

And Cummins & Midlo used the same words - 'triangular plot' - in the perspective of Galton. However Cummins & Midlo correctly suggest that these 'triangular plots' are actually quite rare ("... A triradius may be present when there is no delta in the strict sense."), but with his rule Galton described that a delta is always seen in any loop (one delta) and whorl (two delta).

See how confusing Cummins & Midlo's vocabulary even becomes when we put it in perspective to what Galton described himself!!!

( rolling on the floor )


And sorry Lynn, I think you demonstate not much awareness of how you used the words 'triradial plot' twice in a completely different context... !

How can you deny that as a confusing choice-of-words????


(Lynn, you are talking so 'deffensive' ... you are even denying the facts in your own words... which makes me sad... because I have never seen you doing this before Sad ... am I pushing you too much?)

hi Martijn, I am sorry that my choice of words has confused you. I'm sorry I misunderstood you when you used the word 'described', by thinking that I had missed some information somewhere.
I am not aware that I am being defensive, I thought I was trying to explain. I am also not aware exactly which facts I've denied in my own words. No, you're not pushing me too much.

I do recognize that my use of the words 'triangular plot' became confusing for you and maybe for other people. I apologise for that. As I explained, I did not have either C&M or Galton's work particularly in mind when I used those words, I was just using the term 'triangular plot' in its more general use, to mean a roughly triangular shape (as opposed to a perfectly formed triangle). Ok I guess it would have been less confusing if I had said 'roughly triangular shape'.

re (Everything point in that direction... except that you now state that you had something else in mind)
I understand why you interpreted my words as you did, I agree they were obviously confusing, but I am being honest when I explain what was on my mind when I wrote them ('a roughly triangular shape').

First of all, it was rather confusing to describe Galton's filled black-triangles as a 'triangular plot'... because a 'triradial plot' typically has 3 arms or 'three variables', while Galton's filled black triangles do not have 3 arms like seen in a 'triangular plot'.......

........And sorry Lynn, I think you demonstate not much awareness of how you used the words 'triradial plot' twice in a completely different context... !


I hope you now understand, I just meant 'roughly triangular shape'. I don't think I used the term 'triradial plot' even once, & I wasn't talking about C&M triangular plot. The 3 radiants in my diagram would be the ridges that border my black 'roughly triangular shape'.


Garuto & Plato talk about Galton's delta as if he described the delta as a 'triangular plot', but that is not true at all - Galton is literally using the word triangles only.

Perhaps they were using the term 'triangular plot' in the same way I was using it ?!? Galton talks about a 'rudely formed triangle'. A triangular plot (in everyday language) is a 'roughly triangular shape'. Which could be said to be the same thing as a 'rudely formed triangle'.

by the way, my use of Oh...nooo! was directed more at myself than at you - because it took me some time to understand why you were going into detail about Cummins & Midlo, when I wasn't even talking about Cummins & Midlo. But when you explained, and I understood how my words had confused you, I went Oh...nooo! as an expression of "Oh Nooo! we have misunderstood each other!". I meant no offence by it.

Thumbs up!

Thanks Lynn, yes I now understand what you exactly had in mind. And I am glad to hear that you now finally recognize as well how your word-choice became confusing.


Oeps... thanks: yes, where I wrote:

"... how you used the words 'triradial plot' twice..."

That was a writing mistake, I should have written there 'triangular plot'... of course. But I see that you correctly understood what I meant because I was reffering to your words.


Finally, regarding the words used Garuto & Plato ... well, since they are using the words 'triradius' and 'triangular plot'... it is essential to notice that Galton did not use both words at all.

And there suggestion that Galton was the first who introduced the word 'triradius'... well, since they litterally talk about that Galton had been "introducing the term triradius", that is a clear mistake in their information.

Yes Lynn, I do recognize as well how 'the message' that they communicate is very informative. But obviously, these authors have 'mixed' the vocabulary.

Another illustration how difficult it really is to understand & describe things properly!

(The F.B.I.'s delta method had already been available, but it appears that Garuto & Plato were not aware of that new development when they wrote in their 1991 article, they only comment until the first half of the 80's)


Basically, after reading & studying all these details... I think the F.B.I. system has 2 big advantages above what we called the 'scientific approach':
1 - Only the F.B.I. has defined their concepts very clearly with words & illustrations.
2 - And their method is much more detailed.

The only disadvantage is that it requires a study of the details in the ridge.


While Galton's delta-concept + his famous rule (arch = 0 delta, loop = 1 delta, whorl = 2 delta) might be appealing for a beginner student.

But it requires endless explanations to describe the difference between the related concepts: 'triradius', 'triradial point', and 'area of the triradius'. And because the definitions have developed in time, and some aspects where not described vary well in most of the book (compared to the detailed approach in the F.B.I. book), my preference has gravitated to the following conclusions for how we can continue with discussion other fingerprints:


1 - I think that the F.B.I. system is much more useful approach to continue with in our discussions.

(And additionallly, we can always use the other approach as a confirmation-tool when we are faced with problems)

2 - I think we are not in the position to start introducing new definitions for fingerprint elements that have not been described explicitely in the books at all.

(Especially since all books explicitiely tell use to focuss on the ridges in a fingerprint - I am referring here to your + Patti's ideas about how to define what we called the 'triradial area'; because regarding that aspect I have described why I can not support your 'groove idea'. - I wish I was able to call it a 'groovy-idea'... Razz)


Lynn, how does this sound to you?


Last edited by Martijn (admin) on Sun May 01, 2011 7:30 pm; edited 1 time in total

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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Martijn (admin) on Sun May 01, 2011 7:29 pm

Lynn wrote:
I am thinking of 'triradial area' as the area enlosed by or surrounded by the ridges.

Yes, in the example that Patti & I drew, we have coloured in the grooves.

The grooves are still part of the 3 converging ridge systems, and in this case there is a confluence of 3 grooves around the central triradial point, and they are bordered by the 3 ridges that form the triradius.

Lynn, what additonal purpose could this groove-concept really have?

(We know how to find the triradial point. So I don't see any benefits at all)


By the way, both of you have described this idea only for the 'empty' variant (= the 'island' variant with a dot). But you haven't even started sharing any ideas about the role of the concept in a 'complete triadius'... nor the irregular variants.

But you already started ask me what my thoughts are about this idea. And therefore I have described as an 'unthoughtful' idea.


Then, regarding the 'contradiction' that I have mentioned (and described):

Lynn you just said:

"It is a speculative idea, but I don't see it as a fantasy. We have not drawn in anything that isn't really there."

The funny thing is... that I can not even agree about that. Because I think the phantasy has already started with quite a few elements:

- (1) Because first you had rejected Patti's little yellow triangles in Kiwihands' fingerprint as a 'phantasy'; and now you are using a likewise phantasy-shape as a tool to define the word 'triradial area'!



- (2) Regarding how you drew that black-element in your picture: why did you stop at the three points where it ends? There is no argument at all to stop colouring that picture at these locations: you obviously just wanted to make it look like a triangle!!!

- (3) You describe it as 'rudely shaped triangle', but I can that even describe as a 'phantasy-perception'... just like how I yesterday introduced the word 'quadrilateral'. It is just a perception that requires phantasy to be confimed.

- (4) And how about the situation of a complete triradius? Are you then going to color the three connect radiants as well? And what would become the purpose of colouring the grooves in such an example.


Again... so far you have only been describing your drawing, and you have described how you associate it with the words 'triradial area'. But I have heard a word about the purpose of this definition.

And beyond that I recognize this idea is 'unthoughtfull', because you haven't spent a word about how it would look like for a true triradius... in one of your earlier response you claimed that the idea would not need any further description - because it should speak for itself.

So, I think it is just a phantasy to think that your drawing could serve as a definition for the words 'triradial area', because - beyond the contradiction with your earlier statement about Patti's little yellow triangle in Kiwihands' fingerprint... your proposal also creates a contradiction with Schaumann & Alter's use of the words: 'area of the triradius'.


Sorry Lynn, if you still can not recognize these contradictions... then I might just better give up arguing about this (and then we can only 'agree to disagree' about whether the idea is a phantasy or not).



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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Patti on Sun May 01, 2011 8:58 pm

Galton didn't introduce the word "triradius". Either Wilder or Wentworth introduced "triradius".

Galton introduced the word "delta" which suggests a triangle. C & M said that since "delta" only meant triangular shape and there was also a Star shape, they decided not to use "delta" as a synonym for "triradius"

Wilder and Wentworth in 1918 use the word "triradius" to represent "a three pointed star, and include both the delta and its three radiating lines". These three radianting ridges could be radiating out from the center of centrally meeting ridges, Star. Or, the 3 radiants can be traced from the 3 innermost ridges forming a Delta shape.

I would then interpret the blackened triangles AND the extended radiants to be the triradius. Sometimes the extended radiants meet at the center of the triangular shaped "Delta". Sometimes they are the 3 ridges forming the Delta shape triradius.

Martijn, if you could realize that in English the word delta is a synonym for triangle, it would make sense when you saw the word used, whenever and however it is used. <edit> I should clarify that, as the FBI calls the triradial point a "delta" but they illustrate a triangle shape at the beginning of the book. Fig. 19 has the word "delta" with an line pointing to the little triangle.

Even if there are 3 ridges meeting like a Y these 3 ridges have 3 sets of diverging ridges, converging upon them. There is always a Delta shape present, even with the Y shape. Sometimes there is only the Delta shape without the Y shape present. The delta shape converts to a Y shape the closer into the center the ridges form. In this central groove area between inside the Delta (triangular shape) is all kinds of pieces or fragments of incomplete transformation from Delta to Star of the innermost 3 ridges.

I also think of the childhood game musical chairs (I'm so visual) As the ridges close in from the 3 fields in development, they run out of space to form in. At a certain point the ridge making time period in fetal development is done. The fields close in, in the remaining space. The pattern in the triradius or triradial area, is what it is. Penrose, Schaumann & Alter and especially Loesch recognized the strong influence of geometry (like we see in nature).

All the examples besides the Schaumann & Alter 3.5 A & E are just a few samples of the many, many possible ridge fragments that are found in the groove between the Delta shaped ridges.


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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Lynn on Sun May 01, 2011 9:10 pm

Thanks for explaining that Patti.

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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Lynn on Sun May 01, 2011 9:11 pm

Martijn (admin) wrote:
Sorry Lynn, if you still can not recognize these contradictions... then I might just better give up arguing about this (and then we can only 'agree to disagree' about whether the idea is a phantasy or not).[/color]

Ok I'll stop talking about it.

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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Patti on Sun May 01, 2011 9:11 pm



See the Star and Triangle in the center image. Maybe too much imagination involved, but it's the territory that Loesch and Penrose were headed.


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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Patti on Sun May 01, 2011 9:42 pm

Lynn wrote:I am thinking of 'triradial area' as the area enlosed by or surrounded by the ridges. Yes, in the example that Patti & I drew, we have coloured in the grooves. The grooves are still part of the 3 converging ridge systems, and in this case there is a confluence of 3 grooves around the central triradial point, and they are bordered by the 3 ridges that form the triradius.

Yes, we are in complete agreement here.
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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Patti on Sun May 01, 2011 10:31 pm

frazil ice flow as delta

The ^ link is to a video that I'm trying to embed, but seem unable to upload anything other than a link.

At 1:01 or 1:02 time in, on the lower left is a Delta. Notice also the pointed formation being made on the other side of the flow, pointing back at the delta. (this is probably a quadrangle)


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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Lynn on Sun May 01, 2011 10:37 pm

Martijn (admin) wrote:Lynn, what additonal purpose could this groove-concept really have?
(We know how to find the triradial point. So I don't see any benefits at all)

By the way, both of you have described this idea only for the 'empty' variant (= the 'island' variant with a dot). But you haven't even started sharing any ideas about the role of the concept in a 'complete triadius'... nor the irregular variants.

But you already started ask me what my thoughts are about this idea. And therefore I have described as an 'unthoughtful' idea.

Then, regarding the 'contradiction' that I have mentioned (and described):

Lynn you just said:

"It is a speculative idea, but I don't see it as a fantasy. We have not drawn in anything that isn't really there."

The funny thing is... that I can not even agree about that. Because I think the phantasy has already started with quite a few elements:

- (1) Because first you had rejected Patti's little yellow triangles in Kiwihands' fingerprint as a 'phantasy'; and now you are using a likewise phantasy-shape as a tool to define the word 'triradial area'!



- (2) Regarding how you drew that black-element in your picture: why did you stop at the three points where it ends? There is no argument at all to stop colouring that picture at these locations: you obviously just wanted to make it look like a triangle!!!

- (3) You describe it as 'rudely shaped triangle', but I can that even describe as a 'phantasy-perception'... just like how I yesterday introduced the word 'quadrilateral'. It is just a perception that requires phantasy to be confimed.

- (4) And how about the situation of a complete triradius? Are you then going to color the three connect radiants as well? And what would become the purpose of colouring the grooves in such an example.


Again... so far you have only been describing your drawing, and you have described how you associate it with the words 'triradial area'. But I have heard a word about the purpose of this definition.

And beyond that I recognize this idea is 'unthoughtfull', because you haven't spent a word about how it would look like for a true triradius... in one of your earlier response you claimed that the idea would not need any further description - because it should speak for itself.

So, I think it is just a phantasy to think that your drawing could serve as a definition for the words 'triradial area', because - beyond the contradiction with your earlier statement about Patti's little yellow triangle in Kiwihands' fingerprint... your proposal also creates a contradiction with Schaumann & Alter's use of the words: 'area of the triradius'.


Sorry Lynn, if you still can not recognize these contradictions... then I might just better give up arguing about this (and then we can only 'agree to disagree' about whether the idea is a phantasy or not).



Before I stop talking about it, it is only fair that I try to answer your questions:

i) . what additonal purpose could this groove-concept really have?
It is not the groove concept that is really important. It is the 3 innermost ridges that surround this 'roughly triangular shape' that patti coloured yellow & I coloured black. It is very useful to find these three ridges as a starting area, in order to locate the triradial point.

(We know how to find the triradial point. So I don't see any benefits at all)
How do you know how to find the triradial point without first identifiying the 'area of the triradius' or the 'triradius? When you are looking at a hand or a print, what do you look for first when you are trying to find a triradial point on a fingerprint, or the axial triradius on the palm? Personally I have always looked for those 3 inner converging ridges.

ii). By the way, both of you have described this idea only for the 'empty' variant (= the 'island' variant with a dot). But you haven't even started sharing any ideas about the role of the concept in a 'complete triadius'... nor the irregular variants.
In a 'complete triradius' (what patti calls 'star shape') then the 3 ridges have converged right in, so that they join in the centre. So there is no 'interspace' between them to colour in. Our idea isn't really necessary when there is an obvious 'star' or even 'C&M type delta/triangular' triradius. But when neither of those are there, the idea of the 'triradial area' is very useful.
In the irregular variants, if you look at Schaumann & Alter's examples where there are small ridges in this area, then the 'triradial area' is still useful to locate, because the triradial point is in the centre, regardless which small ridge variants are in that area. When you come to trace the radiants, if there are only small or broken ridges in the centre of this area, then we continue to the next ridge - so we would anyway end up on the ridges that Patti labelled 'triradius'.

(1) Because first you had rejected Patti's little yellow triangles in Kiwihands' fingerprint as a 'phantasy'; and now you are using a likewise phantasy-shape as a tool to define the word 'triradial area'!
The only fantasy is that I coloured it in black. Erase my black & the shape is there.

- (2) Regarding how you drew that black-element in your picture: why did you stop at the three points where it ends? There is no argument at all to stop colouring that picture at these locations: you obviously just wanted to make it look like a triangle!!!
Why did Schaumann and Alter stop their diagrams at a certain point on the ridges? I was looking at "the area of the triradius", or the 'triradial area' or the 'area around the triradial point'. (oh I don't know what words to use because I fear you will dispute them!). I wasn't TRYING to make it look like a triangle. They naturally look like a 'rudely shaped triangle' as Galton put it.

- (3) You describe it as 'rudely shaped triangle', but I can that even describe as a 'phantasy-perception'... just like how I yesterday introduced the word 'quadrilateral'. It is just a perception that requires phantasy to be confimed.
It's not a quadrilateral as that has 4 lines & 4 angles. But Ok I understand that you don't wish to see it as a roughly triangular shape.

- (4) And how about the situation of a complete triradius? Are you then going to color the three connect radiants as well? And what would become the purpose of colouring the grooves in such an example.
I think I already answered this in ii)

Again... so far you have only been describing your drawing, and you have described how you associate it with the words 'triradial area'. But I have heard a word about the purpose of this definition.

And beyond that I recognize this idea is 'unthoughtfull', because you haven't spent a word about how it would look like for a true triradius... in one of your earlier response you claimed that the idea would not need any further description - because it should speak for itself.

So, I think it is just a phantasy to think that your drawing could serve as a definition for the words 'triradial area', because - beyond the contradiction with your earlier statement about Patti's little yellow triangle in Kiwihands' fingerprint... your proposal also creates a contradiction with Schaumann & Alter's use of the words: 'area of the triradius'.


You are focussed on the 'triradial area', and not noticing that we have included the ridges around it, just as Schaumann & Alter did in their 6 examples of 'ridges in the area of the triradius'. I don't see any contraditction with Schaumann & Alter. I have said, and Patti labelled on her drawing, the triraidus is the ridges that surround the triradial area. that is the most important thing to look at. As I said, for a 'true triradius' these 3 ridges meet so there is no 'interspace' (Galton's word, but it is also a word that generally describes 'the area in between') or 'triradial area' to colour in. When there is a true triradius of 3 ridges meeting at 120 degree angles, we don't need to concern ourselves with 'the triradial area' because it has kind-of 'imploded' to become the triradial point itself!

Sorry Lynn, if you still can not recognize these contradictions... then I might just better give up arguing about this (and then we can only 'agree to disagree' about whether the idea is a phantasy or not).
OK, I will stop talking about it, and as you feel it better to give up arguing about it, I will not expect a reply from you.

Thank you! Thank you for the discussion.


Last edited by Lynn on Mon May 02, 2011 12:14 am; edited 2 times in total (Reason for editing : missed a word, typo)

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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Lynn on Sun May 01, 2011 10:40 pm

Patti wrote:
Lynn wrote:I am thinking of 'triradial area' as the area enlosed by or surrounded by the ridges. Yes, in the example that Patti & I drew, we have coloured in the grooves. The grooves are still part of the 3 converging ridge systems, and in this case there is a confluence of 3 grooves around the central triradial point, and they are bordered by the 3 ridges that form the triradius.

Yes, we are in complete agreement here.

Yes I know, thanks Patti for sharing my understanding of it.

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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Lynn on Sun May 01, 2011 10:42 pm

Patti wrote:frazil ice flow as delta

The ^ link is to a video that I'm trying to embed, but seem unable to upload anything other than a link.

At 1:01 or 1:02 time in, on the lower left is a Delta. Notice also the pointed formation being made on the other side of the flow, pointing back at the delta. (this is probably a quadrangle)

lol! so far we've seen skin ridges in gothic windows, mazes, road markings, lanes at traffic lights and now in this really COOL (in more ways than one!) video about ice flows! ;-)

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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Lynn on Sun May 01, 2011 11:05 pm

Martijn (admin) wrote:Basically, after reading & studying all these details... I think the F.B.I. system has 2 big advantages above what we called the 'scientific approach':
1 - Only the F.B.I. has defined their concepts very clearly with words & illustrations.
2 - And their method is much more detailed.

The only disadvantage is that it requires a study of the details in the ridge.

While Galton's delta-concept + his famous rule (arch = 0 delta, loop = 1 delta, whorl = 2 delta) might be appealing for a beginner student.

But it requires endless explanations to describe the difference between the related concepts: 'triradius', 'triradial point', and 'area of the triradius'. And because the definitions have developed in time, and some aspects where not described vary well in most of the book (compared to the detailed approach in the F.B.I. book), my preference has gravitated to the following conclusions for how we can continue with discussion other fingerprints:

1 - I think that the F.B.I. system is much more useful approach to continue with in our discussions.

(And additionallly, we can always use the other approach as a confirmation-tool when we are faced with problems)

2 - I think we are not in the position to start introducing new definitions for fingerprint elements that have not been described explicitely in the books at all.

(Especially since all books explicitiely tell use to focuss on the ridges in a fingerprint - I am referring here to your + Patti's ideas about how to define what we called the 'triradial area'; because regarding that aspect I have described why I can not support your 'groove idea'. - I wish I was able to call it a 'groovy-idea'... Razz)


Lynn, how does this sound to you?
[/color]

(edit - sorry, I missed this earlier post, hence replied in 'reverse order' to the order Martijn posted his comments)

I think that perhaps you still haven't quite understood exactly what Patti & I are trying to convey. Actually the ridges are the important thing in our 'groovy' idea. But if you understand it, and dismiss it, then that's fine by me, I will not try to convince you!

As a handreader, the way I was originally taught has served me well over 15 years of trying to identify fingerprints during a handreading, so of course I will continue to use it. (and I will continue to substitute the word 'triradius' for 'delta' in the following quote: (arch = 0 delta, loop = 1 delta, whorl = 2 delta) , even tho you say it is outdated, it is widely used in many books & scientific studies.

1 - Only the F.B.I. has defined their concepts very clearly with words & illustrations.
2 - And their method is much more detailed.

I agree, but none of us work in forensics, and most of us handreaders do not do detailed research into fingerprints. So in day-to-day practical use, we usually don't need to go into such detail. Most of the time, those "endless explanations" aren't necessary - in fact I never came across them before our recent discussions! However it has been fascinating to learn about it and indeed proves useful for those of us 'geeks' who choose to spend hours discussing one single fingerprint 500x zoomed or whatever! :-)

I think we are probably not going to agree on the scientific system, as some of their definitions are 'open to interpretation' which is much less the case in FBI system - although the 3 of us have even had our differences of opinion on how to interpret their rules,,,,, imagine if 10 people were having these discussions, how much more we may have argued!

Martijn, the last 24 hours it is obvious that you feel you have wasted your time in discussing with me, I have made you frustrated and confused, for which I already apologised. So it's fine if you don't wish to continue what Patti and I were agreeing about.
again.... many Thanks!


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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Patti on Sun May 01, 2011 11:06 pm

Lynn wrote:
Patti wrote:
Lynn wrote:I am thinking of 'triradial area' as the area enlosed by or surrounded by the ridges. Yes, in the example that Patti & I drew, we have coloured in the grooves. The grooves are still part of the 3 converging ridge systems, and in this case there is a confluence of 3 grooves around the central triradial point, and they are bordered by the 3 ridges that form the triradius.

Yes, we are in complete agreement here.

Yes I know, thanks Patti for sharing my understanding of it.

You're welcome!

I have one feature I'd like to discuss further. You speak of the perfect triangular triradius as G in Penrose. He calls it a 'triradial point' in the text and a triangular enclosure.

You also refer to the shape that is formed by 3 converging ridges meeting rather than joining as a 3rd type.

I would strongly continue to argue that they are the same, but Penrose calls shape G "triangular enclosure". I've uploaded the pages in the past. Will do so again, but need to mow more grass before it gets dark. back soon.
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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Martijn (admin) on Mon May 02, 2011 12:06 am

Patti wrote:frazil ice flow as delta

The ^ link is to a video that I'm trying to embed, but seem unable to upload anything other than a link.

At 1:01 or 1:02 time in, on the lower left is a Delta. Notice also the pointed formation being made on the other side of the flow, pointing back at the delta. (this is probably a quadrangle)

Hi Patti,

Did you try to add the video with the button?

(I think it did not work because by using the 'share' button of the video, the link was featured with a '.' between the u and the b, see: http://youtu.be/9V9p4mFEYXc )



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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Lynn on Mon May 02, 2011 12:37 am

Patti wrote:I have one feature I'd like to discuss further. You speak of the perfect triangular triradius as G in Penrose. He calls it a 'triradial point' in the text and a triangular enclosure.

You also refer to the shape that is formed by 3 converging ridges meeting rather than joining as a 3rd type.

I would strongly continue to argue that they are the same, but Penrose calls shape G "triangular enclosure". I've uploaded the pages in the past. Will do so again, but need to mow more grass before it gets dark. back soon.

sorry Patti, I don't have Penrose book, and I can't remember quoting G. (usually when I talk about 'perfect triangular triradius' I am refering to Cummins & Midlo 'delta', as I have that book!) - when you've finished mowing the grass, I hope you can post the pics to remind me.

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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Patti on Mon May 02, 2011 12:49 am

Lynn wrote:
Patti wrote:I have one feature I'd like to discuss further. You speak of the perfect triangular triradius as G in Penrose. He calls it a 'triradial point' in the text and a triangular enclosure.

You also refer to the shape that is formed by 3 converging ridges meeting rather than joining as a 3rd type.

I would strongly continue to argue that they are the same, but Penrose calls shape G "triangular enclosure". I've uploaded the pages in the past. Will do so again, but need to mow more grass before it gets dark. back soon.

sorry Patti, I don't have Penrose book, and I can't remember quoting G. (usually when I talk about 'perfect triangular triradius' I am refering to Cummins & Midlo 'delta', as I have that book!) - when you've finished mowing the grass, I hope you can post the pics to remind me.

Here it is:
The red underlined sentence would be interesting to break down and paraphrase and see how each of would say it.


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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Martijn (admin) on Mon May 02, 2011 12:50 am

Lynn wrote:
I think that perhaps you still haven't quite understood exactly what Patti & I are trying to convey. Actually the ridges are the important thing in our 'groovy' idea. But if you understand it, and dismiss it, then that's fine by me, I will not try to convince you!

Lynn, if you think that the ridges are THE important thing... then why highlightening the groove only? + When I asked 'where is the description?', you responded that the picture should speak for itself, etc.

(... scratch )

However, I think I do understand what you are saying in your words above - and I think it perfectly makes sense that in your perception the ridges 'are the important thing' in this idea ( Thumbs up! ).


By the way, in your earlier message (embraced by Patti) - you did not mentioned that in your perception the ridges 'are the important thing':

Patti wrote:
Lynn wrote:I am thinking of 'triradial area' as the area enlosed by or surrounded by the ridges. Yes, in the example that Patti & I drew, we have coloured in the grooves. The grooves are still part of the 3 converging ridge systems, and in this case there is a confluence of 3 grooves around the central triradial point, and they are bordered by the 3 ridges that form the triradius.

Yes, we are in complete agreement here.


So, are you both really in 'complete agreement' like Patti suggested?
(From my point of view, your new comment raises doubts about that)


Oh, and by ... maybe I could illustrate the problematic aspect of focussing on the 'grooves' (as indicated by the colour in the pictures that you both presented) as follows:

Even the groove between the two diverging ridges in 2nd picture below follows the definition of your 'triradial area':




Last edited by Martijn (admin) on Mon May 02, 2011 1:34 am; edited 1 time in total

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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Patti on Mon May 02, 2011 12:51 am

Martijn (admin) wrote:
Patti wrote:frazil ice flow as delta

The ^ link is to a video that I'm trying to embed, but seem unable to upload anything other than a link.

At 1:01 or 1:02 time in, on the lower left is a Delta. Notice also the pointed formation being made on the other side of the flow, pointing back at the delta. (this is probably a quadrangle)

Hi Patti,

Did you try to add the video with the button?

(I think it did not work because by using the 'share' button of the video, the link was featured with a '.' between the u and the b, see: http://youtu.be/9V9p4mFEYXc )



Thanks! I tried several ways and all I got was code in the posting. I see the 'tu.be' . That was probably the problem.
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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Lynn on Mon May 02, 2011 12:58 am

(Edit - I notice while I was searching, several posts have been made! I can't keep up with you guys!!) Very Happy


Ok Patti I found it!



I understand what you are saying, but I don't agree that they are 'the same', because in one case the ridges join together, in another case there is a groove between them.

Martijn explained to me the difference between this example in G (which is like Cummins & Midlo 'triangular plot') and the examples where the ridges don't join to form a definite angle (or 'perfect triangle'). I accept that there is a difference between the innermost ridges from the 3 fields "joining" and "meeting".
ie a "triangular enclosure" where the ridges join at the angles being different from a 'roughly triangular shape' where the 3 ridge systems join at the grooves.
But...if the 3 fields don't join together at the ridges, then I understand how we then have to look at them 'joining or meeting at the grooves of the ridge system" and that's when our 'triradial area" becomes more important.
(tho I also agree that the area within these 3 joining ridges in fig G is also the triradial area, with the ridges being the triradius and the triradial point being in the centre).

Patti, I am sure that you & I are thinking along the same lines, even if we have sometimes have different ways of expressing it! Thumbs up!


Last edited by Lynn on Mon May 02, 2011 1:56 am; edited 1 time in total (Reason for editing : tried for more clarity)

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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Patti on Mon May 02, 2011 1:13 am

Penrose says:

"From the central point of a triradius, which may be an island, a ridge junction, a ridge end, or even a triangular enclosure,..."

Do you think he is saying? "From the central point which may be an etc. etc.

or do you think he is saying?

"From the triradius, which may be an island, ar ridge junction, a ridge end, or even a triangular enclosure,"

Because, the 'triradial point' or 'fbi delta' is a focus point on a ridge or groove.
The triradius is 3 innermost ridges doing something together.

A focus point on a ridge works with an "island, a ridge junction, a ridge end" but how does it include the entire enclosure as probably is shown in G?

The 'triangular enclosure' is more than a location on a ridge.




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Re: The TRIRADIUS in a fingerprint: how it develops, it's characteristics + a definition!

Post  Martijn (admin) on Mon May 02, 2011 1:15 am

Lynn wrote:
(We know how to find the triradial point. So I don't see any benefits at all)
How do you know how to find the triradial point without first identifiying the 'area of the triradius' or the 'triradius? When you are looking at a hand or a print, what do you look for first when you are trying to find a triradial point on a fingerprint, or the axial triradius on the palm? Personally I have always looked for those 3 inner converging ridges.

Exactly! Which confirms that we have always done that likewise... so we don't need this new 'triadial area' concept at all.


By the way... Lynn, you did not describe any additional benefits for this 'groovy definition': you only sponded with 2 questions in return: which is like presenting me two open doors, and then ask me: 'can you please open the door?'.

This 'groovy definition' is like an empty shell - because it does not anything... except perhaps that it is a concept that Patti will love to use for allowing herself to create many more phatasy triangles.


Lynn, can I ask one more specified question?:

Can you describe what benefits this 'groovy definition' has in the perspective of the knowledge that you already had collected during the past 15 years?


PS. While I forumulate this question... I am having another thought:

Because so far it appears that you have embraced your '15 year old' definition for the triradius again. And now I am beginning to recognize how the specific 'groovy definition' has a side-effect:

Because it (partly) solves another problem that you were confronted with your old definition - because Schaumann & Alter talk about the 'triradius' and the 'area of the triradius', so both can't be exactly the same. But in your old definition both elements appeared to be exactly the same!

So, while thinking about this ... I see how this 'groovy definition' allows Patti to continue to phantasize about 'triangles', and it allows you to continue using your 15-year old triradius definition.

Again, your 15-year old triradius definition relates directly to how Galton described his 'delta'.

I guess... maybe I have just answered my own questions.

Unfortunately, there is no benefit in this 'groovy definition' that could anything to my perspections.

But I can live with that.

wave

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